{"id":1661,"date":"2015-04-22T18:09:53","date_gmt":"2015-04-22T18:09:53","guid":{"rendered":"https:\/\/courses.candelalearning.com\/oschemtemp\/?post_type=chapter&#038;p=1661"},"modified":"2015-09-01T17:27:32","modified_gmt":"2015-09-01T17:27:32","slug":"other-units-for-solution-concentrations-5-formulas-not-working","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/chapter\/other-units-for-solution-concentrations-5-formulas-not-working\/","title":{"raw":"Other Units for Solution Concentrations","rendered":"Other Units for Solution Concentrations"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>LEARNING OBJECTIVES<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n\t<li>Define the concentration units of mass percentage, volume percentage, mass-volume percentage, parts-per-million (ppm), and parts-per-billion (ppb)<\/li>\r\n\t<li>Perform computations relating a solution\u2019s concentration and its components\u2019 volumes and\/or masses using these units<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p id=\"fs-idm32304496\">In the previous section, we introduced molarity, a very useful measurement unit for evaluating the concentration of solutions. However, molarity is only one measure of concentration. In this section, we will introduce some other units of concentration that are commonly used in various applications, either for convenience or by convention.<\/p>\r\n\r\n<section id=\"fs-idm8277808\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Mass Percentage<\/h2>\r\n<p id=\"fs-idm26991728\">Earlier in this chapter, we introduced percent composition as a measure of the relative amount of a given element in a compound. Percentages are also commonly used to express the composition of mixtures, including solutions. The <strong><span data-type=\"term\">mass percentage<\/span><\/strong> of a solution component is defined as the ratio of the component\u2019s mass to the solution\u2019s mass, expressed as a percentage:<\/p>\r\n\r\n<div id=\"fs-idm5911152\" data-type=\"equation\">[latex]\\text{mass percentage}=\\frac{\\text{mass of component}}{\\text{mass of solution}}\\times 100\\%[\/latex]<\/div>\r\n<p id=\"fs-idm30359632\">We are generally most interested in the mass percentages of solutes, but it is also possible to compute the mass percentage of solvent.<\/p>\r\n<p id=\"fs-idm3484528\">Mass percentage is also referred to by similar names such as <em data-effect=\"italics\">percent mass, percent weight, weight\/weight percent<\/em>, and other variations on this theme. The most common symbol for mass percentage is simply the percent sign, %, although more detailed symbols are often used including %mass, %weight, and (w\/w)%. Use of these more detailed symbols can prevent confusion of mass percentages with other types of percentages, such as volume percentages (to be discussed later in this section).<\/p>\r\n<p id=\"fs-idm21823696\">Mass percentages are popular concentration units for consumer products. The label of a typical liquid bleach bottle (Figure 1) cites the concentration of its active ingredient, sodium hypochlorite (NaOCl), as being 7.4%. A 100.0-g sample of bleach would therefore contain 7.4 g of NaOCl.<\/p>\r\n\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"879\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211209\/CNX_Chem_03_05_bleach1.jpg\" alt=\"The sides of two cylindrical containers are shown. Each container\u2019s label is partially visible. The left container\u2019s label reads \u201cBleach.\u201d The right label contains more information about the product including the phrase, \u201cContains: Sodium hypochlorite 7.4 %.\u201d\" width=\"879\" height=\"634\" data-media-type=\"image\/jpeg\" \/> Figure 1. Liquid bleach is an aqueous solution of sodium hypochlorite (NaOCl). This brand has a concentration of 7.4% NaOCl by mass.[\/caption]\r\n\r\n<div id=\"fs-idm23566960\" data-type=\"example\">\r\n<div class=\"textbox shaded\">\r\n<h3>Example 1<\/h3>\r\n<h4 id=\"fs-idm2453280\"><strong><span data-type=\"title\">Calculation of Percent by Mass<\/span><\/strong><\/h4>\r\nA 5.0-g sample of spinal fluid contains 3.75 mg (0.00375 g) of glucose. What is the percent by mass of glucose in spinal fluid?\r\n<h4 id=\"fs-idp19396640\"><span data-type=\"title\">Solution<\/span><\/h4>\r\nThe spinal fluid sample contains roughly 4 mg of glucose in 5000 mg of fluid, so the mass fraction of glucose should be a bit less than one part in 1000, or about 0.1%. Substituting the given masses into the equation defining mass percentage yields:\r\n<div id=\"fs-idm17789648\" data-type=\"equation\">[latex]\\%\\text{glucose}=\\frac{3.75\\text{mg glucose}\\times \\frac{1\\text{g}}{1000\\text{mg}}}{5.0\\text{g spinal fluid}}=0.075\\%[\/latex]<\/div>\r\n<p id=\"fs-idm36099936\">The computed mass percentage agrees with our rough estimate (it\u2019s a bit less than 0.1%).<\/p>\r\n<p id=\"fs-idm6973776\">Note that while any mass unit may be used to compute a mass percentage (mg, g, kg, oz, and so on), the same unit must be used for both the solute and the solution so that the mass units cancel, yielding a dimensionless ratio. In this case, we converted the units of solute in the numerator from mg to g to match the units in the denominator. We could just as easily have converted the denominator from g to mg instead. As long as identical mass units are used for both solute and solution, the computed mass percentage will be correct.<\/p>\r\n\r\n<h4 id=\"fs-idm64146192\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\r\nA bottle of a tile cleanser contains 135 g of HCl and 775 g of water. What is the percent by mass of HCl in this cleanser?\r\n<div id=\"fs-idp47230144\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a014.8%<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Example 2<\/h3>\r\n<h4 id=\"fs-idm32647264\"><strong><span data-type=\"title\">Calculations using Mass Percentage<\/span><\/strong><\/h4>\r\n\u201cConcentrated\u201d hydrochloric acid is an aqueous solution of 37.2% HCl that is commonly used as a laboratory reagent. The density of this solution is 1.19 g\/mL. What mass of HCl is contained in 0.500 L of this solution?\r\n<h4 id=\"fs-idm37499888\"><span data-type=\"title\">Solution<\/span><\/h4>\r\nThe HCl concentration is near 40%, so a 100-g portion of this solution would contain about 40 g of HCl. Since the solution density isn\u2019t greatly different from that of water (1 g\/mL), a reasonable estimate of the HCl mass in 500 g (0.5 L) of the solution is about five times greater than that in a 100 g portion, or [latex]5\\times 40=200\\text{g.}[\/latex] In order to derive the mass of solute in a solution from its mass percentage, we need to know the corresponding mass of the solution. Using the solution density given, we can convert the solution\u2019s volume to mass, and then use the given mass percentage to calculate the solute mass. This mathematical approach is outlined in the flow chart below:\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211211\/CNX_Chem_03_05_Example2_img1.jpg\" alt=\"A diagram of three boxes connected by a right-facing arrow in between each is shown. The box on the left contains the phrase, \u201cVolume of solution ( m L ),\u201d the middle box reads, \u201cMass of solution ( g ),\u201d while the one on the right contains the phrase, \u201cMass of H C l ( g ).\u201d There is a phrase under the left arrow that says, \u201cMultiply by density ( g \/ m L )\u201d and under the right arrow it states, \u201cMultiply by mass percent as ratio ( g H C l \/ g solution ).\u201d\" width=\"877\" height=\"125\" data-media-type=\"image\/jpeg\" \/>\r\n<p id=\"fs-idm3493296\">For proper unit cancellation, the 0.500-L volume is converted into 500 mL, and the mass percentage is expressed as a ratio, 37.2 g HCl\/g solution:<\/p>\r\n\r\n<div id=\"fs-idm17430336\" data-type=\"equation\">[latex]\\text{500 mL solution}\\left(\\frac{1.19\\text{g solution}}{\\text{mL solution}}\\right)\\left(\\frac{37.2\\text{g HCl}}{100\\text{g solution}}\\right)=221\\text{g HCl}[\/latex]<\/div>\r\n<p id=\"fs-idm2814416\">This mass of HCl is consistent with our rough estimate of approximately 200 g.<\/p>\r\n\r\n<h4 id=\"fs-idp18799968\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\r\nWhat volume of concentrated HCl solution contains 125 g of HCl?\r\n<div id=\"fs-idm31069568\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a0282 mL<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><section id=\"fs-idm25064544\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Volume Percentage<\/h2>\r\n<p id=\"fs-idp14105408\">Liquid volumes over a wide range of magnitudes are conveniently measured using common and relatively inexpensive laboratory equipment. The concentration of a solution formed by dissolving a liquid solute in a liquid solvent is therefore often expressed as a <strong><span data-type=\"term\">volume percentage<\/span><\/strong>, %vol or (v\/v)%:<\/p>\r\n\r\n<div id=\"fs-idm2717488\" data-type=\"equation\">[latex]\\text{volume percentage}=\\frac{\\text{volume solute}}{\\text{volume solution}}\\times 100\\%[\/latex]<\/div>\r\n<div id=\"fs-idm1441136\" data-type=\"example\">\r\n<div class=\"textbox shaded\">\r\n<h3>Example 3<\/h3>\r\n<h4 id=\"fs-idm5072752\"><strong><span data-type=\"title\">Calculations using Volume Percentage<\/span><\/strong><\/h4>\r\nRubbing alcohol (isopropanol) is usually sold as a 70%vol aqueous solution. If the density of isopropyl alcohol is 0.785 g\/mL, how many grams of isopropyl alcohol are present in a 355 mL bottle of rubbing alcohol?\r\n<h4 id=\"fs-idm38697728\"><span data-type=\"title\">Solution<\/span><\/h4>\r\nPer the definition of volume percentage, the isopropanol volume is 70% of the total solution volume. Multiplying the isopropanol volume by its density yields the requested mass:\r\n<div id=\"fs-idm3502064\" data-type=\"equation\">[latex]\\left(355\\text{mL solution}\\right)\\left(\\frac{70\\text{mL isopropyl alcohol}}{100\\text{mL solution}}\\right)\\left(\\frac{0.785\\text{g isopropyl alcohol}}{1\\text{mL isopropyl alcohol}}\\right)=195\\text{g isopropyl alchol}[\/latex]<\/div>\r\n<h4 id=\"fs-idp44207936\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\r\nWine is approximately 12% ethanol (CH<sub>3<\/sub>CH<sub>2<\/sub>OH) by volume. Ethanol has a molar mass of 46.06 g\/mol and a density 0.789 g\/mL. How many moles of ethanol are present in a 750-mL bottle of wine?\r\n<div id=\"fs-idp41917088\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a01.5 mol ethanol<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><section id=\"fs-idm6093792\" data-depth=\"1\">\r\n<h1 data-type=\"title\">Mass-Volume Percentage<\/h1>\r\n<p id=\"fs-idm16796176\">\u201cMixed\u201d percentage units, derived from the mass of solute and the volume of solution, are popular for certain biochemical and medical applications. A <strong><span data-type=\"term\">mass-volume percent<\/span><\/strong> is a ratio of a solute\u2019s mass to the solution\u2019s volume expressed as a percentage. The specific units used for solute mass and solution volume may vary, depending on the solution. For example, physiological saline solution, used to prepare intravenous fluids, has a concentration of 0.9% mass\/volume (m\/v), indicating that the composition is 0.9 g of solute per 100 mL of solution. The concentration of glucose in blood (commonly referred to as \u201cblood sugar\u201d) is also typically expressed i n terms of a mass-volume ratio. Though not expressed explicitly as a percentage, its concentration is usually given in milligrams of glucose per deciliter (100 mL) of blood (Figure 2).<\/p>\r\n\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"880\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211213\/CNX_Chem_03_05_saline1.jpg\" alt=\"Two pictures are shown labeled a and b. Picture a depicts a clear, colorless solution in a plastic bag being held in a person\u2019s hand. Picture b shows a person\u2019s hand holding a detection meter with a digital readout screen while another hand holds someone\u2019s finger up to the end of the meter. The meter is pressed to the drop of blood that is at the end of the person\u2019s finger.\" width=\"880\" height=\"433\" data-media-type=\"image\/jpeg\" \/> Figure 2. \u201cMixed\u201d mass-volume units are commonly encountered in medical settings. (a) The NaCl concentration of physiological saline is 0.9% (m\/v). (b) This device measures glucose levels in a sample of blood. The normal range for glucose concentration in blood (fasting) is around 70\u2013100 mg\/dL. (credit a: modification of work by \u201cThe National Guard\u201d\/Flickr; credit b: modification of work by Biswarup Ganguly)[\/caption]\r\n\r\n<\/section><section id=\"fs-idm4329744\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Parts per Million and Parts per Billion<\/h2>\r\n<p id=\"fs-idm39037584\">Very low solute concentrations are often expressed using appropriately small units such as <strong><span data-type=\"term\">parts per million (ppm)<\/span><\/strong> or <strong><span data-type=\"term\">parts per billion (ppb)<\/span><\/strong>. Like percentage (\u201cpart per hundred\u201d) units, ppm and ppb may be defined in terms of masses, volumes, or mixed mass-volume units. There are also ppm and ppb units defined with respect to numbers of atoms and molecules.<\/p>\r\n<p id=\"fs-idm18786352\">The mass-based definitions of ppm and ppb are given below:<\/p>\r\n\r\n<div id=\"fs-idp17696176\" data-type=\"equation\">[latex]\\begin{array}{l}\\\\ \\text{ppm}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{6}\\text{ppm}\\\\ \\text{ppb}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{9}\\text{ppb}\\end{array}[\/latex]<\/div>\r\n<p id=\"fs-idm37568416\">Both ppm and ppb are convenient units for reporting the concentrations of pollutants and other trace contaminants in water. Concentrations of these contaminants are typically very low in treated and natural waters, and their levels cannot exceed relatively low concentration thresholds without causing adverse effects on health and wildlife. For example, the EPA has identified the maximum safe level of fluoride ion in tap water to be 4 ppm. Inline water filters are designed to reduce the concentration of fluoride and several other trace-level contaminants in tap water (Figure 3).<\/p>\r\n\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"880\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211214\/CNX_Chem_03_05_faucet1.jpg\" alt=\"Two pictures are shown labeled a and b. Picture a is a close-up shot of water coming out of a faucet. Picture b shows a machine with the words, \u201cFiltered Water Dispenser.\u201d This machine appears to be inside a refrigerator.\" width=\"880\" height=\"447\" data-media-type=\"image\/jpeg\" \/> Figure 3. (a) In some areas, trace-level concentrations of contaminants can render unfiltered tap water unsafe for drinking and cooking. (b) Inline water filters reduce the concentration of solutes in tap water. (credit a: modification of work by Jenn Durfey; credit b: modification of work by \u201cvastateparkstaff\u201d\/Wikimedia commons)[\/caption]\r\n\r\n<div id=\"fs-idm22950992\" data-type=\"example\">\r\n<div class=\"textbox shaded\">\r\n<h3>Example 4<\/h3>\r\n<section id=\"fs-idm4329744\" data-depth=\"1\">\r\n<div id=\"fs-idm22950992\" data-type=\"example\">\r\n<h4 id=\"fs-idm5826976\"><strong><span data-type=\"title\">Calculation of Parts per Million and Parts per Billion Concentrations<\/span><\/strong><\/h4>\r\nAccording to the EPA, when the concentration of lead in tap water reaches 15 ppb, certain remedial actions must be taken. What is this concentration in ppm? At this concentration, what mass of lead (\u03bcg) would be contained in a typical glass of water (300 mL)?\r\n<h4 id=\"fs-idm2696240\"><span data-type=\"title\">Solution<\/span><\/h4>\r\nThe definitions of the ppm and ppb units may be used to convert the given concentration from ppb to ppm. Comparing these two unit definitions shows that ppm is 1000 times greater than ppb (1 ppm = 10<sup>3<\/sup> ppb). Thus:\r\n<div id=\"fs-idm1779776\" data-type=\"equation\">[latex]15\\text{ppb}\\times \\frac{1\\text{ppm}}{{10}^{3}\\text{ppb}}=0.015\\text{ppm}[\/latex]<\/div>\r\n<p id=\"fs-idm35694560\">The definition of the ppb unit may be used to calculate the requested mass if the mass of the solution is provided. However, only the volume of solution (300 mL) is given, so we must use the density to derive the corresponding mass. We can assume the density of tap water to be roughly the same as that of pure water (~1.00 g\/mL), since the concentrations of any dissolved substances should not be very large. Rearranging the equation defining the ppb unit and substituting the given quantities yields:<\/p>\r\n\r\n<div id=\"fs-idm5250896\" data-type=\"equation\">[latex]\\begin{array}{c}\\\\ \\text{ppb}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{9}\\text{ppb}\\\\ \\\\ \\text{mass solute}=\\frac{\\text{ppb}\\times \\text{mass solution}}{{10}^{9}\\text{ppb}}\\\\ \\\\ \\text{mass solute}=\\frac{15\\text{ppb}\\times 300\\text{mL}\\times \\frac{1.00\\text{g}}{\\text{mL}}}{{10}^{9}\\text{ppb}}=4.5\\times {10}^{-6}\\text{g}\\end{array}[\/latex]<\/div>\r\n<p id=\"fs-idp31649040\">Finally, convert this mass to the requested unit of micrograms:<\/p>\r\n\r\n<div id=\"fs-idm4570368\" data-type=\"equation\">[latex]4.5\\times {10}^{-6}\\text{g}\\times \\frac{1\\mu\\text{g}}{{10}^{-6}\\text{g}}=4.5\\mu\\text{g}[\/latex]<\/div>\r\n<h4 id=\"fs-idp21345280\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\r\nA 50.0-g sample of industrial wastewater was determined to contain 0.48 mg of mercury. Express the mercury concentration of the wastewater in ppm and ppb units.\r\n<div id=\"fs-idm45688384\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a09.6 ppm, 9600 ppb<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<section id=\"fs-idm40478192\" class=\"summary\" data-depth=\"1\">\r\n<div id=\"post-355\" class=\"post-355 chapter type-chapter status-publish hentry type-1\">\r\n<div class=\"entry-content\">\r\n<div class=\"im_section\">\r\n<div class=\"im_section\">\r\n<div id=\"mclean-ch03_s01_s02_n01\" class=\"im_key_takeaways im_editable im_block\">\r\n<div class=\"bcc-box bcc-success\">\r\n<h2>Key Concepts and Summary<\/h2>\r\n<section>\r\n<div data-type=\"note\">\r\n<p id=\"fs-idp236281408\">In addition to molarity, a number of other solution concentration units are used in various applications. Percentage concentrations based on the solution components\u2019 masses, volumes, or both are useful for expressing relatively high concentrations, whereas lower concentrations are conveniently expressed using ppm or ppb units. These units are popular in environmental, medical, and other fields where mole-based units such as molarity are not as commonly used.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"bcc-box bcc-success\">\r\n<h3>Key Equations<\/h3>\r\n<section>\r\n<div data-type=\"note\">\r\n<ul>\r\n\t<li>[latex]\\text{Percent by mass}=\\frac{\\text{mass of solute}}{\\text{mass of solution}}\\times 100[\/latex]<\/li>\r\n\t<li>[latex]\\text{ppm}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{6}\\text{ppm}[\/latex]<\/li>\r\n\t<li>[latex]\\text{ppb}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{9}\\text{ppb}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Chemistry End of Chapter Exercises<\/h3>\r\n<div id=\"fs-idp14147136\" data-type=\"exercise\">\r\n<div id=\"fs-idm39120864\" data-type=\"problem\">\r\n<ol>\r\n\t<li id=\"fs-idm27367376\">Consider this question: What mass of a concentrated solution of nitric acid (68.0% HNO<sub>3<\/sub> by mass) is needed to prepare 400.0 g of a 10.0% solution of HNO<sub>3<\/sub> by mass?\r\n<ol>\r\n\t<li>Outline the steps necessary to answer the question.<\/li>\r\n\t<li>Answer the question.<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>What mass of a 4.00% NaOH solution by mass contains 15.0 g of NaOH?<\/li>\r\n\t<li>What mass of solid NaOH (97.0% NaOH by mass) is required to prepare 1.00 L of a 10.0% solution of NaOH by mass? The density of the 10.0% solution is 1.109 g\/mL.<\/li>\r\n\t<li>What mass of HCl is contained in 45.0 mL of an aqueous HCl solution that has a density of 1.19 g cm<sup>\u20133<\/sup> and contains 37.21% HCl by mass?<\/li>\r\n\t<li>The hardness of water (hardness count) is usually expressed in parts per million (by mass) of CaCO<sub>3<\/sub>, which is equivalent to milligrams of CaCO<sub>3<\/sub> per liter of water. What is the molar concentration of Ca<sup>2+ <\/sup>ions in a water sample with a hardness count of 175 mg CaCO<sub>3<\/sub>\/L?<\/li>\r\n\t<li>The level of mercury in a stream was suspected to be above the minimum considered safe (1 part per billion by weight). An analysis indicated that the concentration was 0.68 parts per billion. Assume a density of 1.0 g\/mL and calculate the molarity of mercury in the stream.<\/li>\r\n\t<li>In Canada and the United Kingdom, devices that measure blood glucose levels provide a reading in millimoles per liter. If a measurement of 5.3 m<em data-effect=\"italics\">M<\/em> is observed, what is the concentration of glucose (C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>) in mg\/dL?<\/li>\r\n\t<li>A throat spray is 1.40% by mass phenol, C<sub>6<\/sub>H<sub>5<\/sub>OH, in water. If the solution has a density of 0.9956 g\/mL, calculate the molarity of the solution.<\/li>\r\n\t<li>Copper(I) iodide (CuI) is often added to table salt as a dietary source of iodine. How many moles of CuI are contained in 1.00 lb (454 g) of table salt containing 0.0100% CuI by mass?<\/li>\r\n\t<li>A cough syrup contains 5.0% ethyl alcohol, C<sub>2<\/sub>H<sub>5<\/sub>OH, by mass. If the density of the solution is 0.9928 g\/mL, determine the molarity of the alcohol in the cough syrup.<\/li>\r\n\t<li>D5W is a solution used as an intravenous fluid. It is a 5.0% by mass solution of dextrose (C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>) in water. If the density of D5W is 1.029 g\/mL, calculate the molarity of dextrose in the solution.<\/li>\r\n\t<li>Find the molarity of a 40.0% by mass aqueous solution of sulfuric acid, H<sub>2<\/sub>SO<sub>4<\/sub>, for which the density is 1.3057 g\/mL.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"post-355\" class=\"post-355 chapter type-chapter status-publish hentry type-1\">\r\n<div class=\"entry-content\">\r\n<div class=\"im_section\">\r\n<div class=\"im_section\">\r\n<div id=\"mclean-ch03_s01_s02_n01\" class=\"im_key_takeaways im_editable im_block\">\r\n<div class=\"bcc-box bcc-info\">\r\n<h4>Selected Answers<\/h4>\r\n1. (a) The dilution equation can be used, appropriately modified to accommodate mass-based concentration units:\r\n<div data-type=\"newline\">[latex]\\%{\\text{mass}}_{1}\\times {\\text{mass}}_{1}=\\%{\\text{mass}}_{2}\\times {\\text{mass}}_{2}[\/latex]<\/div>\r\n<div data-type=\"newline\">This equation can be rearranged to isolate mass<sub>1<\/sub> and the given quantities substituted into this equation.<\/div>\r\n<div data-type=\"newline\"><\/div>\r\n<div data-type=\"newline\">(b) [latex]{\\text{mass}}_{1}=\\frac{\\%{\\text{mass}}_{2}\\times {\\text{mass}}_{2}}{\\%{\\text{mass}}_{1}}=\\frac{10.0\\%\\times 400.0\\text{g}}{68.0\\%}=58.8\\text{g}[\/latex]<\/div>\r\n<div data-type=\"newline\">\r\n\r\n3. The mass of the 10% solution is\r\n<div data-type=\"newline\">\u00a0[latex]1000{\\cancel{\\text{cm}}}^{3}\\times \\frac{1.109\\text{g}}{{\\cancel{\\text{cm}}}^{3}}=1.11\\times {10}^{3}\\text{g.}[\/latex]<\/div>\r\n<div data-type=\"newline\"><\/div>\r\n<div data-type=\"newline\">\u00a0The mass of pure NaOH required is<\/div>\r\n<div data-type=\"newline\"><\/div>\r\n<div data-type=\"newline\">\u00a0[latex]\\text{mass}\\left(\\text{NaOH}\\right)=\\frac{10.0\\%}{100.0\\%}\\times 1.11\\times {10}^{3}\\text{g}=1.11\\times {10}^{2}\\text{g.}[\/latex]<\/div>\r\n<div data-type=\"newline\"><\/div>\r\n<div data-type=\"newline\">\u00a0This mass of NaOH must come from the 97.0% solution:<\/div>\r\n<div data-type=\"newline\"><\/div>\r\n<div data-type=\"newline\">\u00a0[latex]\\begin{array}{l}\\\\ \\text{mass}\\left(\\text{NaOH solution}\\right)=\\frac{97.0\\%}{100.0\\%}=1.11\\times {10}^{2}\\text{g}\\\\ \\text{mass}\\left(\\text{NaOH solution}\\right)=\\frac{1.11\\times {10}^{2}\\text{g}}{0.970}=114\\text{g}\\end{array}[\/latex]<\/div>\r\n<div data-type=\"newline\">\r\n<div data-type=\"exercise\"><\/div>\r\n<div id=\"fs-idm5149536\" data-type=\"exercise\">5. \u00a0Since CaCO<sub>3<\/sub> contains 1 mol Ca<sup>2+<\/sup> per mol of CaCO<sub>3<\/sub>, the molar concentration of Ca<sup>2+<\/sup> equals the molarity of CaCO<sub>3<\/sub>:[latex]M{\\text{Ca}}^{2+}=\\frac{\\text{mol}{\\text{CaCO}}_{3}}{\\text{L}}=\\frac{175\\cancel{\\text{mg}}\\times \\left(\\frac{1\\text{mol}}{100.0792\\cancel{\\text{g}}}\\right)\\times \\left(\\frac{1\\cancel{\\text{g}}}{1000\\text{mg}}\\right)}{1\\text{L}}=1.75\\times {10}^{-3}M[\/latex]<\/div>\r\n<div data-type=\"exercise\">\r\n\r\n&nbsp;\r\n\r\n7. 1 mg\/dL = 0.01 g\/L and 1 L = 10 dL\r\n<div data-type=\"newline\">[latex]5.3\\cancel{\\text{mmol}}\\text{\/L}\\times 180.158\\text{mg\/}\\cancel{\\text{mmol}}=9.5\\times {10}^{2}\\text{mg\/L}[\/latex]<\/div>\r\n[latex]9.5\\times {10}^{2}\\text{mg\/L}\\times \\frac{1\\text{L}}{10\\text{dL}}=95\\text{mg\/dL}[\/latex]\r\n\r\n&nbsp;\r\n<div data-type=\"newline\">\r\n\r\n9. 0.0100% of 454 g is [latex]\\left(0.000100\\times 454\\text{g}\\right)=0.0454\\text{g;}[\/latex]\r\n<div id=\"fs-idm39075008\" data-type=\"exercise\">\r\n<div id=\"fs-idm138218400\" data-type=\"solution\">\r\n<div data-type=\"newline\">Molar mass of CuI = 63.546 + 126.90447 = 190.450 g\/mol;<\/div>\r\n<div data-type=\"newline\">[latex]\\text{mol CuI}=\\frac{0.0454\\text{g}}{190.450\\text{g}{\\text{mol}}^{-1}}=0.000238\\text{mol}=2.38\\times {10}^{-4}\\text{mol}[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp22072496\" data-type=\"exercise\">\r\n\r\n&nbsp;\r\n<div data-type=\"newline\">\r\n\r\n11. The molar mass of C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub> is [latex]6\\times 12.011+12\\times 1.00794+6\\times 15.9994=180.2\\text{g\/mol.}[\/latex] In 1.000 L, there are: [latex]\\begin{array}{l}\\left(1000\\cancel{\\text{mL}}\\times 1.029\\text{g}{\\cancel{\\text{mL}}}^{-1}\\right)=1029\\text{g}\\\\ \\text{mol dextrose}=1029\\cancel{\\text{g}}\\times 0.050\\times \\frac{1\\text{mol}}{180.2\\cancel{\\text{g}}}=0.29\\text{mol}\\end{array}[\/latex] C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>.\r\n<div data-type=\"newline\">Since we selected the volume to be 1.00 L, the molarity of dextrose is<\/div>\r\n<div data-type=\"newline\">[latex]\\text{molarity}=\\frac{\\text{mol}}{\\text{L}}=\\frac{0.29\\text{mol}}{1.00\\text{L}}=0.29\\text{mol.}[\/latex]<\/div>\r\n<div data-type=\"newline\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>\r\n<div class=\"bcc-box bcc-success\"><section id=\"glossary\">\r\n<h3>Glossary<\/h3>\r\n<div data-type=\"definition\">\r\n<div id=\"fs-idm8143856\" data-type=\"definition\">\r\n<p data-type=\"definition\"><strong><span data-type=\"term\">mass percentage\r\n<\/span><\/strong>ratio of solute-to-solution mass expressed as a percentage<\/p>\r\n<p data-type=\"definition\"><strong><span data-type=\"term\">mass-volume percent\r\n<\/span><\/strong>ratio of solute mass to solution volume, expressed as a percentage<\/p>\r\n<p data-type=\"definition\"><strong><span data-type=\"term\">parts per billion (ppb)\r\n<\/span><\/strong>ratio of solute-to-solution mass multiplied by 10<sup>9<\/sup><\/p>\r\n<p data-type=\"definition\"><strong><span data-type=\"term\">parts per million (ppm)\r\n<\/span><\/strong>ratio of solute-to-solution mass multiplied by 10<sup>6<\/sup><\/p>\r\n\r\n<div id=\"fs-idp17597424\" data-type=\"definition\">\r\n\r\n<strong><span data-type=\"term\">volume percentage\r\n<\/span><\/strong>ratio of solute-to-solution volume expressed as a percentage\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/section>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>LEARNING OBJECTIVES<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Define the concentration units of mass percentage, volume percentage, mass-volume percentage, parts-per-million (ppm), and parts-per-billion (ppb)<\/li>\n<li>Perform computations relating a solution\u2019s concentration and its components\u2019 volumes and\/or masses using these units<\/li>\n<\/ul>\n<\/div>\n<p id=\"fs-idm32304496\">In the previous section, we introduced molarity, a very useful measurement unit for evaluating the concentration of solutions. However, molarity is only one measure of concentration. In this section, we will introduce some other units of concentration that are commonly used in various applications, either for convenience or by convention.<\/p>\n<section id=\"fs-idm8277808\" data-depth=\"1\">\n<h2 data-type=\"title\">Mass Percentage<\/h2>\n<p id=\"fs-idm26991728\">Earlier in this chapter, we introduced percent composition as a measure of the relative amount of a given element in a compound. Percentages are also commonly used to express the composition of mixtures, including solutions. The <strong><span data-type=\"term\">mass percentage<\/span><\/strong> of a solution component is defined as the ratio of the component\u2019s mass to the solution\u2019s mass, expressed as a percentage:<\/p>\n<div id=\"fs-idm5911152\" data-type=\"equation\">[latex]\\text{mass percentage}=\\frac{\\text{mass of component}}{\\text{mass of solution}}\\times 100\\%[\/latex]<\/div>\n<p id=\"fs-idm30359632\">We are generally most interested in the mass percentages of solutes, but it is also possible to compute the mass percentage of solvent.<\/p>\n<p id=\"fs-idm3484528\">Mass percentage is also referred to by similar names such as <em data-effect=\"italics\">percent mass, percent weight, weight\/weight percent<\/em>, and other variations on this theme. The most common symbol for mass percentage is simply the percent sign, %, although more detailed symbols are often used including %mass, %weight, and (w\/w)%. Use of these more detailed symbols can prevent confusion of mass percentages with other types of percentages, such as volume percentages (to be discussed later in this section).<\/p>\n<p id=\"fs-idm21823696\">Mass percentages are popular concentration units for consumer products. The label of a typical liquid bleach bottle (Figure 1) cites the concentration of its active ingredient, sodium hypochlorite (NaOCl), as being 7.4%. A 100.0-g sample of bleach would therefore contain 7.4 g of NaOCl.<\/p>\n<div style=\"width: 889px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211209\/CNX_Chem_03_05_bleach1.jpg\" alt=\"The sides of two cylindrical containers are shown. Each container\u2019s label is partially visible. The left container\u2019s label reads \u201cBleach.\u201d The right label contains more information about the product including the phrase, \u201cContains: Sodium hypochlorite 7.4 %.\u201d\" width=\"879\" height=\"634\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 1. Liquid bleach is an aqueous solution of sodium hypochlorite (NaOCl). This brand has a concentration of 7.4% NaOCl by mass.<\/p>\n<\/div>\n<div id=\"fs-idm23566960\" data-type=\"example\">\n<div class=\"textbox shaded\">\n<h3>Example 1<\/h3>\n<h4 id=\"fs-idm2453280\"><strong><span data-type=\"title\">Calculation of Percent by Mass<\/span><\/strong><\/h4>\n<p>A 5.0-g sample of spinal fluid contains 3.75 mg (0.00375 g) of glucose. What is the percent by mass of glucose in spinal fluid?<\/p>\n<h4 id=\"fs-idp19396640\"><span data-type=\"title\">Solution<\/span><\/h4>\n<p>The spinal fluid sample contains roughly 4 mg of glucose in 5000 mg of fluid, so the mass fraction of glucose should be a bit less than one part in 1000, or about 0.1%. Substituting the given masses into the equation defining mass percentage yields:<\/p>\n<div id=\"fs-idm17789648\" data-type=\"equation\">[latex]\\%\\text{glucose}=\\frac{3.75\\text{mg glucose}\\times \\frac{1\\text{g}}{1000\\text{mg}}}{5.0\\text{g spinal fluid}}=0.075\\%[\/latex]<\/div>\n<p id=\"fs-idm36099936\">The computed mass percentage agrees with our rough estimate (it\u2019s a bit less than 0.1%).<\/p>\n<p id=\"fs-idm6973776\">Note that while any mass unit may be used to compute a mass percentage (mg, g, kg, oz, and so on), the same unit must be used for both the solute and the solution so that the mass units cancel, yielding a dimensionless ratio. In this case, we converted the units of solute in the numerator from mg to g to match the units in the denominator. We could just as easily have converted the denominator from g to mg instead. As long as identical mass units are used for both solute and solution, the computed mass percentage will be correct.<\/p>\n<h4 id=\"fs-idm64146192\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\n<p>A bottle of a tile cleanser contains 135 g of HCl and 775 g of water. What is the percent by mass of HCl in this cleanser?<\/p>\n<div id=\"fs-idp47230144\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a014.8%<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Example 2<\/h3>\n<h4 id=\"fs-idm32647264\"><strong><span data-type=\"title\">Calculations using Mass Percentage<\/span><\/strong><\/h4>\n<p>\u201cConcentrated\u201d hydrochloric acid is an aqueous solution of 37.2% HCl that is commonly used as a laboratory reagent. The density of this solution is 1.19 g\/mL. What mass of HCl is contained in 0.500 L of this solution?<\/p>\n<h4 id=\"fs-idm37499888\"><span data-type=\"title\">Solution<\/span><\/h4>\n<p>The HCl concentration is near 40%, so a 100-g portion of this solution would contain about 40 g of HCl. Since the solution density isn\u2019t greatly different from that of water (1 g\/mL), a reasonable estimate of the HCl mass in 500 g (0.5 L) of the solution is about five times greater than that in a 100 g portion, or [latex]5\\times 40=200\\text{g.}[\/latex] In order to derive the mass of solute in a solution from its mass percentage, we need to know the corresponding mass of the solution. Using the solution density given, we can convert the solution\u2019s volume to mass, and then use the given mass percentage to calculate the solute mass. This mathematical approach is outlined in the flow chart below:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211211\/CNX_Chem_03_05_Example2_img1.jpg\" alt=\"A diagram of three boxes connected by a right-facing arrow in between each is shown. The box on the left contains the phrase, \u201cVolume of solution ( m L ),\u201d the middle box reads, \u201cMass of solution ( g ),\u201d while the one on the right contains the phrase, \u201cMass of H C l ( g ).\u201d There is a phrase under the left arrow that says, \u201cMultiply by density ( g \/ m L )\u201d and under the right arrow it states, \u201cMultiply by mass percent as ratio ( g H C l \/ g solution ).\u201d\" width=\"877\" height=\"125\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p id=\"fs-idm3493296\">For proper unit cancellation, the 0.500-L volume is converted into 500 mL, and the mass percentage is expressed as a ratio, 37.2 g HCl\/g solution:<\/p>\n<div id=\"fs-idm17430336\" data-type=\"equation\">[latex]\\text{500 mL solution}\\left(\\frac{1.19\\text{g solution}}{\\text{mL solution}}\\right)\\left(\\frac{37.2\\text{g HCl}}{100\\text{g solution}}\\right)=221\\text{g HCl}[\/latex]<\/div>\n<p id=\"fs-idm2814416\">This mass of HCl is consistent with our rough estimate of approximately 200 g.<\/p>\n<h4 id=\"fs-idp18799968\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\n<p>What volume of concentrated HCl solution contains 125 g of HCl?<\/p>\n<div id=\"fs-idm31069568\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a0282 mL<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"fs-idm25064544\" data-depth=\"1\">\n<h2 data-type=\"title\">Volume Percentage<\/h2>\n<p id=\"fs-idp14105408\">Liquid volumes over a wide range of magnitudes are conveniently measured using common and relatively inexpensive laboratory equipment. The concentration of a solution formed by dissolving a liquid solute in a liquid solvent is therefore often expressed as a <strong><span data-type=\"term\">volume percentage<\/span><\/strong>, %vol or (v\/v)%:<\/p>\n<div id=\"fs-idm2717488\" data-type=\"equation\">[latex]\\text{volume percentage}=\\frac{\\text{volume solute}}{\\text{volume solution}}\\times 100\\%[\/latex]<\/div>\n<div id=\"fs-idm1441136\" data-type=\"example\">\n<div class=\"textbox shaded\">\n<h3>Example 3<\/h3>\n<h4 id=\"fs-idm5072752\"><strong><span data-type=\"title\">Calculations using Volume Percentage<\/span><\/strong><\/h4>\n<p>Rubbing alcohol (isopropanol) is usually sold as a 70%vol aqueous solution. If the density of isopropyl alcohol is 0.785 g\/mL, how many grams of isopropyl alcohol are present in a 355 mL bottle of rubbing alcohol?<\/p>\n<h4 id=\"fs-idm38697728\"><span data-type=\"title\">Solution<\/span><\/h4>\n<p>Per the definition of volume percentage, the isopropanol volume is 70% of the total solution volume. Multiplying the isopropanol volume by its density yields the requested mass:<\/p>\n<div id=\"fs-idm3502064\" data-type=\"equation\">[latex]\\left(355\\text{mL solution}\\right)\\left(\\frac{70\\text{mL isopropyl alcohol}}{100\\text{mL solution}}\\right)\\left(\\frac{0.785\\text{g isopropyl alcohol}}{1\\text{mL isopropyl alcohol}}\\right)=195\\text{g isopropyl alchol}[\/latex]<\/div>\n<h4 id=\"fs-idp44207936\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\n<p>Wine is approximately 12% ethanol (CH<sub>3<\/sub>CH<sub>2<\/sub>OH) by volume. Ethanol has a molar mass of 46.06 g\/mol and a density 0.789 g\/mL. How many moles of ethanol are present in a 750-mL bottle of wine?<\/p>\n<div id=\"fs-idp41917088\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a01.5 mol ethanol<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"fs-idm6093792\" data-depth=\"1\">\n<h1 data-type=\"title\">Mass-Volume Percentage<\/h1>\n<p id=\"fs-idm16796176\">\u201cMixed\u201d percentage units, derived from the mass of solute and the volume of solution, are popular for certain biochemical and medical applications. A <strong><span data-type=\"term\">mass-volume percent<\/span><\/strong> is a ratio of a solute\u2019s mass to the solution\u2019s volume expressed as a percentage. The specific units used for solute mass and solution volume may vary, depending on the solution. For example, physiological saline solution, used to prepare intravenous fluids, has a concentration of 0.9% mass\/volume (m\/v), indicating that the composition is 0.9 g of solute per 100 mL of solution. The concentration of glucose in blood (commonly referred to as \u201cblood sugar\u201d) is also typically expressed i n terms of a mass-volume ratio. Though not expressed explicitly as a percentage, its concentration is usually given in milligrams of glucose per deciliter (100 mL) of blood (Figure 2).<\/p>\n<div style=\"width: 890px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211213\/CNX_Chem_03_05_saline1.jpg\" alt=\"Two pictures are shown labeled a and b. Picture a depicts a clear, colorless solution in a plastic bag being held in a person\u2019s hand. Picture b shows a person\u2019s hand holding a detection meter with a digital readout screen while another hand holds someone\u2019s finger up to the end of the meter. The meter is pressed to the drop of blood that is at the end of the person\u2019s finger.\" width=\"880\" height=\"433\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 2. \u201cMixed\u201d mass-volume units are commonly encountered in medical settings. (a) The NaCl concentration of physiological saline is 0.9% (m\/v). (b) This device measures glucose levels in a sample of blood. The normal range for glucose concentration in blood (fasting) is around 70\u2013100 mg\/dL. (credit a: modification of work by \u201cThe National Guard\u201d\/Flickr; credit b: modification of work by Biswarup Ganguly)<\/p>\n<\/div>\n<\/section>\n<section id=\"fs-idm4329744\" data-depth=\"1\">\n<h2 data-type=\"title\">Parts per Million and Parts per Billion<\/h2>\n<p id=\"fs-idm39037584\">Very low solute concentrations are often expressed using appropriately small units such as <strong><span data-type=\"term\">parts per million (ppm)<\/span><\/strong> or <strong><span data-type=\"term\">parts per billion (ppb)<\/span><\/strong>. Like percentage (\u201cpart per hundred\u201d) units, ppm and ppb may be defined in terms of masses, volumes, or mixed mass-volume units. There are also ppm and ppb units defined with respect to numbers of atoms and molecules.<\/p>\n<p id=\"fs-idm18786352\">The mass-based definitions of ppm and ppb are given below:<\/p>\n<div id=\"fs-idp17696176\" data-type=\"equation\">[latex]\\begin{array}{l}\\\\ \\text{ppm}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{6}\\text{ppm}\\\\ \\text{ppb}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{9}\\text{ppb}\\end{array}[\/latex]<\/div>\n<p id=\"fs-idm37568416\">Both ppm and ppb are convenient units for reporting the concentrations of pollutants and other trace contaminants in water. Concentrations of these contaminants are typically very low in treated and natural waters, and their levels cannot exceed relatively low concentration thresholds without causing adverse effects on health and wildlife. For example, the EPA has identified the maximum safe level of fluoride ion in tap water to be 4 ppm. Inline water filters are designed to reduce the concentration of fluoride and several other trace-level contaminants in tap water (Figure 3).<\/p>\n<div style=\"width: 890px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23211214\/CNX_Chem_03_05_faucet1.jpg\" alt=\"Two pictures are shown labeled a and b. Picture a is a close-up shot of water coming out of a faucet. Picture b shows a machine with the words, \u201cFiltered Water Dispenser.\u201d This machine appears to be inside a refrigerator.\" width=\"880\" height=\"447\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 3. (a) In some areas, trace-level concentrations of contaminants can render unfiltered tap water unsafe for drinking and cooking. (b) Inline water filters reduce the concentration of solutes in tap water. (credit a: modification of work by Jenn Durfey; credit b: modification of work by \u201cvastateparkstaff\u201d\/Wikimedia commons)<\/p>\n<\/div>\n<div id=\"fs-idm22950992\" data-type=\"example\">\n<div class=\"textbox shaded\">\n<h3>Example 4<\/h3>\n<section id=\"fs-idm4329744\" data-depth=\"1\">\n<div id=\"fs-idm22950992\" data-type=\"example\">\n<h4 id=\"fs-idm5826976\"><strong><span data-type=\"title\">Calculation of Parts per Million and Parts per Billion Concentrations<\/span><\/strong><\/h4>\n<p>According to the EPA, when the concentration of lead in tap water reaches 15 ppb, certain remedial actions must be taken. What is this concentration in ppm? At this concentration, what mass of lead (\u03bcg) would be contained in a typical glass of water (300 mL)?<\/p>\n<h4 id=\"fs-idm2696240\"><span data-type=\"title\">Solution<\/span><\/h4>\n<p>The definitions of the ppm and ppb units may be used to convert the given concentration from ppb to ppm. Comparing these two unit definitions shows that ppm is 1000 times greater than ppb (1 ppm = 10<sup>3<\/sup> ppb). Thus:<\/p>\n<div id=\"fs-idm1779776\" data-type=\"equation\">[latex]15\\text{ppb}\\times \\frac{1\\text{ppm}}{{10}^{3}\\text{ppb}}=0.015\\text{ppm}[\/latex]<\/div>\n<p id=\"fs-idm35694560\">The definition of the ppb unit may be used to calculate the requested mass if the mass of the solution is provided. However, only the volume of solution (300 mL) is given, so we must use the density to derive the corresponding mass. We can assume the density of tap water to be roughly the same as that of pure water (~1.00 g\/mL), since the concentrations of any dissolved substances should not be very large. Rearranging the equation defining the ppb unit and substituting the given quantities yields:<\/p>\n<div id=\"fs-idm5250896\" data-type=\"equation\">[latex]\\begin{array}{c}\\\\ \\text{ppb}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{9}\\text{ppb}\\\\ \\\\ \\text{mass solute}=\\frac{\\text{ppb}\\times \\text{mass solution}}{{10}^{9}\\text{ppb}}\\\\ \\\\ \\text{mass solute}=\\frac{15\\text{ppb}\\times 300\\text{mL}\\times \\frac{1.00\\text{g}}{\\text{mL}}}{{10}^{9}\\text{ppb}}=4.5\\times {10}^{-6}\\text{g}\\end{array}[\/latex]<\/div>\n<p id=\"fs-idp31649040\">Finally, convert this mass to the requested unit of micrograms:<\/p>\n<div id=\"fs-idm4570368\" data-type=\"equation\">[latex]4.5\\times {10}^{-6}\\text{g}\\times \\frac{1\\mu\\text{g}}{{10}^{-6}\\text{g}}=4.5\\mu\\text{g}[\/latex]<\/div>\n<h4 id=\"fs-idp21345280\"><strong><span data-type=\"title\">Check Your Learning<\/span><\/strong><\/h4>\n<p>A 50.0-g sample of industrial wastewater was determined to contain 0.48 mg of mercury. Express the mercury concentration of the wastewater in ppm and ppb units.<\/p>\n<div id=\"fs-idm45688384\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div style=\"text-align: right;\" data-type=\"title\"><strong>Answer<\/strong>:\u00a09.6 ppm, 9600 ppb<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<section id=\"fs-idm40478192\" class=\"summary\" data-depth=\"1\">\n<div id=\"post-355\" class=\"post-355 chapter type-chapter status-publish hentry type-1\">\n<div class=\"entry-content\">\n<div class=\"im_section\">\n<div class=\"im_section\">\n<div id=\"mclean-ch03_s01_s02_n01\" class=\"im_key_takeaways im_editable im_block\">\n<div class=\"bcc-box bcc-success\">\n<h2>Key Concepts and Summary<\/h2>\n<section>\n<div data-type=\"note\">\n<p id=\"fs-idp236281408\">In addition to molarity, a number of other solution concentration units are used in various applications. Percentage concentrations based on the solution components\u2019 masses, volumes, or both are useful for expressing relatively high concentrations, whereas lower concentrations are conveniently expressed using ppm or ppb units. These units are popular in environmental, medical, and other fields where mole-based units such as molarity are not as commonly used.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"bcc-box bcc-success\">\n<h3>Key Equations<\/h3>\n<section>\n<div data-type=\"note\">\n<ul>\n<li>[latex]\\text{Percent by mass}=\\frac{\\text{mass of solute}}{\\text{mass of solution}}\\times 100[\/latex]<\/li>\n<li>[latex]\\text{ppm}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{6}\\text{ppm}[\/latex]<\/li>\n<li>[latex]\\text{ppb}=\\frac{\\text{mass solute}}{\\text{mass solution}}\\times {10}^{9}\\text{ppb}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Chemistry End of Chapter Exercises<\/h3>\n<div id=\"fs-idp14147136\" data-type=\"exercise\">\n<div id=\"fs-idm39120864\" data-type=\"problem\">\n<ol>\n<li id=\"fs-idm27367376\">Consider this question: What mass of a concentrated solution of nitric acid (68.0% HNO<sub>3<\/sub> by mass) is needed to prepare 400.0 g of a 10.0% solution of HNO<sub>3<\/sub> by mass?\n<ol>\n<li>Outline the steps necessary to answer the question.<\/li>\n<li>Answer the question.<\/li>\n<\/ol>\n<\/li>\n<li>What mass of a 4.00% NaOH solution by mass contains 15.0 g of NaOH?<\/li>\n<li>What mass of solid NaOH (97.0% NaOH by mass) is required to prepare 1.00 L of a 10.0% solution of NaOH by mass? The density of the 10.0% solution is 1.109 g\/mL.<\/li>\n<li>What mass of HCl is contained in 45.0 mL of an aqueous HCl solution that has a density of 1.19 g cm<sup>\u20133<\/sup> and contains 37.21% HCl by mass?<\/li>\n<li>The hardness of water (hardness count) is usually expressed in parts per million (by mass) of CaCO<sub>3<\/sub>, which is equivalent to milligrams of CaCO<sub>3<\/sub> per liter of water. What is the molar concentration of Ca<sup>2+ <\/sup>ions in a water sample with a hardness count of 175 mg CaCO<sub>3<\/sub>\/L?<\/li>\n<li>The level of mercury in a stream was suspected to be above the minimum considered safe (1 part per billion by weight). An analysis indicated that the concentration was 0.68 parts per billion. Assume a density of 1.0 g\/mL and calculate the molarity of mercury in the stream.<\/li>\n<li>In Canada and the United Kingdom, devices that measure blood glucose levels provide a reading in millimoles per liter. If a measurement of 5.3 m<em data-effect=\"italics\">M<\/em> is observed, what is the concentration of glucose (C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>) in mg\/dL?<\/li>\n<li>A throat spray is 1.40% by mass phenol, C<sub>6<\/sub>H<sub>5<\/sub>OH, in water. If the solution has a density of 0.9956 g\/mL, calculate the molarity of the solution.<\/li>\n<li>Copper(I) iodide (CuI) is often added to table salt as a dietary source of iodine. How many moles of CuI are contained in 1.00 lb (454 g) of table salt containing 0.0100% CuI by mass?<\/li>\n<li>A cough syrup contains 5.0% ethyl alcohol, C<sub>2<\/sub>H<sub>5<\/sub>OH, by mass. If the density of the solution is 0.9928 g\/mL, determine the molarity of the alcohol in the cough syrup.<\/li>\n<li>D5W is a solution used as an intravenous fluid. It is a 5.0% by mass solution of dextrose (C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>) in water. If the density of D5W is 1.029 g\/mL, calculate the molarity of dextrose in the solution.<\/li>\n<li>Find the molarity of a 40.0% by mass aqueous solution of sulfuric acid, H<sub>2<\/sub>SO<sub>4<\/sub>, for which the density is 1.3057 g\/mL.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"post-355\" class=\"post-355 chapter type-chapter status-publish hentry type-1\">\n<div class=\"entry-content\">\n<div class=\"im_section\">\n<div class=\"im_section\">\n<div id=\"mclean-ch03_s01_s02_n01\" class=\"im_key_takeaways im_editable im_block\">\n<div class=\"bcc-box bcc-info\">\n<h4>Selected Answers<\/h4>\n<p>1. (a) The dilution equation can be used, appropriately modified to accommodate mass-based concentration units:<\/p>\n<div data-type=\"newline\">[latex]\\%{\\text{mass}}_{1}\\times {\\text{mass}}_{1}=\\%{\\text{mass}}_{2}\\times {\\text{mass}}_{2}[\/latex]<\/div>\n<div data-type=\"newline\">This equation can be rearranged to isolate mass<sub>1<\/sub> and the given quantities substituted into this equation.<\/div>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\">(b) [latex]{\\text{mass}}_{1}=\\frac{\\%{\\text{mass}}_{2}\\times {\\text{mass}}_{2}}{\\%{\\text{mass}}_{1}}=\\frac{10.0\\%\\times 400.0\\text{g}}{68.0\\%}=58.8\\text{g}[\/latex]<\/div>\n<div data-type=\"newline\">\n<p>3. The mass of the 10% solution is<\/p>\n<div data-type=\"newline\">\u00a0[latex]1000{\\cancel{\\text{cm}}}^{3}\\times \\frac{1.109\\text{g}}{{\\cancel{\\text{cm}}}^{3}}=1.11\\times {10}^{3}\\text{g.}[\/latex]<\/div>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\">\u00a0The mass of pure NaOH required is<\/div>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\">\u00a0[latex]\\text{mass}\\left(\\text{NaOH}\\right)=\\frac{10.0\\%}{100.0\\%}\\times 1.11\\times {10}^{3}\\text{g}=1.11\\times {10}^{2}\\text{g.}[\/latex]<\/div>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\">\u00a0This mass of NaOH must come from the 97.0% solution:<\/div>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\">\u00a0[latex]\\begin{array}{l}\\\\ \\text{mass}\\left(\\text{NaOH solution}\\right)=\\frac{97.0\\%}{100.0\\%}=1.11\\times {10}^{2}\\text{g}\\\\ \\text{mass}\\left(\\text{NaOH solution}\\right)=\\frac{1.11\\times {10}^{2}\\text{g}}{0.970}=114\\text{g}\\end{array}[\/latex]<\/div>\n<div data-type=\"newline\">\n<div data-type=\"exercise\"><\/div>\n<div id=\"fs-idm5149536\" data-type=\"exercise\">5. \u00a0Since CaCO<sub>3<\/sub> contains 1 mol Ca<sup>2+<\/sup> per mol of CaCO<sub>3<\/sub>, the molar concentration of Ca<sup>2+<\/sup> equals the molarity of CaCO<sub>3<\/sub>:[latex]M{\\text{Ca}}^{2+}=\\frac{\\text{mol}{\\text{CaCO}}_{3}}{\\text{L}}=\\frac{175\\cancel{\\text{mg}}\\times \\left(\\frac{1\\text{mol}}{100.0792\\cancel{\\text{g}}}\\right)\\times \\left(\\frac{1\\cancel{\\text{g}}}{1000\\text{mg}}\\right)}{1\\text{L}}=1.75\\times {10}^{-3}M[\/latex]<\/div>\n<div data-type=\"exercise\">\n<p>&nbsp;<\/p>\n<p>7. 1 mg\/dL = 0.01 g\/L and 1 L = 10 dL<\/p>\n<div data-type=\"newline\">[latex]5.3\\cancel{\\text{mmol}}\\text{\/L}\\times 180.158\\text{mg\/}\\cancel{\\text{mmol}}=9.5\\times {10}^{2}\\text{mg\/L}[\/latex]<\/div>\n<p>[latex]9.5\\times {10}^{2}\\text{mg\/L}\\times \\frac{1\\text{L}}{10\\text{dL}}=95\\text{mg\/dL}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<div data-type=\"newline\">\n<p>9. 0.0100% of 454 g is [latex]\\left(0.000100\\times 454\\text{g}\\right)=0.0454\\text{g;}[\/latex]<\/p>\n<div id=\"fs-idm39075008\" data-type=\"exercise\">\n<div id=\"fs-idm138218400\" data-type=\"solution\">\n<div data-type=\"newline\">Molar mass of CuI = 63.546 + 126.90447 = 190.450 g\/mol;<\/div>\n<div data-type=\"newline\">[latex]\\text{mol CuI}=\\frac{0.0454\\text{g}}{190.450\\text{g}{\\text{mol}}^{-1}}=0.000238\\text{mol}=2.38\\times {10}^{-4}\\text{mol}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idp22072496\" data-type=\"exercise\">\n<p>&nbsp;<\/p>\n<div data-type=\"newline\">\n<p>11. The molar mass of C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub> is [latex]6\\times 12.011+12\\times 1.00794+6\\times 15.9994=180.2\\text{g\/mol.}[\/latex] In 1.000 L, there are: [latex]\\begin{array}{l}\\left(1000\\cancel{\\text{mL}}\\times 1.029\\text{g}{\\cancel{\\text{mL}}}^{-1}\\right)=1029\\text{g}\\\\ \\text{mol dextrose}=1029\\cancel{\\text{g}}\\times 0.050\\times \\frac{1\\text{mol}}{180.2\\cancel{\\text{g}}}=0.29\\text{mol}\\end{array}[\/latex] C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>.<\/p>\n<div data-type=\"newline\">Since we selected the volume to be 1.00 L, the molarity of dextrose is<\/div>\n<div data-type=\"newline\">[latex]\\text{molarity}=\\frac{\\text{mol}}{\\text{L}}=\\frac{0.29\\text{mol}}{1.00\\text{L}}=0.29\\text{mol.}[\/latex]<\/div>\n<div data-type=\"newline\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<div class=\"bcc-box bcc-success\">\n<section id=\"glossary\">\n<h3>Glossary<\/h3>\n<div data-type=\"definition\">\n<div id=\"fs-idm8143856\" data-type=\"definition\">\n<p data-type=\"definition\"><strong><span data-type=\"term\">mass percentage<br \/>\n<\/span><\/strong>ratio of solute-to-solution mass expressed as a percentage<\/p>\n<p data-type=\"definition\"><strong><span data-type=\"term\">mass-volume percent<br \/>\n<\/span><\/strong>ratio of solute mass to solution volume, expressed as a percentage<\/p>\n<p data-type=\"definition\"><strong><span data-type=\"term\">parts per billion (ppb)<br \/>\n<\/span><\/strong>ratio of solute-to-solution mass multiplied by 10<sup>9<\/sup><\/p>\n<p data-type=\"definition\"><strong><span data-type=\"term\">parts per million (ppm)<br \/>\n<\/span><\/strong>ratio of solute-to-solution mass multiplied by 10<sup>6<\/sup><\/p>\n<div id=\"fs-idp17597424\" data-type=\"definition\">\n<p><strong><span data-type=\"term\">volume percentage<br \/>\n<\/span><\/strong>ratio of solute-to-solution volume expressed as a percentage<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/section>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1661\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Chemistry. <strong>Provided by<\/strong>: OpenStax College. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/openstaxcollege.org\">http:\/\/openstaxcollege.org<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":5,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry\",\"author\":\"\",\"organization\":\"OpenStax College\",\"url\":\"http:\/\/openstaxcollege.org\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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