{"id":2818,"date":"2016-08-24T19:17:45","date_gmt":"2016-08-24T19:17:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/?post_type=chapter&#038;p=2818"},"modified":"2017-08-28T21:48:53","modified_gmt":"2017-08-28T21:48:53","slug":"the-ph-scale","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/chapter\/the-ph-scale\/","title":{"raw":"The pH Scale","rendered":"The pH Scale"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define pH.<\/li>\r\n \t<li>List pH values of common materials.<\/li>\r\n \t<li>Perform pH calculations for acidic and basic solutions.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3><strong>Why is grapefruit juice acidic? <\/strong><\/h3>\r\n<p id=\"x-ck12-YWIyOTE3MzkwNmVhYmQ3NjlkYjk1NzJhNTA3OWZjNWU.-rz2\"><img class=\"alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213248\/20140811155915053266.jpeg\" alt=\"Grapefruit juice is quite acidic\" width=\"263\" height=\"175\" \/>Grapefruit juice has a pH of somewhere between 2.9-3.3, depending on the specific product. Excessive exposure to this juice can cause erosion of tooth enamel and can lead to tooth damage. The acids in grapefruit juice are carbon-based, with citric acid being one of the major constituents.<\/p>\r\nThis compound has three ionizable hydrogens on each molecule which contribute to the relatively low pH of the juice. Another component of grape juice is malic acid, containing two ionizable hydrogens per molecule.\r\n\r\n<\/div>\r\n<h2>The pH Scale<\/h2>\r\n<p id=\"x-ck12-YjAwZDcwNzMxNTgwZjQ0NDM5MDNlNjE1YjM4OWIxNGE.-vh5\">Expressing the acidity of a solution by using the molarity of the hydrogen ion is cumbersome because the quantities are generally very small. Danish scientist S\u00f8ren S\u00f8renson (1868-1939) proposed an easier system for indicating the concentration of H <sup> + <\/sup> called the pH scale. The letters pH stand for the power of the hydrogen ion. The <strong> pH <\/strong> of a solution is the negative logarithm of the hydrogen-ion concentration.<\/p>\r\n<p id=\"x-ck12-Y2IzZTJiOTk1Y2ZkMWYyNmU3MzQxMWI4MmI5ZWZlNjg.-cur\">pH = -log[H <sup> + <\/sup> ]<\/p>\r\n<p id=\"x-ck12-OGFiMDc5NGRiZTlmMmY1YzUzMTZmYzhjZTE4ZmQzYjE.-d1m\">In pure water or a neutral solution the [H <sup> + <\/sup> ]\u00a0=\u00a01.0\u00a0\u00d7\u00a010 <sup> -7 <\/sup> \u00a0M. Substituting into the pH expression:<\/p>\r\n<p id=\"x-ck12-4aq\">pH = -log[1.0 \u00d7 10 <sup> -7 <\/sup> ] = -(-7.00) = 7.00<\/p>\r\n<p id=\"x-ck12-YjhlZjlkMWViNWUyMTNkMmNmNGUxOGM2YTQwMThjMzA.-a6b\">The pH of pure water or any neutral solution is thus 7.00. For recording purposes, the numbers to the right of the decimal point in the pH value are the significant figures. Since\u00a01.0\u00a0\u00d7\u00a010 <sup> -7 <\/sup> has two significant figures, the pH can be reported as 7.00.<\/p>\r\n<p id=\"x-ck12-MWFiYjIzOGViYmQzNzE2M2E4OTA2YTUwNzQ0MGY0NWY.-n1t\">A logarithmic scale condenses the range of acidity to numbers that are easy to use. Consider a solution with [H <sup> + <\/sup> ]\u00a0=\u00a01.0\u00a0\u00d7\u00a010 <sup> -4 <\/sup> \u00a0M. That is a hydrogen-ion concentration that is 1000 times higher than the concentration in pure water. The pH of such a solution is 4.00, a difference of just 3 pH units. Notice that when the [H <sup> + <\/sup> ] is written in scientific notation and the coefficient is 1, the pH is simply the exponent with the sign changed. The pH of a solution with the [H <sup> + <\/sup> ]\u00a0=\u00a01\u00a0\u00d7\u00a010 <sup> -2 <\/sup> \u00a0M is 2 and the pH of a solution with the\u00a0[H <sup> + <\/sup> ]\u00a0=\u00a01\u00a0\u00d7\u00a010 <sup> -10 <\/sup> \u00a0M is 10.<\/p>\r\n<p id=\"x-ck12-N2M0YTRlNWMyN2Y0YTY1NTg2ZGE5MmZlNmJlOTBkMWM.-ed1\">As we saw earlier, a solution with the [H <sup> + <\/sup> ] higher than\u00a01.0 \u00d7 10 <sup> -7 <\/sup> is acidic, while a solution with the [H <sup> + <\/sup> ] lower than\u00a01.0 \u00d7 10 <sup> -7 <\/sup> is basic. Consequently, solutions whose pH is less than 7 are acidic, while those with a pH higher than 7 are basic. <strong>Figure 1\u00a0<\/strong>illustrates this relationship, along with some examples of various solutions.<\/p>\r\n\r\n<div id=\"x-ck12-MmU1ZDQzMmY5ZTk0ZGIyMWIxYmMwNjhiMzNmMzA4ZmM.-wm8\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"403\"]<img id=\"x-ck12-OTgwNDUtMTM2NDk3NTgwOS05LTY4LTUuNS41LjEwLjI.\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213250\/20140811155915175893.png\" alt=\"pH values of several common materials\" width=\"403\" height=\"500\" longdesc=\"The%20pH%20values%20for%20several%20common%20materials.\" \/> Figure 1.\u00a0The pH values for several common materials.[\/caption]\r\n\r\n<\/div>\r\n<h2>Calculating pH of Acids and Bases<\/h2>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<div class=\"textbox examples\">\r\n<h3>Raising tropical fish<\/h3>\r\n<p id=\"x-ck12-YmMyOGE5YTQwYzhjMTE4OWQxMWFhMzAwZjZiNGMwMWI.-gjg\"><span class=\"x-ck12-img-inline\"><img class=\"alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213251\/20140811155915280955.jpeg\" alt=\"It is important that the pH in a fish bowl remains in a certain range\" width=\"248\" height=\"177\" \/><\/span><\/p>\r\n<p id=\"x-ck12-ZmFkMzQyZjk1ODA3OWY2Y2VlOGI3ZGQ2OTBmYjgxODQ.-9gn\">Many people enjoy having tropical fish in their homes or businesses. These brightly-colored creatures are relaxing to watch, but do require a certain amount of maintenance in order for them to survive.<\/p>\r\nTap water is usually too alkaline when it comes out of the faucet, so some adjustments need to be made. The pH of the water will change over time while it is in the tank, which means you need to test it every so often. Then you get to be a chemist for your fish.\r\n\r\n<\/div>\r\n<h3>Calculating pH of Acids and Bases<\/h3>\r\n<p id=\"x-ck12-ZDYyZjgwZDc4ZjdkMmM5OThlNDFkMDZiYjFlM2MxZDg.-8aw\">Calculation of pH is simple when there is a 1\u00a0\u00d7\u00a010 <sup> power <\/sup> problem. However, in real life that is rarely the situation. If the coefficient is not equal to 1, a calculator must be used to find the pH. For example, the pH of a solution with [H <sup> + <\/sup> ]\u00a0=\u00a02.3\u00a0\u00d7\u00a010 <sup> -5 <\/sup> \u00a0M\u00a0 can be found as shown below.<\/p>\r\n<p id=\"x-ck12-nhb\">pH = -log[2.3 \u00d7\u00a010 <sup> -5 <\/sup> ] = 4.64<\/p>\r\n<p id=\"x-ck12-ZTI2MmU2Nzg0N2MxMTI3ZDhiNjljNmE4YmFkODQ1MDA.-2b9\">When the pH of a solution is known, the concentration of the hydrogen ion can be calculated. The inverse of the logarithm (or antilog) is the 10 <em> <sup> x <\/sup><\/em> key on a calculator.<\/p>\r\n<p id=\"x-ck12-c21\">[H <sup> + <\/sup> ] = 10 <sup> -pH <\/sup><\/p>\r\n<p id=\"x-ck12-OTBmMjRiNjk0NzVkOGFhNzk4Yjc2NzNhNmRhMjUzY2E.-ex3\">For example, suppose that you have a solution with a pH of 9.14. To find the [H <sup> + <\/sup> ] use the 10 <em> <sup> x <\/sup><\/em> key.<\/p>\r\n<p id=\"x-ck12-vsd\">[H <sup> + <\/sup> ] = 10 <sup> -pH <\/sup> = 10 <sup> -9.14 <\/sup> = 7.24 \u00d7 10 <sup> -10 <\/sup> M<\/p>\r\n\r\n<h4>Hydroxide Ion Concentration and pH<\/h4>\r\n<p id=\"x-ck12-MTZlMWJkMzkyMjliZGI2ZGUwYjY1MzRmNjczNWIyYWU.-hhd\">As we saw earlier, the hydroxide ion concentration of any aqueous solution is related to the hydrogen ion concentration through the value of <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213240\/20ad2eefd31aa21b83daf6314f529858.png\" alt=\"K_w\" width=\"24\" height=\"15\" \/> . We can use that relationship to calculate the pH of a solution of a base.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h4>Sample Problem: The pH of a Base<\/h4>\r\n<p id=\"x-ck12-ZjllMTJlYmVkYzI2MjczNDU0YmFlNjI0MmJhMmM5ZTk.-5ud\">Sodium hydroxide is a strong base. Find the pH of a solution prepared by dissolving 1.0 g of NaOH into enough water to make 1.0 L of solution.<\/p>\r\n<p id=\"x-ck12-OGM1ZTljNzdiMjc4MjQyMjY3OTljNDI4OTk2ZmY0MTE.-icw\"><em> Step 1: List the known values and plan the problem <\/em> .<\/p>\r\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-8ki\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-ZWE3ODc0NDU3MTg0NmQ3NWUwMTY2ZjVjZTAwZjM3MWI.-ayq\">\r\n \t<li>mass NaOH = 1.0 g<\/li>\r\n \t<li>molar mass NaOH = 40.00 g\/mol<\/li>\r\n \t<li>volume solution = 1.0 L<\/li>\r\n \t<li><em>K<sub>w<\/sub><\/em> = 1.0\u00a0\u00d7 10<sup>\u201314<\/sup><\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-h4d\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-YmEzMGRhNjg2OGQ5ZTRkZTY5ZjkzM2NiYjIyNWE2ODI.-mv4\">\r\n \t<li>pH of solution = ?<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-MzI5MzU5NzEzM2IzNWY2N2MyNmY5MDZlMWMwNjQ4ODk.-580\">First, convert the mass of NaOH to moles. Second, calculate the molarity of the NaOH solution. Because NaOH is a strong base and is soluble, the [OH <sup> \u2212 <\/sup> ] will be equal to the concentration of the NaOH. Third, use\u00a0 <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213240\/20ad2eefd31aa21b83daf6314f529858.png\" alt=\"K_w\" width=\"24\" height=\"15\" \/> to calculate the [H <sup> + <\/sup> ] in the solution. Lastly, calculate the pH.<\/p>\r\n<p id=\"x-ck12-ZmYxNjkxNzA3ODcxNDhkYjhmZGUyOTFlNDk1NmEzZjE.-2wm\"><em> Step 2: Solve <\/em> .<\/p>\r\n<p id=\"x-ck12-n4d\"><img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213253\/6d7f87139d79ba4932134d60d7de7d7f.png\" alt=\"&amp; 1.00 {cancel{text{g NaOH}}} times frac{1 text{mol NaOH}}{40.00 {cancel{text{g NaOH}}}}=0.025 text{mol NaOH} \\&amp; text{Molarity}=frac{0.025 text{mol NaOH}}{1.00 text{L}}=0.025 text{M NaOH}=0.025 text{M OH}^- \\&amp; left [ text{H}^+ right ]=frac{K_w}{left [ text{OH}^- right ]}=frac{1.0 times 10^{-14}}{0.025 text{M}}=4.0 times 10^{-13} text{M} \\&amp; text{pH}=- log left [ text{H}^+ right ]=- log(4.0 times 10^{-13})=12.40\" width=\"498\" height=\"166\" \/><\/p>\r\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-pqi\"><em> Step 3: Think about your result <\/em> .<\/p>\r\n<p id=\"x-ck12-M2Q1YTAyNWIzMGY0NWNiMDE2OWJhNDAzZGVkMTFjYWM.-1ml\">The solution is basic and so its pH is greater than 7. The reported pH is rounded to two decimal places because the original mass and volume has two significant figures.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-ZjYwOGFmMGEwODdjYjViMmFiYTIyNTVjNmMwMTY3M2E.-9o7\">\r\n \t<li>The concept of pH is defined.<\/li>\r\n \t<li>pH values for several common materials are listed.<\/li>\r\n \t<li>Calculations of pH for acidic and basic solutions are described.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-ZDA1NTE4MmE3ZWNhMTc1ZjZmZjlhNTc2YTQzZWI5ZTg.-ozt\">Read the material at the link below and answer the following questions:<\/p>\r\n<p id=\"x-ck12-NmEyZDc5N2IwZWYwZGFmODNkNjEzNWY2Zjk2N2M5Yzk.-h1w\"><a href=\"https:\/\/web.archive.org\/web\/20081223062050\/http:\/\/staff.jccc.net\/pdecell\/chemistry\/phscale.html\" target=\"_blank\" rel=\"noopener\">pH scale<\/a><\/p>\r\n\r\n<ol id=\"x-ck12-MmIzZWEwNDE4Mjg5MzU2MGVmZjdiMjBlYmEwYmYxN2I.-oot\">\r\n \t<li>What is a buffer?<\/li>\r\n \t<li>How much more acidic is vinegar than grapefruit?<\/li>\r\n \t<li>How much more basic is soapy water than milk of magnesia?<\/li>\r\n<\/ol>\r\n<p id=\"x-ck12-ODZhMGMwYjczZWY5YWJjYWEzMDkxMDU1NmM3M2RiNTc.-qx6\">Carry out the requested calculations at the link below:<\/p>\r\n<p id=\"x-ck12-YmIyYjJlZTcxOTE2ZjNjNTAyYjJhOTM4NWI1NjlmZmI.-wix\"><a href=\"http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/pHcalculations.htm\"> http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/pHcalculations.htm<\/a><\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<ol id=\"x-ck12-ZDEwOGFlMTRlYjIxYTZjODY4NmQ3MTllZThkZGQwOGE.-adp\">\r\n \t<li>What is one value of using pH instead of molar concentrations?<\/li>\r\n \t<li>Is coffee an acidic or a basic substance?<\/li>\r\n \t<li>If a material has a pH of 9.3, is it acidic or basic?<\/li>\r\n \t<li>What is the pH of a 4.5 \u00d7 10 <sup> -3 <\/sup> M HI solution?<\/li>\r\n \t<li>What is the pH of a 3.67 \u00d7 10 <sup> -5 <\/sup> M NaBr solution?<\/li>\r\n \t<li>If we have a weak base with a low ionization constant, can we assume that the [OH <sup> - <\/sup> ] in the solution is equal to the concentration of the base?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<h3 class=\"x-ck12-data-problem-set\">Glossary<\/h3>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-MDYxZmRmOGUyNWUxZjVkYTMxOWJiZjJmMzI5MGE0MjE.-vne\">\r\n \t<li><strong> pH: <\/strong> The negative logarithm of the hydrogen-ion concentration.<\/li>\r\n<\/ul>\r\n[reveal-answer q=\"836080\"]Show References[\/reveal-answer]\r\n[hidden-answer a=\"836080\"]\r\n<h2>References<\/h2>\r\n<ol>\r\n \t<li>Courtesy of Renee Comet, National Cancer Institute.<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Grapefruit_%281%29.jpg\">https:\/\/commons.wikimedia.org\/wiki\/File:Grapefruit_%281%29.jpg <\/a>.<\/li>\r\n \t<li>CK-12 Foundation - Hana Zavadska and Zachary Wilson. .<\/li>\r\n \t<li>Adrian Pingstone. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Clown.fish.arp.750pix.jpg\">http:\/\/commons.wikimedia.org\/wiki\/File:Clown.fish.arp.750pix.jpg <\/a>.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define pH.<\/li>\n<li>List pH values of common materials.<\/li>\n<li>Perform pH calculations for acidic and basic solutions.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox examples\">\n<h3><strong>Why is grapefruit juice acidic? <\/strong><\/h3>\n<p id=\"x-ck12-YWIyOTE3MzkwNmVhYmQ3NjlkYjk1NzJhNTA3OWZjNWU.-rz2\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213248\/20140811155915053266.jpeg\" alt=\"Grapefruit juice is quite acidic\" width=\"263\" height=\"175\" \/>Grapefruit juice has a pH of somewhere between 2.9-3.3, depending on the specific product. Excessive exposure to this juice can cause erosion of tooth enamel and can lead to tooth damage. The acids in grapefruit juice are carbon-based, with citric acid being one of the major constituents.<\/p>\n<p>This compound has three ionizable hydrogens on each molecule which contribute to the relatively low pH of the juice. Another component of grape juice is malic acid, containing two ionizable hydrogens per molecule.<\/p>\n<\/div>\n<h2>The pH Scale<\/h2>\n<p id=\"x-ck12-YjAwZDcwNzMxNTgwZjQ0NDM5MDNlNjE1YjM4OWIxNGE.-vh5\">Expressing the acidity of a solution by using the molarity of the hydrogen ion is cumbersome because the quantities are generally very small. Danish scientist S\u00f8ren S\u00f8renson (1868-1939) proposed an easier system for indicating the concentration of H <sup> + <\/sup> called the pH scale. The letters pH stand for the power of the hydrogen ion. The <strong> pH <\/strong> of a solution is the negative logarithm of the hydrogen-ion concentration.<\/p>\n<p id=\"x-ck12-Y2IzZTJiOTk1Y2ZkMWYyNmU3MzQxMWI4MmI5ZWZlNjg.-cur\">pH = -log[H <sup> + <\/sup> ]<\/p>\n<p id=\"x-ck12-OGFiMDc5NGRiZTlmMmY1YzUzMTZmYzhjZTE4ZmQzYjE.-d1m\">In pure water or a neutral solution the [H <sup> + <\/sup> ]\u00a0=\u00a01.0\u00a0\u00d7\u00a010 <sup> -7 <\/sup> \u00a0M. Substituting into the pH expression:<\/p>\n<p id=\"x-ck12-4aq\">pH = -log[1.0 \u00d7 10 <sup> -7 <\/sup> ] = -(-7.00) = 7.00<\/p>\n<p id=\"x-ck12-YjhlZjlkMWViNWUyMTNkMmNmNGUxOGM2YTQwMThjMzA.-a6b\">The pH of pure water or any neutral solution is thus 7.00. For recording purposes, the numbers to the right of the decimal point in the pH value are the significant figures. Since\u00a01.0\u00a0\u00d7\u00a010 <sup> -7 <\/sup> has two significant figures, the pH can be reported as 7.00.<\/p>\n<p id=\"x-ck12-MWFiYjIzOGViYmQzNzE2M2E4OTA2YTUwNzQ0MGY0NWY.-n1t\">A logarithmic scale condenses the range of acidity to numbers that are easy to use. Consider a solution with [H <sup> + <\/sup> ]\u00a0=\u00a01.0\u00a0\u00d7\u00a010 <sup> -4 <\/sup> \u00a0M. That is a hydrogen-ion concentration that is 1000 times higher than the concentration in pure water. The pH of such a solution is 4.00, a difference of just 3 pH units. Notice that when the [H <sup> + <\/sup> ] is written in scientific notation and the coefficient is 1, the pH is simply the exponent with the sign changed. The pH of a solution with the [H <sup> + <\/sup> ]\u00a0=\u00a01\u00a0\u00d7\u00a010 <sup> -2 <\/sup> \u00a0M is 2 and the pH of a solution with the\u00a0[H <sup> + <\/sup> ]\u00a0=\u00a01\u00a0\u00d7\u00a010 <sup> -10 <\/sup> \u00a0M is 10.<\/p>\n<p id=\"x-ck12-N2M0YTRlNWMyN2Y0YTY1NTg2ZGE5MmZlNmJlOTBkMWM.-ed1\">As we saw earlier, a solution with the [H <sup> + <\/sup> ] higher than\u00a01.0 \u00d7 10 <sup> -7 <\/sup> is acidic, while a solution with the [H <sup> + <\/sup> ] lower than\u00a01.0 \u00d7 10 <sup> -7 <\/sup> is basic. Consequently, solutions whose pH is less than 7 are acidic, while those with a pH higher than 7 are basic. <strong>Figure 1\u00a0<\/strong>illustrates this relationship, along with some examples of various solutions.<\/p>\n<div id=\"x-ck12-MmU1ZDQzMmY5ZTk0ZGIyMWIxYmMwNjhiMzNmMzA4ZmM.-wm8\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\n<div style=\"width: 413px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2NDk3NTgwOS05LTY4LTUuNS41LjEwLjI.\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213250\/20140811155915175893.png\" alt=\"pH values of several common materials\" width=\"403\" height=\"500\" longdesc=\"The%20pH%20values%20for%20several%20common%20materials.\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 1.\u00a0The pH values for several common materials.<\/p>\n<\/div>\n<\/div>\n<h2>Calculating pH of Acids and Bases<\/h2>\n<div class=\"x-ck12-data-vocabulary\">\n<div class=\"textbox examples\">\n<h3>Raising tropical fish<\/h3>\n<p id=\"x-ck12-YmMyOGE5YTQwYzhjMTE4OWQxMWFhMzAwZjZiNGMwMWI.-gjg\"><span class=\"x-ck12-img-inline\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213251\/20140811155915280955.jpeg\" alt=\"It is important that the pH in a fish bowl remains in a certain range\" width=\"248\" height=\"177\" \/><\/span><\/p>\n<p id=\"x-ck12-ZmFkMzQyZjk1ODA3OWY2Y2VlOGI3ZGQ2OTBmYjgxODQ.-9gn\">Many people enjoy having tropical fish in their homes or businesses. These brightly-colored creatures are relaxing to watch, but do require a certain amount of maintenance in order for them to survive.<\/p>\n<p>Tap water is usually too alkaline when it comes out of the faucet, so some adjustments need to be made. The pH of the water will change over time while it is in the tank, which means you need to test it every so often. Then you get to be a chemist for your fish.<\/p>\n<\/div>\n<h3>Calculating pH of Acids and Bases<\/h3>\n<p id=\"x-ck12-ZDYyZjgwZDc4ZjdkMmM5OThlNDFkMDZiYjFlM2MxZDg.-8aw\">Calculation of pH is simple when there is a 1\u00a0\u00d7\u00a010 <sup> power <\/sup> problem. However, in real life that is rarely the situation. If the coefficient is not equal to 1, a calculator must be used to find the pH. For example, the pH of a solution with [H <sup> + <\/sup> ]\u00a0=\u00a02.3\u00a0\u00d7\u00a010 <sup> -5 <\/sup> \u00a0M\u00a0 can be found as shown below.<\/p>\n<p id=\"x-ck12-nhb\">pH = -log[2.3 \u00d7\u00a010 <sup> -5 <\/sup> ] = 4.64<\/p>\n<p id=\"x-ck12-ZTI2MmU2Nzg0N2MxMTI3ZDhiNjljNmE4YmFkODQ1MDA.-2b9\">When the pH of a solution is known, the concentration of the hydrogen ion can be calculated. The inverse of the logarithm (or antilog) is the 10 <em> <sup> x <\/sup><\/em> key on a calculator.<\/p>\n<p id=\"x-ck12-c21\">[H <sup> + <\/sup> ] = 10 <sup> -pH <\/sup><\/p>\n<p id=\"x-ck12-OTBmMjRiNjk0NzVkOGFhNzk4Yjc2NzNhNmRhMjUzY2E.-ex3\">For example, suppose that you have a solution with a pH of 9.14. To find the [H <sup> + <\/sup> ] use the 10 <em> <sup> x <\/sup><\/em> key.<\/p>\n<p id=\"x-ck12-vsd\">[H <sup> + <\/sup> ] = 10 <sup> -pH <\/sup> = 10 <sup> -9.14 <\/sup> = 7.24 \u00d7 10 <sup> -10 <\/sup> M<\/p>\n<h4>Hydroxide Ion Concentration and pH<\/h4>\n<p id=\"x-ck12-MTZlMWJkMzkyMjliZGI2ZGUwYjY1MzRmNjczNWIyYWU.-hhd\">As we saw earlier, the hydroxide ion concentration of any aqueous solution is related to the hydrogen ion concentration through the value of <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213240\/20ad2eefd31aa21b83daf6314f529858.png\" alt=\"K_w\" width=\"24\" height=\"15\" \/> . We can use that relationship to calculate the pH of a solution of a base.<\/p>\n<div class=\"textbox shaded\">\n<h4>Sample Problem: The pH of a Base<\/h4>\n<p id=\"x-ck12-ZjllMTJlYmVkYzI2MjczNDU0YmFlNjI0MmJhMmM5ZTk.-5ud\">Sodium hydroxide is a strong base. Find the pH of a solution prepared by dissolving 1.0 g of NaOH into enough water to make 1.0 L of solution.<\/p>\n<p id=\"x-ck12-OGM1ZTljNzdiMjc4MjQyMjY3OTljNDI4OTk2ZmY0MTE.-icw\"><em> Step 1: List the known values and plan the problem <\/em> .<\/p>\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-8ki\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\n<ul id=\"x-ck12-ZWE3ODc0NDU3MTg0NmQ3NWUwMTY2ZjVjZTAwZjM3MWI.-ayq\">\n<li>mass NaOH = 1.0 g<\/li>\n<li>molar mass NaOH = 40.00 g\/mol<\/li>\n<li>volume solution = 1.0 L<\/li>\n<li><em>K<sub>w<\/sub><\/em> = 1.0\u00a0\u00d7 10<sup>\u201314<\/sup><\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-h4d\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-YmEzMGRhNjg2OGQ5ZTRkZTY5ZjkzM2NiYjIyNWE2ODI.-mv4\">\n<li>pH of solution = ?<\/li>\n<\/ul>\n<p id=\"x-ck12-MzI5MzU5NzEzM2IzNWY2N2MyNmY5MDZlMWMwNjQ4ODk.-580\">First, convert the mass of NaOH to moles. Second, calculate the molarity of the NaOH solution. Because NaOH is a strong base and is soluble, the [OH <sup> \u2212 <\/sup> ] will be equal to the concentration of the NaOH. Third, use\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213240\/20ad2eefd31aa21b83daf6314f529858.png\" alt=\"K_w\" width=\"24\" height=\"15\" \/> to calculate the [H <sup> + <\/sup> ] in the solution. Lastly, calculate the pH.<\/p>\n<p id=\"x-ck12-ZmYxNjkxNzA3ODcxNDhkYjhmZGUyOTFlNDk1NmEzZjE.-2wm\"><em> Step 2: Solve <\/em> .<\/p>\n<p id=\"x-ck12-n4d\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213253\/6d7f87139d79ba4932134d60d7de7d7f.png\" alt=\"&amp; 1.00 {cancel{text{g NaOH}}} times frac{1 text{mol NaOH}}{40.00 {cancel{text{g NaOH}}}}=0.025 text{mol NaOH} \\&amp; text{Molarity}=frac{0.025 text{mol NaOH}}{1.00 text{L}}=0.025 text{M NaOH}=0.025 text{M OH}^- \\&amp; left [ text{H}^+ right ]=frac{K_w}{left [ text{OH}^- right ]}=frac{1.0 times 10^{-14}}{0.025 text{M}}=4.0 times 10^{-13} text{M} \\&amp; text{pH}=- log left [ text{H}^+ right ]=- log(4.0 times 10^{-13})=12.40\" width=\"498\" height=\"166\" \/><\/p>\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-pqi\"><em> Step 3: Think about your result <\/em> .<\/p>\n<p id=\"x-ck12-M2Q1YTAyNWIzMGY0NWNiMDE2OWJhNDAzZGVkMTFjYWM.-1ml\">The solution is basic and so its pH is greater than 7. The reported pH is rounded to two decimal places because the original mass and volume has two significant figures.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-ZjYwOGFmMGEwODdjYjViMmFiYTIyNTVjNmMwMTY3M2E.-9o7\">\n<li>The concept of pH is defined.<\/li>\n<li>pH values for several common materials are listed.<\/li>\n<li>Calculations of pH for acidic and basic solutions are described.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-ZDA1NTE4MmE3ZWNhMTc1ZjZmZjlhNTc2YTQzZWI5ZTg.-ozt\">Read the material at the link below and answer the following questions:<\/p>\n<p id=\"x-ck12-NmEyZDc5N2IwZWYwZGFmODNkNjEzNWY2Zjk2N2M5Yzk.-h1w\"><a href=\"https:\/\/web.archive.org\/web\/20081223062050\/http:\/\/staff.jccc.net\/pdecell\/chemistry\/phscale.html\" target=\"_blank\" rel=\"noopener\">pH scale<\/a><\/p>\n<ol id=\"x-ck12-MmIzZWEwNDE4Mjg5MzU2MGVmZjdiMjBlYmEwYmYxN2I.-oot\">\n<li>What is a buffer?<\/li>\n<li>How much more acidic is vinegar than grapefruit?<\/li>\n<li>How much more basic is soapy water than milk of magnesia?<\/li>\n<\/ol>\n<p id=\"x-ck12-ODZhMGMwYjczZWY5YWJjYWEzMDkxMDU1NmM3M2RiNTc.-qx6\">Carry out the requested calculations at the link below:<\/p>\n<p id=\"x-ck12-YmIyYjJlZTcxOTE2ZjNjNTAyYjJhOTM4NWI1NjlmZmI.-wix\"><a href=\"http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/pHcalculations.htm\"> http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/pHcalculations.htm<\/a><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<ol id=\"x-ck12-ZDEwOGFlMTRlYjIxYTZjODY4NmQ3MTllZThkZGQwOGE.-adp\">\n<li>What is one value of using pH instead of molar concentrations?<\/li>\n<li>Is coffee an acidic or a basic substance?<\/li>\n<li>If a material has a pH of 9.3, is it acidic or basic?<\/li>\n<li>What is the pH of a 4.5 \u00d7 10 <sup> -3 <\/sup> M HI solution?<\/li>\n<li>What is the pH of a 3.67 \u00d7 10 <sup> -5 <\/sup> M NaBr solution?<\/li>\n<li>If we have a weak base with a low ionization constant, can we assume that the [OH <sup> &#8211; <\/sup> ] in the solution is equal to the concentration of the base?<\/li>\n<\/ol>\n<\/div>\n<h3 class=\"x-ck12-data-problem-set\">Glossary<\/h3>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-MDYxZmRmOGUyNWUxZjVkYTMxOWJiZjJmMzI5MGE0MjE.-vne\">\n<li><strong> pH: <\/strong> The negative logarithm of the hydrogen-ion concentration.<\/li>\n<\/ul>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q836080\">Show References<\/span><\/p>\n<div id=\"q836080\" class=\"hidden-answer\" style=\"display: none\">\n<h2>References<\/h2>\n<ol>\n<li>Courtesy of Renee Comet, National Cancer Institute.<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Grapefruit_%281%29.jpg\">https:\/\/commons.wikimedia.org\/wiki\/File:Grapefruit_%281%29.jpg <\/a>.<\/li>\n<li>CK-12 Foundation &#8211; Hana Zavadska and Zachary Wilson. .<\/li>\n<li>Adrian Pingstone. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Clown.fish.arp.750pix.jpg\">http:\/\/commons.wikimedia.org\/wiki\/File:Clown.fish.arp.750pix.jpg <\/a>.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\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-2818\">\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 Concepts Intermediate. <strong>Authored by<\/strong>: Calbreath, Baxter, et al.. <strong>Provided by<\/strong>: CK12.org. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\">http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/\">CC BY-NC: Attribution-NonCommercial<\/a><\/em><\/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":17,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry Concepts Intermediate\",\"author\":\"Calbreath, Baxter, et al.\",\"organization\":\"CK12.org\",\"url\":\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\",\"project\":\"\",\"license\":\"cc-by-nc\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2818","chapter","type-chapter","status-publish","hentry"],"part":2342,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2818","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/users\/17"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2818\/revisions"}],"predecessor-version":[{"id":3601,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2818\/revisions\/3601"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/parts\/2342"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2818\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/media?parent=2818"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapter-type?post=2818"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/contributor?post=2818"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/license?post=2818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}