{"id":2817,"date":"2016-08-24T19:14:40","date_gmt":"2016-08-24T19:14:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/?post_type=chapter&#038;p=2817"},"modified":"2016-08-24T22:06:44","modified_gmt":"2016-08-24T22:06:44","slug":"ion-product-of-water","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/chapter\/ion-product-of-water\/","title":{"raw":"Ion-Product of Water","rendered":"Ion-Product of Water"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define the ion-product constant of water.<\/li>\r\n \t<li>Define acidic solution.<\/li>\r\n \t<li>Define basic solution.<\/li>\r\n \t<li>Use the constant to calculate [H<sup>+<\/sup>] or [OH<sup>\u2212<\/sup>] when the other is known.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3><strong>What\u2019s inside? <\/strong><\/h3>\r\n<p id=\"x-ck12-ZDdjNTEyM2E2ZWY4N2I0ZTM3NTMyNWYxNjgzMDZkMjY.-cut\">At one time, you could take the little caps off the top of a car battery and check the condition of the sulfuric acid inside. If it got low, you could add more acid. But, sulfuric acid is hazardous stuff, so the batteries are now sealed to protect people. Because of the acid's dangerous nature, it is not a good idea to cut into a battery to see what it looks like\u2014you could get acid burns.<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213237\/20140811155914897937.jpeg\" alt=\"Car batteries contain sulfuric acid\" width=\"250\" \/>\r\n\r\n<\/div>\r\n<h2>The Ion-Product of Water<\/h2>\r\n<p id=\"x-ck12-YTJiYjgxZjZjZWI1M2RjZDEyMGEwMTJhYzlhODhhOTE.-lct\">The <strong> self-ionization of water <\/strong> (the process in which water ionizes to hydronium ions and hydroxide ions) occurs to a very limited extent. When two molecules of water collide, there can be a transfer of a hydrogen ion from one molecule to the other. The products are a positively charged hydronium ion and a negatively charged hydroxide ion.<\/p>\r\n<p id=\"x-ck12-zea\"><img id=\"x-ck12-MTM2Nzk5MzgxNjUyMw..\" 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\/19213238\/9901138b771c5c38414cf99bd2028cda.png\" alt=\"text{H}_2text{O}(l)+text{H}_2text{O}(l) rightleftarrows text{H}_3text{O}^+(aq)+text{OH}^-(aq)\" width=\"327\" height=\"21\" \/><\/p>\r\n<p id=\"x-ck12-NDQyNDRhN2Q0ZDdiZGIyZWJmZDQxYzMxZTg0OTBhZTk.-xfb\">We often use the simplified form of the reaction:<\/p>\r\n<p id=\"x-ck12-ozc\"><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\/19213239\/b33f97ac1855ec1bbbf8fe0506604809.png\" alt=\"text{H}_2text{O}(l) rightleftarrows text{H}^+(aq)+text{OH}^-(aq)\" width=\"230\" height=\"21\" \/><\/p>\r\n<p id=\"x-ck12-OWY3YTRmODFkMmNlY2RkN2IzMzY0ZGEwYmE5N2U1MTA.-cfv\">The equilibrium constant for the self-ionization of water is referred to as the ion-product for water and is given the symbol <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\" \/> .<\/p>\r\n<p id=\"x-ck12-s92\"><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\/19213241\/5e7004e3b607ffef8435a4047261a4fd.png\" alt=\"K_w = [ text{H}^+ ][ text{OH}^- ]\" width=\"130\" height=\"22\" \/><\/p>\r\n<p id=\"x-ck12-NzAzYTM0YzQ5YTMxZjIxODBkM2YwNmE1NTM0NTkzNjI.-tyd\">The <strong> ion-product of water\u00a0 <img id=\"x-ck12-MTM2Nzk5MzgxNjUyNA..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213241\/d09a3a698f1b8a06813c90b84190ab72.png\" alt=\"(K_w)\" width=\"38\" height=\"18\" \/><\/strong> is the mathematical product of the concentration of hydrogen ions and hydroxide ions. Note that H <sub> 2 <\/sub> O is not included in the ion-product expression because it is a pure liquid. The value of\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\" \/> is very small, in accordance with a reaction that favors the reactants. At 25\u00b0C, the experimentally determined value of\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\" \/> in pure water is 1.0\u00a0\u00d7\u00a010 <sup> -14 <\/sup> .<\/p>\r\n<p id=\"x-ck12-ing\"><img id=\"x-ck12-MTM2Nzk5MzgxNjUyNQ..\" 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\/19213242\/af2a840b3d4700a674dd9219c6f500a1.png\" alt=\"K_w=[text{H}^+][text{OH}^-]=1.0 times 10^{-14}\" width=\"242\" height=\"22\" \/><\/p>\r\n<p id=\"x-ck12-ZTI2N2VhZTQxODk2MWVjYTZhNzI3MzVjMmRmMjliNzA.-mrc\">In pure water, the concentrations of hydrogen and hydroxide ions are equal to one another. Pure water or any other aqueous solution in which this ratio holds is said to be neutral. To find the molarity of each ion, the square root of\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\" \/> is taken.<\/p>\r\n<p id=\"x-ck12-woc\"><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\/19213242\/9c0eead67e5c0422e3732c584a23846e.png\" alt=\"[text{H}^+]=[text{OH}^-]=1.0 times 10^{-7} text{M}\" width=\"230\" height=\"22\" \/><\/p>\r\n<p id=\"x-ck12-MjY1OWFkOTZiNjgyNzc2OWE1ZmE0MzZiNmU4ZDU2YWQ.-zfo\">An <strong> acidic solution <\/strong> is a solution in which the concentration of hydrogen ions is greater than the concentration of hydroxide ions. For example, hydrogen chloride ionizes to produce H <sup> + <\/sup> and Cl <sup> \u2212 <\/sup> ions upon dissolving in water.<\/p>\r\n<p id=\"x-ck12-dlb\"><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\/19213243\/44b52a87038360ee981aeeb8a3a5afd6.png\" alt=\"text{HCl}(g) rightarrow text{H}^+(aq) + text{Cl}^-(aq)\" width=\"221\" height=\"21\" \/><\/p>\r\n<p id=\"x-ck12-NDIwY2NjMDA2YjgzMDY5NGM5MDYyMWQzMmM2N2IxMTU.-zxn\">This increases the concentration of H <sup> + <\/sup> ions in the solution. According to LeCh\u00e2telier\u2019s principle, the equilibrium represented by <img id=\"x-ck12-MTM2Nzk5MzgxNjUyNg..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213244\/f3f2415c0baba65300526ac3e24c8400.png\" alt=\"text{H}_2text{O}(l) rightleftarrows text{H}^+(aq)+text{OH}^-(aq)\" width=\"230\" height=\"20\" \/> is forced to the left, towards the reactant. As a result, the concentration of the hydroxide ion decreases.<\/p>\r\n<p id=\"x-ck12-Nzk2OWEzOWEyYjk0ODE4YTE3YmFhYWVlYjY1ZTFkOTY.-uz7\">A <strong> basic solution <\/strong> is a solution in which the concentration of hydroxide ions is greater than the concentration of hydrogen ions. Solid potassium hydroxide dissociates in water to yield potassium ions and hydroxide ions.<\/p>\r\n<p id=\"x-ck12-py3\"><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\/19213245\/682c6bdb0b1f8b4476937483764c30f6.png\" alt=\"text{KOH}(s) rightarrow text{K}^+(aq)+text{OH}^-(aq)\" width=\"239\" height=\"21\" \/><\/p>\r\n<p id=\"x-ck12-OGI3MTVmZTVlODZmMDc5OWQ3OGIxZjM4N2UyNWQ2OGM.-b7p\">The increase in concentration of the OH <sup> \u2212 <\/sup> ions causes a decrease in the concentration of the H <sup> + <\/sup> ions and the ion-product of [H <sup> + <\/sup> ][OH <sup> \u2212 <\/sup> ] remains constant<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h4>Sample Problem: Use of\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\" \/> for an Aqueous Solution<\/h4>\r\n<p id=\"x-ck12-ZGE1YTk2NzMyYzM3MzBjYjFlY2RhMmFmMjlhN2E3MjE.-wui\">Hydrochloric acid (HCl) is a strong acid, meaning it is 100% ionized in solution. What is the [H <sup> + <\/sup> ] and the [OH <sup> \u2212 <\/sup> ] in a solution of 2.0\u00a0\u00d7\u00a010 <sup> 3 <\/sup> \u00a0M HCl?<\/p>\r\n<p id=\"x-ck12-OGM1ZTljNzdiMjc4MjQyMjY3OTljNDI4OTk2ZmY0MTE.-rz2\"><em> Step 1: List the known values and plan the problem <\/em> .<\/p>\r\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-mbp\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-MDk0ODJmNDU3MzY1MWVlYjRjNjMxNDA4YmY0MGExM2M.-tuo\">\r\n \t<li>[HCl] = 2.0 \u00d7 10 <sup> -3 <\/sup> M<\/li>\r\n \t<li><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\/19213246\/62839984fce04976b993ed4609bfc6c6.png\" alt=\"K_w=1.0 times 10^{-14}\" width=\"136\" height=\"18\" \/><\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-xmu\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-NjI0ODExYzQ0ZTBlOTc4NDQ0ODg5MzY1ZDYzMDczNTU.-na2\">\r\n \t<li>[H <sup> + <\/sup> ] = ? M<\/li>\r\n \t<li>[OH <sup> - <\/sup> ] = ? M<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-NDIzY2QzNTQ0MWMzOWEzZDM5YjhjOTU3YzZlOGFmNTA.-pic\">Because HCl is 100% ionized, the concentration of H <sup> + <\/sup> ions in solution will be equal to the original concentration of HCl. Each HCl molecule that was originally present ionizes into one H <sup> + <\/sup> ion and one Cl <sup> \u2212 <\/sup> ion. The concentration of OH <sup> \u2212 <\/sup> can then be determined from the [H <sup> + <\/sup> ] and <img id=\"x-ck12-MTM2Nzk5MzgxNjUyNw..\" 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\" \/> .<\/p>\r\n<p id=\"x-ck12-ZmYxNjkxNzA3ODcxNDhkYjhmZGUyOTFlNDk1NmEzZjE.-b7k\"><em> Step 2: Solve <\/em> .<\/p>\r\n<p id=\"x-ck12-kjs\"><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\/19213246\/219a3d7213f601047b9b93ab8dfc8281.png\" alt=\"left [ text{H}^+ right ]&amp;=2.0 times 10^{-3} text{M} \\K_w &amp;=left [ text{H}^+ right ] left [ text{OH}^- right ]=1.0 times 10^{-14} \\left [ text{OH}^- right ] &amp;=frac{K_w}{left [ text{H}^+ right ]}=frac{1.0 times 10^{-14}}{2.0 times 10^{-3}}=5.0 times 10^{-12} text{M}\" width=\"365\" height=\"104\" \/><\/p>\r\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-09j\"><em> Step 3: Think about your result<\/em>.<\/p>\r\n<p id=\"x-ck12-YTkzOTgzM2Y1YjZjNmI2MjdiNjVkOGZhYWNkMGNjMmY.-b3w\">The [H <sup> + <\/sup> ] is much higher than the [OH <sup> \u2212 <\/sup> ] because the solution is acidic. As with other equilibrium constants, the unit for\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\" \/> is customarily omitted.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-YzQyN2UwNzhlNThjNWE3ZjIyNzg4N2ZiNGJjNTdiNWY.-q0y\">\r\n \t<li>The self-ionization of water is described and an ionization constant for the process is stated.<\/li>\r\n \t<li>Acidic and basic solutions are defined.<\/li>\r\n \t<li>Calculations using\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\" \/> are illustrated.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-NWQ2ZjQwOTNmM2NhZWEyZmE1Mzc1MmQyODMzYWI1Y2Y.-c0l\">Read the first two pages of <a href=\"http:\/\/www.vigoschools.org\/~mmc3\/Chem%201\/Lecture%20Notes\/L2%20-%20Hydrogen%20Ions%20and%20pH%20-%2015.1.pdf\" target=\"_blank\">this handout on Water Ionization<\/a>\u00a0and do those practice problems.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<ol id=\"x-ck12-Mjg5MTVjODczMDdmNzhjYTNkNzU1MjVjYjQyMTU4MWI.-esq\">\r\n \t<li>What is an acidic solution?<\/li>\r\n \t<li>What is a basic solution?<\/li>\r\n \t<li>What is the [OH <sup> - <\/sup> ] of a solution which has a [H <sup> + <\/sup> ] 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\/19213248\/76ce092504ce2d0fa03a14cdd938e5e7.png\" alt=\"1 times 10^{-5} M\" width=\"91\" height=\"16\" \/> ?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<h2 class=\"x-ck12-data-problem-set\">Glossary<\/h2>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-OTY4OWJjODNhN2RiNTQ3MjcwYjU3ZGIzNzhlMWQ2ZTk.-98y\">\r\n \t<li><strong> acidic solution: <\/strong> A solution in which the concentration of hydrogen ions is greater than the concentration of hydroxide ions.<\/li>\r\n \t<li><strong> basic solution: <\/strong> A solution in which the concentration of hydroxide ions is greater than the concentration of hydrogen ions.<\/li>\r\n \t<li><strong> ion-product of water <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\/19213241\/d09a3a698f1b8a06813c90b84190ab72.png\" alt=\"(K_w)\" width=\"38\" height=\"18\" \/> : <\/strong> The mathematical product of the concentration of hydrogen ions and hydroxide ions.<\/li>\r\n \t<li><strong> self-ionization of water: <\/strong> The process in which water ionizes to hydronium ions and hydroxide ions.<\/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>User:Shaddack\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Photo-CarBattery.jpg\">http:\/\/commons.wikimedia.org\/wiki\/File:Photo-CarBattery.jpg <\/a>.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define the ion-product constant of water.<\/li>\n<li>Define acidic solution.<\/li>\n<li>Define basic solution.<\/li>\n<li>Use the constant to calculate [H<sup>+<\/sup>] or [OH<sup>\u2212<\/sup>] when the other is known.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox examples\">\n<h3><strong>What\u2019s inside? <\/strong><\/h3>\n<p id=\"x-ck12-ZDdjNTEyM2E2ZWY4N2I0ZTM3NTMyNWYxNjgzMDZkMjY.-cut\">At one time, you could take the little caps off the top of a car battery and check the condition of the sulfuric acid inside. If it got low, you could add more acid. But, sulfuric acid is hazardous stuff, so the batteries are now sealed to protect people. Because of the acid&#8217;s dangerous nature, it is not a good idea to cut into a battery to see what it looks like\u2014you could get acid burns.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213237\/20140811155914897937.jpeg\" alt=\"Car batteries contain sulfuric acid\" width=\"250\" \/><\/p>\n<\/div>\n<h2>The Ion-Product of Water<\/h2>\n<p id=\"x-ck12-YTJiYjgxZjZjZWI1M2RjZDEyMGEwMTJhYzlhODhhOTE.-lct\">The <strong> self-ionization of water <\/strong> (the process in which water ionizes to hydronium ions and hydroxide ions) occurs to a very limited extent. When two molecules of water collide, there can be a transfer of a hydrogen ion from one molecule to the other. The products are a positively charged hydronium ion and a negatively charged hydroxide ion.<\/p>\n<p id=\"x-ck12-zea\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM2Nzk5MzgxNjUyMw..\" 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\/19213238\/9901138b771c5c38414cf99bd2028cda.png\" alt=\"text{H}_2text{O}(l)+text{H}_2text{O}(l) rightleftarrows text{H}_3text{O}^+(aq)+text{OH}^-(aq)\" width=\"327\" height=\"21\" \/><\/p>\n<p id=\"x-ck12-NDQyNDRhN2Q0ZDdiZGIyZWJmZDQxYzMxZTg0OTBhZTk.-xfb\">We often use the simplified form of the reaction:<\/p>\n<p id=\"x-ck12-ozc\"><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\/19213239\/b33f97ac1855ec1bbbf8fe0506604809.png\" alt=\"text{H}_2text{O}(l) rightleftarrows text{H}^+(aq)+text{OH}^-(aq)\" width=\"230\" height=\"21\" \/><\/p>\n<p id=\"x-ck12-OWY3YTRmODFkMmNlY2RkN2IzMzY0ZGEwYmE5N2U1MTA.-cfv\">The equilibrium constant for the self-ionization of water is referred to as the ion-product for water and is given the symbol <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\" \/> .<\/p>\n<p id=\"x-ck12-s92\"><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\/19213241\/5e7004e3b607ffef8435a4047261a4fd.png\" alt=\"K_w = [ text{H}^+ ][ text{OH}^- ]\" width=\"130\" height=\"22\" \/><\/p>\n<p id=\"x-ck12-NzAzYTM0YzQ5YTMxZjIxODBkM2YwNmE1NTM0NTkzNjI.-tyd\">The <strong> ion-product of water\u00a0 <img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM2Nzk5MzgxNjUyNA..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213241\/d09a3a698f1b8a06813c90b84190ab72.png\" alt=\"(K_w)\" width=\"38\" height=\"18\" \/><\/strong> is the mathematical product of the concentration of hydrogen ions and hydroxide ions. Note that H <sub> 2 <\/sub> O is not included in the ion-product expression because it is a pure liquid. The value of\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\" \/> is very small, in accordance with a reaction that favors the reactants. At 25\u00b0C, the experimentally determined value of\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\" \/> in pure water is 1.0\u00a0\u00d7\u00a010 <sup> -14 <\/sup> .<\/p>\n<p id=\"x-ck12-ing\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM2Nzk5MzgxNjUyNQ..\" 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\/19213242\/af2a840b3d4700a674dd9219c6f500a1.png\" alt=\"K_w=[text{H}^+][text{OH}^-]=1.0 times 10^{-14}\" width=\"242\" height=\"22\" \/><\/p>\n<p id=\"x-ck12-ZTI2N2VhZTQxODk2MWVjYTZhNzI3MzVjMmRmMjliNzA.-mrc\">In pure water, the concentrations of hydrogen and hydroxide ions are equal to one another. Pure water or any other aqueous solution in which this ratio holds is said to be neutral. To find the molarity of each ion, the square root of\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\" \/> is taken.<\/p>\n<p id=\"x-ck12-woc\"><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\/19213242\/9c0eead67e5c0422e3732c584a23846e.png\" alt=\"[text{H}^+]=[text{OH}^-]=1.0 times 10^{-7} text{M}\" width=\"230\" height=\"22\" \/><\/p>\n<p id=\"x-ck12-MjY1OWFkOTZiNjgyNzc2OWE1ZmE0MzZiNmU4ZDU2YWQ.-zfo\">An <strong> acidic solution <\/strong> is a solution in which the concentration of hydrogen ions is greater than the concentration of hydroxide ions. For example, hydrogen chloride ionizes to produce H <sup> + <\/sup> and Cl <sup> \u2212 <\/sup> ions upon dissolving in water.<\/p>\n<p id=\"x-ck12-dlb\"><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\/19213243\/44b52a87038360ee981aeeb8a3a5afd6.png\" alt=\"text{HCl}(g) rightarrow text{H}^+(aq) + text{Cl}^-(aq)\" width=\"221\" height=\"21\" \/><\/p>\n<p id=\"x-ck12-NDIwY2NjMDA2YjgzMDY5NGM5MDYyMWQzMmM2N2IxMTU.-zxn\">This increases the concentration of H <sup> + <\/sup> ions in the solution. According to LeCh\u00e2telier\u2019s principle, the equilibrium represented by <img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM2Nzk5MzgxNjUyNg..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19213244\/f3f2415c0baba65300526ac3e24c8400.png\" alt=\"text{H}_2text{O}(l) rightleftarrows text{H}^+(aq)+text{OH}^-(aq)\" width=\"230\" height=\"20\" \/> is forced to the left, towards the reactant. As a result, the concentration of the hydroxide ion decreases.<\/p>\n<p id=\"x-ck12-Nzk2OWEzOWEyYjk0ODE4YTE3YmFhYWVlYjY1ZTFkOTY.-uz7\">A <strong> basic solution <\/strong> is a solution in which the concentration of hydroxide ions is greater than the concentration of hydrogen ions. Solid potassium hydroxide dissociates in water to yield potassium ions and hydroxide ions.<\/p>\n<p id=\"x-ck12-py3\"><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\/19213245\/682c6bdb0b1f8b4476937483764c30f6.png\" alt=\"text{KOH}(s) rightarrow text{K}^+(aq)+text{OH}^-(aq)\" width=\"239\" height=\"21\" \/><\/p>\n<p id=\"x-ck12-OGI3MTVmZTVlODZmMDc5OWQ3OGIxZjM4N2UyNWQ2OGM.-b7p\">The increase in concentration of the OH <sup> \u2212 <\/sup> ions causes a decrease in the concentration of the H <sup> + <\/sup> ions and the ion-product of [H <sup> + <\/sup> ][OH <sup> \u2212 <\/sup> ] remains constant<\/p>\n<div class=\"textbox shaded\">\n<h4>Sample Problem: Use of\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\" \/> for an Aqueous Solution<\/h4>\n<p id=\"x-ck12-ZGE1YTk2NzMyYzM3MzBjYjFlY2RhMmFmMjlhN2E3MjE.-wui\">Hydrochloric acid (HCl) is a strong acid, meaning it is 100% ionized in solution. What is the [H <sup> + <\/sup> ] and the [OH <sup> \u2212 <\/sup> ] in a solution of 2.0\u00a0\u00d7\u00a010 <sup> 3 <\/sup> \u00a0M HCl?<\/p>\n<p id=\"x-ck12-OGM1ZTljNzdiMjc4MjQyMjY3OTljNDI4OTk2ZmY0MTE.-rz2\"><em> Step 1: List the known values and plan the problem <\/em> .<\/p>\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-mbp\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\n<ul id=\"x-ck12-MDk0ODJmNDU3MzY1MWVlYjRjNjMxNDA4YmY0MGExM2M.-tuo\">\n<li>[HCl] = 2.0 \u00d7 10 <sup> -3 <\/sup> M<\/li>\n<li><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\/19213246\/62839984fce04976b993ed4609bfc6c6.png\" alt=\"K_w=1.0 times 10^{-14}\" width=\"136\" height=\"18\" \/><\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-xmu\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-NjI0ODExYzQ0ZTBlOTc4NDQ0ODg5MzY1ZDYzMDczNTU.-na2\">\n<li>[H <sup> + <\/sup> ] = ? M<\/li>\n<li>[OH <sup> &#8211; <\/sup> ] = ? M<\/li>\n<\/ul>\n<p id=\"x-ck12-NDIzY2QzNTQ0MWMzOWEzZDM5YjhjOTU3YzZlOGFmNTA.-pic\">Because HCl is 100% ionized, the concentration of H <sup> + <\/sup> ions in solution will be equal to the original concentration of HCl. Each HCl molecule that was originally present ionizes into one H <sup> + <\/sup> ion and one Cl <sup> \u2212 <\/sup> ion. The concentration of OH <sup> \u2212 <\/sup> can then be determined from the [H <sup> + <\/sup> ] and <img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM2Nzk5MzgxNjUyNw..\" 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\" \/> .<\/p>\n<p id=\"x-ck12-ZmYxNjkxNzA3ODcxNDhkYjhmZGUyOTFlNDk1NmEzZjE.-b7k\"><em> Step 2: Solve <\/em> .<\/p>\n<p id=\"x-ck12-kjs\"><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\/19213246\/219a3d7213f601047b9b93ab8dfc8281.png\" alt=\"left [ text{H}^+ right ]&amp;=2.0 times 10^{-3} text{M} \\K_w &amp;=left [ text{H}^+ right ] left [ text{OH}^- right ]=1.0 times 10^{-14} \\left [ text{OH}^- right ] &amp;=frac{K_w}{left [ text{H}^+ right ]}=frac{1.0 times 10^{-14}}{2.0 times 10^{-3}}=5.0 times 10^{-12} text{M}\" width=\"365\" height=\"104\" \/><\/p>\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-09j\"><em> Step 3: Think about your result<\/em>.<\/p>\n<p id=\"x-ck12-YTkzOTgzM2Y1YjZjNmI2MjdiNjVkOGZhYWNkMGNjMmY.-b3w\">The [H <sup> + <\/sup> ] is much higher than the [OH <sup> \u2212 <\/sup> ] because the solution is acidic. As with other equilibrium constants, the unit for\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\" \/> is customarily omitted.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-YzQyN2UwNzhlNThjNWE3ZjIyNzg4N2ZiNGJjNTdiNWY.-q0y\">\n<li>The self-ionization of water is described and an ionization constant for the process is stated.<\/li>\n<li>Acidic and basic solutions are defined.<\/li>\n<li>Calculations using\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\" \/> are illustrated.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-NWQ2ZjQwOTNmM2NhZWEyZmE1Mzc1MmQyODMzYWI1Y2Y.-c0l\">Read the first two pages of <a href=\"http:\/\/www.vigoschools.org\/~mmc3\/Chem%201\/Lecture%20Notes\/L2%20-%20Hydrogen%20Ions%20and%20pH%20-%2015.1.pdf\" target=\"_blank\">this handout on Water Ionization<\/a>\u00a0and do those practice problems.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<ol id=\"x-ck12-Mjg5MTVjODczMDdmNzhjYTNkNzU1MjVjYjQyMTU4MWI.-esq\">\n<li>What is an acidic solution?<\/li>\n<li>What is a basic solution?<\/li>\n<li>What is the [OH <sup> &#8211; <\/sup> ] of a solution which has a [H <sup> + <\/sup> ] 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\/19213248\/76ce092504ce2d0fa03a14cdd938e5e7.png\" alt=\"1 times 10^{-5} M\" width=\"91\" height=\"16\" \/> ?<\/li>\n<\/ol>\n<\/div>\n<h2 class=\"x-ck12-data-problem-set\">Glossary<\/h2>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-OTY4OWJjODNhN2RiNTQ3MjcwYjU3ZGIzNzhlMWQ2ZTk.-98y\">\n<li><strong> acidic solution: <\/strong> A solution in which the concentration of hydrogen ions is greater than the concentration of hydroxide ions.<\/li>\n<li><strong> basic solution: <\/strong> A solution in which the concentration of hydroxide ions is greater than the concentration of hydrogen ions.<\/li>\n<li><strong> ion-product of water <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\/19213241\/d09a3a698f1b8a06813c90b84190ab72.png\" alt=\"(K_w)\" width=\"38\" height=\"18\" \/> : <\/strong> The mathematical product of the concentration of hydrogen ions and hydroxide ions.<\/li>\n<li><strong> self-ionization of water: <\/strong> The process in which water ionizes to hydronium ions and hydroxide ions.<\/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>User:Shaddack\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Photo-CarBattery.jpg\">http:\/\/commons.wikimedia.org\/wiki\/File:Photo-CarBattery.jpg <\/a>.<\/li>\n<\/ol>\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-2817\">\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":5,"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-2817","chapter","type-chapter","status-publish","hentry"],"part":2342,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2817","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":3,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2817\/revisions"}],"predecessor-version":[{"id":3033,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2817\/revisions\/3033"}],"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\/2817\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/media?parent=2817"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapter-type?post=2817"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/contributor?post=2817"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/license?post=2817"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}