- \r\n \t
- Battery acid: 0.8<\/li>\r\n \t
- Stomach acid: 2.7<\/li>\r\n \t
- Orange juice: 3.3<\/li>\r\n \t
- Pure water: 7 (at 25\u00b0 C)<\/li>\r\n \t
- Human blood: 7.35<\/li>\r\n \t
- Fresh coconut: 7.8<\/li>\r\n \t
- Sodium hydroxide (lye): 14<\/li>\r\n<\/ul>\r\nTo determine whether a solution is acidic or alkaline, we find its pH which is a measure of the number of active positive hydrogen ions in the solution. The pH is defined by the following formula where [latex]a[\/latex]\u00a0is the concentration of hydrogen ion in the solution.\r\n
[latex]\\begin{array}{lll}\\text{pH} & = -\\mathrm{log}\\left(\\left[{H}^{+}\\right]\\right)\\hfill \\\\ \\text{} & =\\mathrm{log}\\left(\\frac{1}{\\left[{H}^{+}\\right]}\\right)\\hfill \\end{array}[\/latex]<\/p>\r\n[latex]-\\mathrm{log}\\left(\\left[{H}^{+}\\right]\\right)[\/latex]\u00a0is equal to\u00a0[latex]\\mathrm{log}\\left(\\frac{1}{\\left[{H}^{+}\\right]}\\right)[\/latex] due to\u00a0one of\u00a0the logarithm properties we will examine in this section.","rendered":"
![\"Testing](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/11\/03170558\/CNX_Precalc_Figure_04_05_001F2.jpg\")
<\/p>\nThe pH of hydrochloric acid is tested with litmus paper. (credit: David Berardan)<\/p>\n<\/div>\n
What you\u2019ll learn to do: Rewrite logarithmic expressions using a combination of logarithm rules and formulas<\/h2>\n
In chemistry, pH<\/strong> is used as a measure of the acidity or alkalinity of a substance. The pH scale runs from 0 to 14. Substances with a pH less than 7 are considered acidic and substances with a pH greater than 7 are said to be alkaline. Our bodies, for instance, must maintain a pH close to 7.35 in order for enzymes to work properly. To get a feel for what is acidic and what is alkaline, consider the following pH levels of some common substances:<\/p>\n
- \n
- Battery acid: 0.8<\/li>\n
- Stomach acid: 2.7<\/li>\n
- Orange juice: 3.3<\/li>\n
- Pure water: 7 (at 25\u00b0 C)<\/li>\n
- Human blood: 7.35<\/li>\n
- Fresh coconut: 7.8<\/li>\n
- Sodium hydroxide (lye): 14<\/li>\n<\/ul>\n
To determine whether a solution is acidic or alkaline, we find its pH which is a measure of the number of active positive hydrogen ions in the solution. The pH is defined by the following formula where [latex]a[\/latex]\u00a0is the concentration of hydrogen ion in the solution.<\/p>\n
[latex]\\begin{array}{lll}\\text{pH} & = -\\mathrm{log}\\left(\\left[{H}^{+}\\right]\\right)\\hfill \\\\ \\text{} & =\\mathrm{log}\\left(\\frac{1}{\\left[{H}^{+}\\right]}\\right)\\hfill \\end{array}[\/latex]<\/p>\n
[latex]-\\mathrm{log}\\left(\\left[{H}^{+}\\right]\\right)[\/latex]\u00a0is equal to\u00a0[latex]\\mathrm{log}\\left(\\frac{1}{\\left[{H}^{+}\\right]}\\right)[\/latex] due to\u00a0one of\u00a0the logarithm properties we will examine in this section.<\/p>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCC licensed content, Original<\/div>- Revision and Adaptation. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
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- College Algebra. Authored by<\/strong>: Abramson, Jay et al.. Provided by<\/strong>: OpenStax. Located at<\/strong>: http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em>. License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/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":395986,"menu_order":42,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\"}]","CANDELA_OUTCOMES_GUID":"a6718ccc-8694-4a98-8d1d-9b5a753b5ae6","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-281","chapter","type-chapter","status-publish","hentry"],"part":251,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/281","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/281\/revisions"}],"predecessor-version":[{"id":1535,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/281\/revisions\/1535"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/251"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/281\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=281"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=281"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=281"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Precalculus. Authored by<\/strong>: Jay Abramson, et al.. Provided by<\/strong>: OpenStax. Located at<\/strong>: http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em>. License Terms<\/strong>: Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li>
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