{"id":1422,"date":"2026-05-12T21:47:48","date_gmt":"2026-05-12T21:47:48","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-22\/"},"modified":"2026-05-13T03:39:47","modified_gmt":"2026-05-13T03:39:47","slug":"solution-exercise-22","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-22\/","title":{"raw":"Solution Exercise 22","rendered":"Solution Exercise 22"},"content":{"raw":"
\r\n
\r\n
For column D: Divide the concentration in mg\/L by the atomic weight of each ion to convert the concentration from mg\/L to molarity (mmol\/L).<\/blockquote>\r\n<\/div>\r\n
\r\n
For column F: Multiply the molarity by the valence charge to calculate the concentration in milliequivalents per liter (meq\/L).<\/blockquote>\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
A<\/strong><\/td>\r\nB<\/strong><\/td>\r\nC<\/strong><\/td>\r\nD<\/strong><\/td>\r\nE<\/strong><\/td>\r\nF<\/strong><\/td>\r\n<\/tr>\r\n
Solute<\/strong><\/td>\r\nMeasured Concentration (mg\/L)<\/strong><\/td>\r\nAtomic weight(g)<\/strong><\/td>\r\nMolarity (mmol\/L)<\/strong><\/td>\r\nValence (charge)<\/strong><\/td>\r\nmeq\/L<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Ca}_{}^{2 +}[\/latex]<\/td>\r\n75<\/td>\r\n40.08<\/td>\r\n1.87<\/strong><\/td>\r\n2<\/td>\r\n3.74<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Mg}_{}^{2 +}[\/latex]<\/td>\r\n25<\/td>\r\n24.31<\/td>\r\n1.03<\/strong><\/td>\r\n2<\/td>\r\n2.06<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Na}_{}^{+}[\/latex]<\/td>\r\n5.6<\/td>\r\n23<\/td>\r\n0.24<\/strong><\/td>\r\n1<\/td>\r\n0.24<\/strong><\/td>\r\n<\/tr>\r\n
[latex]K_{}^{+}[\/latex]<\/td>\r\n2.1<\/td>\r\n39.1<\/td>\r\n0.05<\/strong><\/td>\r\n1<\/td>\r\n0.054<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Fe(III)}_{}^{}[\/latex]<\/td>\r\n0.2<\/td>\r\n55.8<\/td>\r\n0.004<\/strong><\/td>\r\n3<\/td>\r\n0.011<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{HCO}_{3}^{-}[\/latex]<\/td>\r\n109<\/td>\r\n61<\/td>\r\n1.79<\/strong><\/td>\r\n1<\/td>\r\n1.79<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{SO}_{4}^{2 -}[\/latex]<\/td>\r\n242<\/td>\r\n96<\/td>\r\n2.52<\/strong><\/td>\r\n2<\/td>\r\n5.04<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Cl}_{}^{-}[\/latex]<\/td>\r\n9.3<\/td>\r\n35.5<\/td>\r\n0.26<\/strong><\/td>\r\n1<\/td>\r\n0.26<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{NO}_{3}^{-}[\/latex]<\/td>\r\n15<\/td>\r\n62<\/td>\r\n0.24<\/strong><\/td>\r\n1<\/td>\r\n0.24<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
The sum of the cation milliequivalents (i.e., positively charged ions) is 6.11 meq\/L. The sum of the anion milliequivalents (i.e., negatively charged ions) is 7.33 meq\/L. The charge balance is calculated as:<\/blockquote>\r\n<\/div>\r\n
\r\n\r\n[latex]C.B. = \\frac{\\left( \\Sigma_{cations} - \\ \\Sigma_{anions} \\right)}{\\left( \\Sigma_{cations} + \\ \\Sigma_{anions} \\right)}(100)[\/latex]\r\n\r\n<\/div>\r\n
\r\n
[latex]\\frac{\\left( 6.11\\frac{meq}{L} - 7.33\\frac{meq}{L} \\right)}{\\left( 6.11\\frac{meq}{L} + 7.33\\frac{meq}{L} \\right)}(100) = - 0.091(100) = - 9.1\\%[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
The absolute value of the charge balance is greater than 5%, which means that the charge balance is unacceptable. The calculated value is negative, which means that there are excess anions (or insufficient cations) represented in the analytical results.<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nReturn to Exercise 22<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n
\r\n\r\nReturn to where text linked to Exercise 22<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

For column D: Divide the concentration in mg\/L by the atomic weight of each ion to convert the concentration from mg\/L to molarity (mmol\/L).<\/p><\/blockquote>\n<\/div>\n

\n

For column F: Multiply the molarity by the valence charge to calculate the concentration in milliequivalents per liter (meq\/L).<\/p><\/blockquote>\n<\/div>\n\n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n\n\n
A<\/strong><\/td>\nB<\/strong><\/td>\nC<\/strong><\/td>\nD<\/strong><\/td>\nE<\/strong><\/td>\nF<\/strong><\/td>\n<\/tr>\n
Solute<\/strong><\/td>\nMeasured Concentration (mg\/L)<\/strong><\/td>\nAtomic weight(g)<\/strong><\/td>\nMolarity (mmol\/L)<\/strong><\/td>\nValence (charge)<\/strong><\/td>\nmeq\/L<\/strong><\/td>\n<\/tr>\n
[latex]{Ca}_{}^{2 +}[\/latex]<\/td>\n75<\/td>\n40.08<\/td>\n1.87<\/strong><\/td>\n2<\/td>\n3.74<\/strong><\/td>\n<\/tr>\n
[latex]{Mg}_{}^{2 +}[\/latex]<\/td>\n25<\/td>\n24.31<\/td>\n1.03<\/strong><\/td>\n2<\/td>\n2.06<\/strong><\/td>\n<\/tr>\n
[latex]{Na}_{}^{+}[\/latex]<\/td>\n5.6<\/td>\n23<\/td>\n0.24<\/strong><\/td>\n1<\/td>\n0.24<\/strong><\/td>\n<\/tr>\n
[latex]K_{}^{+}[\/latex]<\/td>\n2.1<\/td>\n39.1<\/td>\n0.05<\/strong><\/td>\n1<\/td>\n0.054<\/strong><\/td>\n<\/tr>\n
[latex]{Fe(III)}_{}^{}[\/latex]<\/td>\n0.2<\/td>\n55.8<\/td>\n0.004<\/strong><\/td>\n3<\/td>\n0.011<\/strong><\/td>\n<\/tr>\n
[latex]{HCO}_{3}^{-}[\/latex]<\/td>\n109<\/td>\n61<\/td>\n1.79<\/strong><\/td>\n1<\/td>\n1.79<\/strong><\/td>\n<\/tr>\n
[latex]{SO}_{4}^{2 -}[\/latex]<\/td>\n242<\/td>\n96<\/td>\n2.52<\/strong><\/td>\n2<\/td>\n5.04<\/strong><\/td>\n<\/tr>\n
[latex]{Cl}_{}^{-}[\/latex]<\/td>\n9.3<\/td>\n35.5<\/td>\n0.26<\/strong><\/td>\n1<\/td>\n0.26<\/strong><\/td>\n<\/tr>\n
[latex]{NO}_{3}^{-}[\/latex]<\/td>\n15<\/td>\n62<\/td>\n0.24<\/strong><\/td>\n1<\/td>\n0.24<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

The sum of the cation milliequivalents (i.e., positively charged ions) is 6.11 meq\/L. The sum of the anion milliequivalents (i.e., negatively charged ions) is 7.33 meq\/L. The charge balance is calculated as:<\/p><\/blockquote>\n<\/div>\n

\n

[latex]C.B. = \\frac{\\left( \\Sigma_{cations} - \\ \\Sigma_{anions} \\right)}{\\left( \\Sigma_{cations} + \\ \\Sigma_{anions} \\right)}(100)[\/latex]<\/p>\n<\/div>\n

\n

[latex]\\frac{\\left( 6.11\\frac{meq}{L} - 7.33\\frac{meq}{L} \\right)}{\\left( 6.11\\frac{meq}{L} + 7.33\\frac{meq}{L} \\right)}(100) = - 0.091(100) = - 9.1\\%[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

The absolute value of the charge balance is greater than 5%, which means that the charge balance is unacceptable. The calculated value is negative, which means that there are excess anions (or insufficient cations) represented in the analytical results.<\/p><\/blockquote>\n<\/div>\n

\n

Return to Exercise 22<\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n

\n

Return to where text linked to Exercise 22<\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":133,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1422","chapter","type-chapter","status-publish","hentry"],"part":1531,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1422","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":2,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1422\/revisions"}],"predecessor-version":[{"id":1840,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1422\/revisions\/1840"}],"part":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1531"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1422\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1422"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapter-type?post=1422"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/contributor?post=1422"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/license?post=1422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}