{"id":133,"date":"2026-04-10T02:53:10","date_gmt":"2026-04-10T02:53:10","guid":{"rendered":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/ch054-xhtml\/"},"modified":"2026-05-12T02:06:14","modified_gmt":"2026-05-12T02:06:14","slug":"exercise-1","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/exercise-1\/","title":{"raw":"Exercise\u00a01","rendered":"Exercise\u00a01"},"content":{"raw":"
\r\n
\r\n\r\nExercise\u00a01 is in two parts: a) and b).\r\n\r\n<\/div>\r\n
    \r\n \t
  1. Use Equation\u00a0(4)<\/span><\/a> in Section 2.3 to calculate the concentrations of dissolved [latex]He,\\ Ne,\\ N_{2},\\ Ar,\\ Kr,[\/latex] and [latex]Xe[\/latex] (in units of ccSTP\/g) in equilibrium with the moist atmosphere at a temperature of 10\u00a0\u00b0C and an elevation of 450\u00a0m above mean sea level. The equation is shown here.<\/li>\r\n<\/ol>\r\n<\/colgroup>\r\n\r\n\r\n
    <\/th>\r\n[latex]C_{i,eq} = \\frac{\\left( P - e(T) \\right)x_{i}}{K_{w,i}(T,S)}[\/latex]<\/th>\r\n<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
    \r\n\r\nwhere:\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]C_{i,eq}[\/latex]<\/th>\r\n=<\/th>\r\nconcentration of air\u2011saturated water (ASW, ccSTP\/g)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    P<\/em><\/td>\r\n=<\/td>\r\natmospheric pressure (atm)<\/td>\r\n<\/tr>\r\n
    e(T)<\/em><\/td>\r\n=<\/td>\r\nvapor pressure of water at temperature T<\/em> (atm)<\/td>\r\n<\/tr>\r\n
    [latex]K_{w,i}(T,S)[\/latex]<\/td>\r\n=<\/td>\r\nHenry Coefficient of gas i<\/em> at temperature T<\/em> and salinity S<\/em> (g\u2011atm\/ccSTP)<\/td>\r\n<\/tr>\r\n
    [latex]x_{i}[\/latex]<\/td>\r\n=<\/td>\r\nfraction of gas i<\/em> (mixing ratio) in the dry atmosphere<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
    \r\n
    As with all equations, it is important to use consistent units throughout the calculation (i.e., for Ci,eq<\/sub><\/em> in units of ccSTP\/g, and P<\/em> and e<\/em> in atm, Kw,i<\/sub><\/em> should be in g\u2011atm\/ccSTP).<\/blockquote>\r\n<\/div>\r\n
    \r\n
    Assume that the recharge salinity is zero. Use Table 1<\/span><\/a> (Section 2.1) for Henry Coefficient. A good approximation for atmospheric pressure is [latex]P = P_{0}\\exp\\left( - \\frac{Z}{Z_{s}} \\right)[\/latex] where P0<\/sub><\/em> is the pressure at elevation (Z<\/em>) of zero (i.e., 1\u00a0atm) and [latex]Z_{s}[\/latex] is a scaling factor equal to 8,300 as shown in Equation\u00a0(5)<\/span><\/a>. Use the Antoine equation [latex]e = 10^{A - \\frac{B}{C + T}}[\/latex] where A\u00a0<\/em>= ]8.07131, B\u00a0<\/em>= 1730.63, C\u00a0<\/em>= 233.426 and T<\/em> is temperature in \u00b0C and e<\/em> is the vapor pressure of water in units of mmHg as shown in Equation\u00a0(6)<\/span><\/a>. Both Equation\u00a0(5)<\/span><\/a> and Equation\u00a0(6)<\/span><\/a> follow Equation\u00a0(4)<\/span><\/a> in Section 2.3. e<\/em> needs to be converted to units of atm for use in Equation\u00a0(4)<\/span><\/a>.<\/blockquote>\r\n<\/div>\r\n
      \r\n \t
    1. Now add 0.003\u00a0ccSTP\/g of UA to each of these values. On a percentage basis, calculate how much this changes the concentrations relative to the equilibrium values computed in Exercise\u00a01a).<\/li>\r\n<\/ol>\r\n
      \r\n\r\nSolution to Exercise\u00a01<\/u><\/span><\/a>\u2ba7\r\n\r\n<\/div>\r\n
      \r\n\r\nReturn to where text linked to Exercise\u00a01<\/u><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"
      \n
      \n

      Exercise\u00a01 is in two parts: a) and b).<\/p>\n<\/div>\n

        \n
      1. Use Equation\u00a0(4)<\/span><\/a> in Section 2.3 to calculate the concentrations of dissolved [latex]He,\\ Ne,\\ N_{2},\\ Ar,\\ Kr,[\/latex] and [latex]Xe[\/latex] (in units of ccSTP\/g) in equilibrium with the moist atmosphere at a temperature of 10\u00a0\u00b0C and an elevation of 450\u00a0m above mean sea level. The equation is shown here.<\/li>\n<\/ol>\n\n\n\n\n<\/colgroup>\n\n\n
        <\/th>\n[latex]C_{i,eq} = \\frac{\\left( P - e(T) \\right)x_{i}}{K_{w,i}(T,S)}[\/latex]<\/th>\n<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
        \n

        where:<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n
        [latex]C_{i,eq}[\/latex]<\/th>\n=<\/th>\nconcentration of air\u2011saturated water (ASW, ccSTP\/g)<\/th>\n<\/tr>\n<\/thead>\n
        P<\/em><\/td>\n=<\/td>\natmospheric pressure (atm)<\/td>\n<\/tr>\n
        e(T)<\/em><\/td>\n=<\/td>\nvapor pressure of water at temperature T<\/em> (atm)<\/td>\n<\/tr>\n
        [latex]K_{w,i}(T,S)[\/latex]<\/td>\n=<\/td>\nHenry Coefficient of gas i<\/em> at temperature T<\/em> and salinity S<\/em> (g\u2011atm\/ccSTP)<\/td>\n<\/tr>\n
        [latex]x_{i}[\/latex]<\/td>\n=<\/td>\nfraction of gas i<\/em> (mixing ratio) in the dry atmosphere<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
        \n

        As with all equations, it is important to use consistent units throughout the calculation (i.e., for Ci,eq<\/sub><\/em> in units of ccSTP\/g, and P<\/em> and e<\/em> in atm, Kw,i<\/sub><\/em> should be in g\u2011atm\/ccSTP).<\/p><\/blockquote>\n<\/div>\n

        \n

        Assume that the recharge salinity is zero. Use Table 1<\/span><\/a> (Section 2.1) for Henry Coefficient. A good approximation for atmospheric pressure is [latex]P = P_{0}\\exp\\left( - \\frac{Z}{Z_{s}} \\right)[\/latex] where P0<\/sub><\/em> is the pressure at elevation (Z<\/em>) of zero (i.e., 1\u00a0atm) and [latex]Z_{s}[\/latex] is a scaling factor equal to 8,300 as shown in Equation\u00a0(5)<\/span><\/a>. Use the Antoine equation [latex]e = 10^{A - \\frac{B}{C + T}}[\/latex] where A\u00a0<\/em>= ]8.07131, B\u00a0<\/em>= 1730.63, C\u00a0<\/em>= 233.426 and T<\/em> is temperature in \u00b0C and e<\/em> is the vapor pressure of water in units of mmHg as shown in Equation\u00a0(6)<\/span><\/a>. Both Equation\u00a0(5)<\/span><\/a> and Equation\u00a0(6)<\/span><\/a> follow Equation\u00a0(4)<\/span><\/a> in Section 2.3. e<\/em> needs to be converted to units of atm for use in Equation\u00a0(4)<\/span><\/a>.<\/p><\/blockquote>\n<\/div>\n

          \n
        1. Now add 0.003\u00a0ccSTP\/g of UA to each of these values. On a percentage basis, calculate how much this changes the concentrations relative to the equilibrium values computed in Exercise\u00a01a).<\/li>\n<\/ol>\n
          \n

          Solution to Exercise\u00a01<\/u><\/span><\/a>\u2ba7<\/p>\n<\/div>\n

          \n

          Return to where text linked to Exercise\u00a01<\/u><\/span><\/a>\u2ba5<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":7,"menu_order":36,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-133","chapter","type-chapter","status-publish","hentry"],"part":39,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/users\/7"}],"version-history":[{"count":7,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/133\/revisions"}],"predecessor-version":[{"id":447,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/133\/revisions\/447"}],"part":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/parts\/39"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/133\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/media?parent=133"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapter-type?post=133"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/contributor?post=133"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/license?post=133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}