◎エクセル用式(1) 以下の式に数値を代入して計算すること。(a1が変数） =8.31*298*((n1a0+a1)*ln((n1a0+a1)/(n1a0+(Y)*a1)) +(-(X)*a1)*ln((-(X)*a1)/(n1a0+(Y)*a1)) +(-a1)*ln((-a1)/(n2b0-(Y)*a1))+(n2b0+(X)*a1)*ln((n2b0+(X)*a1)/(n2b0-(Y)*a1))) ただし、X=n2b0/n1b0, Y=(n1a0-n2b0)/n1a0 である。 ○本文の例題@　系A(NaCl 20g), 系B(H2O 80g), M(NaCl)=58.5, M(H2O)=18　　 （１）式の検証 n1a0=0.342, n2a0=0, n1b0=0, n2b0=4.444, X=12.994, Y=-11.994 =8.31*298*((0.342+a1)*ln((0.342+a1)/(0.342+(-11.994)*a1))+(-(12.994)*a1)*ln((-(12.994)*a1)/(0.342+(-11.994)*a1))+(-a1)*ln((-a1)/(4.444-(-11.994)*a1))+(4.444+(12.994)*a1)*ln((4.444+(12.994)*a1)/(4.444-(-11.994)*a1))) ○応用例題　系A(NaCl 10g), 系B(H2O 90g), M(NaCl)=58.5, M(H2O)=18　　 （１）式の検証 n1a0=0.171, n2a0=0, n1b0=0, n2b0=5, X=29.24, Y=-28.24 =8.31*298*((0.171+a1)*ln((0.171+a1)/(0.171+(-28.24)*a1))+(-(29.24)*a1)*ln((-(29.24)*a1)/(0.171+(-28.24)*a1))+(-a1)*ln((-a1)/(5-(-28.24)*a1))+(5+(29.24)*a1)*ln((5+(29.24)*a1)/(5-(-28.24)*a1))) ○応用例題　系A(EtOH 10g), 系B(H2O 90g), M(EtOH)=46, M(H2O)=18　 n1a0=0.2174, n2a0=0, n1b0=0, n2b0=5, X=22.999, Y=-21.999 =8.31*298*((0.2174+a1)*ln((0.2174+a1)/(0.2174+(-21.999)*a1))+(-(22.999)*a1)*ln((-(22.999)*a1)/(0.2174+(-21.999)*a1))+(-a1)*ln((-a1)/(5-(-21.999)*a1))+(5+(22.999)*a1)*ln((5+(22.999)*a1)/(5-(-21.999)*a1))) ＠等モル純物質の場合 （１）式 n1a0=0.5, n2a0=0, n1b0=0, n2b0=0.5 X=n2b0/n1b0=1, Y=(n1a0-n2b0)/n1a0=0 =8.31*298*((0.5+a1)*ln((0.5+a1)/(0.5+(0)*a1))+(-(1)*a1)*ln((-(1)*a1)/(0.5+(0)*a1))+(-a1)*ln((-a1)/(0.5-(0)*a1))+(0.5+(1)*a1)*ln((0.5+(1)*a1)/(0.5-(0)*a1))) ◎エクセル用式(2) 以下の式に数値を代入して計算すること。(a1が変数） =8.31*298*((n1a0+a1)*ln(n1a0+a1)-n1a0*ln(n1a0) -(C)*((n1a0+a1)+(B/C))*ln((C)*(n1a0+a1)+(B))+(C)*(n1a0+(B/C))*ln((C)*n1a0+(B)) +(A)*((n1a0+a1)+(B/A))*ln((A)*(n1a0+a1)+(B))-(A)*(n1a0+(B/A))*ln((A)*n1a0+(B)) -((n1a0+a1)-(D))*ln(-(n1a0+a1)+(D))+(n1a0-(D))*ln(-n1a0+(D)) +(C)*((n1a0+a1)-(F/C))*ln(-(C)*(n1a0+a1)+(F))-(C)*(n1a0-(F/C))*ln(-(C)*n1a0+(F)) -(A)*((n1a0+a1)-(E/A))*ln(-(A)*(n1a0+a1)+(E))+(A)*(n1a0-(E/A))*ln(-(A)*n1a0+(E))) ただし、A=(n2a0-n2b0)/(n1a0-n1b0), B=(n1a0*n2b0-n1b0*n2a0)/(n1a0-n1b0), C=(n1a0+n2a0-n1b0-n2b0)/(n1a0-n1b0), D=n1a0+n1b0, E=(n1a0*n2a0-n1b0*n2b0)/(n1a0-n1b0), F=(n1a0*(n1a0+n2a0)-n1b0*(n1b0+n2b0))/(n1a0-n1b0) である。 ○本文の例題A　系A(NaCl 10g, H2O 190g), 系B(NaCl 20g, H2O 80g), M(NaCl)=58.5, M(H2O)=18 n1a0=0.171, n2a0=10.556, n1b0=0.342, n2b0=4.444, A=(10.556-4.444)/(0.171-0.342), B=(0.171*4.444-0.342*10.556)/(0.172-0.342), C=(0.171+10.556-0.342-4.444)/(0.171-0.342), D=0.171+0.342, E=(0.171*10.556-0.342*4.444)/(0.172-0.342), F=(0.171*(0.171+10.556)-0.342*(0.342+4.444))/(0.171-0.342) A=-35.743, B=16.766, C=-34.743, D=0.513, E=-1.678, F=-1.155 B/C=-0.483, B/A=-0.469, F/C=0.0332, E/A=0.0469 =8.31*298*((0.171+a1)*ln(0.171+a1)-0.171*ln(0.171)-(-34.743)*((0.171+a1)+(-0.483))*ln((-34.743)*(0.171+a1)+(16.766))+(-34.743)*(0.171+(-0.483))*ln((-34.743)*0.171+(16.766))+(-35.743)*((0.171+a1)+(-0.469))*ln((-35.743)*(0.171+a1)+(16.766))-(-35.743)*(0.171+(-0.469))*ln((-35.743)*0.171+(16.766))-((0.171+a1)-(0.513))*ln(-(0.171+a1)+(0.513))+(0.171-(0.513))*ln(-0.171+(0.513))+(-34.743)*((0.171+a1)-(0.0332))*ln(-(-34.743)*(0.171+a1)+(-1.155))-(-34.743)*(0.171-(0.0332))*ln(-(-34.743)*0.171+(-1.155))-(-35.743)*((0.171+a1)-(0.0469))*ln(-(-35.743)*(0.171+a1)+(-1.678))+(-35.743)*(0.171-(0.0469))*ln(-(-35.743)*0.171+(-1.678))) ○例題@の追試　系A(NaCl 20g), 系B(H2O 80g), M(NaCl)=58.5, M(H2O)=18　　 （１）式を用いて（２）式の結果を検証する。 n1a0=0.342 n2a0=0, n1b0=0, n2b0=4.444, A=(0-4.444)/(0.342-0), B=(0.3419*4.4444-0*0)/(0.3419-0), C=(0.3419+0-0-4.4444)/(0.3419-0), D=0.3419+0, E=(0.3419*0-0*4.4444)/(0.3419-0), F=(0.3419*(0.3419+0)-0*(0+4.4444))/(0.3419-0) A=-12.994, B=4.444, C=-11.994, D=0.342, E=0, F=0.342 B/C=-0.371, B/A=-0.342, F/C=-0.0285, E/A=0 =8.31*298*((0.342+a1)*ln(0.342+a1)-0.342*ln(0.342)-(-11.994)*((0.342+a1)+(-0.371))*ln((-11.994)*(0.342+a1)+(4.444))+(-11.994)*(0.342+(-0.371))*ln((-11.994)*0.342+(4.444))+(-12.994)*((0.342+a1)+(-0.342))*ln((-12.994)*(0.342+a1)+(4.444))-((0.342+a1)-(0.342))*ln(-(0.342+a1)+(0.342))+(-11.994)*((0.342+a1)-(-0.0285))*ln(-(-11.994)*(0.342+a1)+(0.342))-(-11.994)*(0.342-(-0.0285))*ln(-(-11.994)*0.342+(0.342))-(-12.994)*((0.342+a1)-(0))*ln(-(-12.994)*(0.342+a1)+(0))+(-12.994)*(0.342-(0))*ln(-(-12.994)*0.342+(0))) ○応用例題　系A(EtOH 50g, H2O 50g), 系B(EtOH 0g, H2O 100g), M(EtOH)=46, M(H2O)=18 n1a0=1.087, n2a0=2.778, n1b0=0, n2b0=5.556 A=(2.778-5.556)/(1.087-0), B=(1.087*5.556-0*2.778)/(1.087-0), C=(1.087+2.778-0-5.556)/(1.087-0), D=1.087+0, E=(1.087*2.778-0*5.556)/(1.087-0), F=(1.087*(1.087+2.778)-0*(0+5.556))/(1.087-0) A=-2.556, B=5.556, C=-1.556, D=1.087, E=2.778, F=3.865 B/C=-3.571, B/A=-2.174, F/C=-2.484, E/A=-1.087 =8.31*298*((1.087+a1)*ln(1.087+a1)-1.087*ln(1.087)-(-1.556)*((1.087+a1)+(-3.571))*ln((-1.556)*(1.087+a1)+(5.556))+(-1.556)*(1.087+(-3.571))*ln((-1.556)*1.087+(5.556))+(-2.556)*((1.087+a1)+(-2.174))*ln((-2.556)*(1.087+a1)+(5.556))-(-2.556)*(1.087+(-2.174))*ln((-2.556)*1.087+(5.556))-((1.087+a1)-(1.087))*ln(-(1.087+a1)+(1.087))+(-1.556)*((1.087+a1)-(-2.484))*ln(-(-1.556)*(1.087+a1)+(3.865))-(-1.556)*(1.087-(-2.484))*ln(-(-1.556)*1.087+(3.865))-(-2.556)*((1.087+a1)-(-1.087))*ln(-(-2.556)*(1.087+a1)+(2.778))+(-2.556)*(1.087-(-1.087))*ln(-(-2.556)*1.087+(2.778))) ○応用例題　系A(EtOH 20g, H2O 80g), 系B(EtOH 10g, H2O 90g), M(EtOH)=46, M(H2O)=18 n1a0=0.435, n2a0=4.444, n1b0=0.217, n2b0=5 A=(4.444-5)/(0.435-0.217), B=(0.435*5-0.217*4.444)/(0.435-0.217), C=(0.435+4.444-0.217-5)/(0.435-0.217), D=0.435+0.217, E=(0.435*4.444-0.217*5)/(0.435-0.217), F=(0.435*(0.435+4.444)-0.217*(0.217+5))/(0.435-0.217) A=-2.55, B=5.553, C=-1.55, D=0.652, E=3.891, F=4.543 B/C=-3.582, B/A=-2.177, F/C=-2.93, E/A=-1.525 =8.31*298*((0.435+a1)*ln(0.435+a1)-0.435*ln(0.435)-(-1.55)*((0.435+a1)+(-3.582))*ln((-1.55)*(0.435+a1)+(5.553))+(-1.55)*(0.435+(-3.582))*ln((-1.55)*0.435+(5.553))+(-2.55)*((0.435+a1)+(-2.177))*ln((-2.55)*(0.435+a1)+(5.553))-(-2.55)*(0.435+(-2.177))*ln((-2.55)*0.435+(5.553))-((0.435+a1)-(0.652))*ln(-(0.435+a1)+(0.652))+(0.435-(0.652))*ln(-0.435+(0.652))+(-1.55)*((0.435+a1)-(-2.93))*ln(-(-1.55)*(0.435+a1)+(4.543))-(-1.55)*(0.435-(-2.93))*ln(-(-1.55)*0.435+(4.543))-(-2.55)*((0.435+a1)-(-1.525))*ln(-(-2.55)*(0.435+a1)+(3.891))+(-2.55)*(0.435-(-1.525))*ln(-(-2.55)*0.435+(3.891))) ○応用例題　系A(EtOH 10g), 系B(H2O 90g), M(EtOH)=46, M(H2O)=18 (2)式を用いて(1)式を検証する。　 n1a0=0.2174, n2a0=0, n1b0=0, n2b0=5 A=(0-5)/(0.2174-0), B=(0.2174*5-0*0)/(0.2174-0), C=(0.2174+0-0-5)/(0.2174-0), D=0.2174+0, E=(0.2174*0-0*5)/(0.2174-0), F=(0.2174*(0.2174+0)-0*(0+5))/(0.2174-0) A=-22.9991, B=5, C=-21.9991, D=0.2174, E=0, F=0.2174 B/C=-0.2273, B/A=-0.2174, F/C=-0.0099, E/A=0 =8.31*298*((0.2174+a1)*ln(0.2174+a1)-0.2174*ln(0.2174)-(-21.9991)*((0.2174+a1)+(-0.2273))*ln((-21.9991)*(0.2174+a1)+(5))+(-21.9991)*(0.2174+(-0.2273))*ln((-21.9991)*0.2174+(5))+(-22.9991)*((0.2174+a1)+(-0.2174))*ln((-22.9991)*(0.2174+a1)+(5))-((0.2174+a1)-(0.2174))*ln(-(0.2174+a1)+(0.2174))+(-21.9991)*((0.2174+a1)-(-0.0099))*ln(-(-21.9991)*(0.2174+a1)+(0.2174))-(-21.9991)*(0.2174-(-0.0099))*ln(-(-21.9991)*0.2174+(0.2174))-(-22.9991)*((0.2174+a1)-(0))*ln(-(-22.9991)*(0.2174+a1)+(0))+(-22.9991)*(0.2174-(0))*ln(-(-22.9991)*0.2174+(0)))