If I post the script it looks like this right now.
Kw = 10^-14;
pHfix = 3;
F = 96485.3328959;
R = 8.314472;
T = 298.15;
KSOH2 = 10^4;
KSO = 10^-8.8;
KSOH2Cl = 10^5.82;
KSONa = 10^-7;
TCl = 10^-3;
TNa = 10^-3;
TSOH = 9.9635 10^-6;
s = 1;
a = 1;
C1 = 1.05;
C2 = 3.36;
C3 = 0.27;
epsi0 = 8.85418787 10^-12;
epsi = 78.45203;
zOH = -1;
zH = 1;
zCl = -1;
zNa = 1;
f1[H_] := H - 10^-pHfix;
f2[H_, OH_] := Log10[OH] + Log10[H] - Log10[Kw];
f3[H_, SOH_, SOH2_, psiO_] :=
Log10[SOH] + Log10[H] + Log10[Exp[(-F psiO)/(R T)]] + Log10[KSOH2] -
Log10[SOH2];
f4[H_, SO_, SOH_, psiO_] :=
Log10[SOH] - Log10[H] - Log10[Exp[(-F psiO)/(R T)]] + Log10[KSO] -
Log10[SO];
f5[H_, Cl_, SOH_, SOH2Cl_, psiO_, psiA_] :=
Log10[SOH] + Log10[H] + Log10[Exp[(-F psiO)/(R T)]] + Log10[Cl] -
Log10[Exp[(-F psiA)/(R T)]] + Log10[KSOH2Cl] - Log10[SOH2Cl];
f6[H_, Na_, SOH_, SONa_, psiO_, psiC_] :=
Log10[SOH] - Log10[H] - Log10[Exp[(-F psiO)/(R T)]] + Log10[Na] +
Log10[Exp[(-F psiC)/(R T)]] + Log10[KSONa] - Log10[SONa];
f7[Cl_, SOH2Cl_] := Cl + SOH2Cl - TCl;
f8[Na_, SONa_] := Na + SONa - TNa;
f9[SOH_, SOH2_, SOH2Cl_, SONa_] := SOH + SOH2 + SOH2Cl + SONa - TSOH;
f10[SO_, SOH2_, SOH2Cl_, SONa_, psiO_, psiC_] :=
SOH2 - SO + SOH2Cl - SONa - ((s*a)/F)*C1*(psiO - psiC);
f11[SONa_, psiO_, psiC_, psiA_] :=
SONa - ((s*a)/F)*(C1*(psiC - psiO) + C2*(psiC - psiA));
f12[SOH2Cl_, psiC_, psiA_,
psiD_] := -SOH2Cl - ((s*a)/F)*(C2*(psiA - psiC) + C3*(psiA - psiD));
f13[H_, OH_, Cl_, Na_, psiA_,
psiD_] := -Sqrt[
8*epsi*epsi0*R*
T*1000*0.5*(H*zH^2 + OH*zOH^2 + Na*zNa^2 + Cl*zCl^2)]*
Sinh[(F*psiD)/(2*R*T)] - ((s*a)/F)*C3*(psiD - psiA);
FindRoot[{f1[H] == 0, f2[H, OH] == 0, f3[H, SOH, SOH2, psiO] == 0,
f4[H, SO, SOH, psiO] == 0, f5[H, Cl, SOH, SOH2Cl, psiO, psiA] == 0,
f6[H, Na, SOH, SONa, psiO, psiC] == 0, f7[Cl, SOH2Cl] == 0,
f8[Na, SONa] == 0, f9[SOH, SOH2, SOH2Cl, SONa] == 0,
f10[SO, SOH2, SOH2Cl, SONa, psiO, psiC] == 0,
f11[SONa, psiO, psiC, psiA] == 0,
f12[SOH2Cl, psiC, psiA, psiD] == 0,
f13[H, OH, Cl, Na, psiA, psiD] == 0 }, {{H, 10^-3}, {OH,
10^-7}, {SOH2, 3.189 10^-8}, {SO, 4.844 10^-8}, {SOH2Cl,
7.2569 10^-10}, {SONa, 9.9035 10^-9}, {Cl, 9.9999 10^-4}, {Na,
9.9999 10^-4}, {SOH,
9.9635 10^-6}, {psiA, -0.258}, {psiC, -0.258}, {psiO, -0.258}, \
{psiD, 0}}]
FindRoot::nlnum: The function value {f1[0.001],f2[0.001,1.*10^-7],f3[0.001,9.9635*10^-6,3.189*10^-8,-0.258],f4[0.001,4.844*10^-8,9.9635*10^-6,-0.258],f5[0.001,0.00099999,9.9635*10^-6,7.2569*10^-10,-0.258,-0.258],f6[0.001,0.00099999,9.9635*10^-6,9.9035*10^-9,-0.258,-0.258],0.000999991 -1. TCl,0.001 -1. TNa,0.000010006 -1. TSOH,-2.57278*10^-8,9.9035*10^-9,-7.2569*10^-10-(1. a (0. -0.258 C3) s)/F,0. -(0.258 a C3 s)/F} is not a list of numbers with dimensions {13} at {H,OH,SOH2,SO,SOH2Cl,SONa,Cl,Na,SOH,psiA,psiC,psiO,psiD} = {0.001,1.*10^-7,3.189*10^-8,4.844*10^-8,7.2569*10^-10,9.9035*10^-9,0.00099999,0.00099999,9.9635*10^-6,-0.258,-0.258,-0.258,0.}.
FindRoot[{f1[H] == 0, f2[H, OH] == 0, f3[H, SOH, SOH2, psiO] == 0,
f4[H, SO, SOH, psiO] == 0, f5[H, Cl, SOH, SOH2Cl, psiO, psiA] == 0,
f6[H, Na, SOH, SONa, psiO, psiC] == 0, f7[Cl, SOH2Cl] == 0,
f8[Na, SONa] == 0, f9[SOH, SOH2, SOH2Cl, SONa] == 0,
f10[SO, SOH2, SOH2Cl, SONa, psiO, psiC] == 0,
f11[SONa, psiO, psiC, psiA] == 0,
f12[SOH2Cl, psiC, psiA, psiD] == 0,
f13[H, OH, Cl, Na, psiA, psiD] == 0}, {{H, 1/10^3}, {OH, 1/
10^7}, {SOH2, 3.189/10^8}, {SO, 4.844/10^8}, {SOH2Cl, 7.2569/
10^10}, {SONa, 9.9035/10^9}, {Cl, 9.9999/10^4}, {Na, 9.9999/
10^4}, {SOH, 9.9635/
10^6}, {psiA, -0.258}, {psiC, -0.258}, {psiO, -0.258}, {psiD, 0}}]