Question

The reaction below is used as a visual humidity indicator. What is the equilibrium vapor pressure of water (in mmHg) for the reaction at 35C?

CoCl2(s)+ 6H2O(g)<> Co((H2O)s)Cl2(s)

Delta H= -352kj/mol

Delta S= -899 j/mol.K

Answer 1

CoCl2(s)+ 6H2O(g)<> Co((H2O)s)Cl2(s)

Given H = -352kJ/mol

S = -899 J/mol.K*(10^-3kJ/J) = -0.899 kJ/mol-K

T = Temperature = 35oC = 35+273 = 308K

We know that G = H-TS

                            = -352 (kJ/mol) - [308K*(-0.899kJ/mol-K)]

                            = -75.1 kJ/mol

For the above reaction Equilibrium constant , K = 1/p⁶_H2O(g)

We have G = -RT ln K

Where

R = gas constant = 8.314x10^-3 kJ/mol-K

T = temperature = 35oC = 35+273 = 308K

Plug the values we get

ln K = - G/(RT)

      = -(-75.1 kJ/mol) / ( 8.314x10^-3 kJ/mol-K x 308K)

     = 29.3

K = e^29.3 = 5.47x10¹²

K = 1/p⁶_H2O(g) = 5.47x10¹²

p_H2O(g) = 7.533*10^-3 atm (760 mm Hg/1 atm)

               = 5.72 mm Hg