Question

Consider the system:

A (aq) → B (aq)

at 257 K where ΔGoform A = -13.9 kJ/mol and ΔGoform B = -18.5 kJ/mol. Calculate the concentration of A at equilibrium when 2.25 mol of A and 1.83 mol of B are mixed in water to form exactly one liter of solution.

Answer 1

Get dGrxn = Gproduct s- Greactants = -18.5 - -13.9 = -4.6 kJ/mol = -4600 J/mol

dG = -RT*ln(K)

K = exp(-dG/(RT))

K = exp(4600 / (8.314*257))

K = 8.609

initially

[A] = 2.25

[B] = 1.83

Q = [B]/[A] = 1.83/2.25 = 0.813

expect A to form more B

in equilbirium

[A] = 2.25 - x

[B] = 1.83 + x

substitute

8.609= (1.83 + x)/(2.25 - x)

8.609*2.25 -8.609x = 1.83 +x

(9.609)x = 8.609*2.25-1.83

x = (17.540) / 609

x =0.02880

then

[A] = 2.25 - 0.02880 = 2.2212 M

[B] = 1.83 + 0.02880 = 1.8588 M