Respuesta :
Answer: The concentration of A, B and C is 0.14 M, 0.24 M and 0.16 M respectively.
Explanation:
Relation between standard Gibbs free energy and equilibrium constant follows:
[tex]\Delta G^o=-RT\ln K_c[/tex]
where,
[tex]\Delta G^o[/tex] = standard Gibbs free energy = -3.87 kJ/mol = -3870 J/mol (Conversion factor: 1 kJ = 1000 J)
R = Gas constant = [tex]8.314J/K mol[/tex]
T = temperature = [tex]25^oC=[273+25]K=298K[/tex]
[tex]K_c[/tex] = equilibrium constant in terms of concentration
Putting values in above equation, we get:
[tex]-3870J/mol=-(8.314J/Kmol)\times 298K\times \ln K_c\\\\K_c=e^{1.562}=4.77[/tex]
The given chemical reaction follows:
[tex]A(aq.)+B(aq.)\rightleftharpoons C(aq.)[/tex]
Initial: 0.30 0.40 0
At eqllm: 0.30-x 0.40-x x
The expression of [tex]K_c[/tex] for above equation follows:
[tex]K_c=\frac{[C]}{[A]\times [B]}[/tex]
We are given:
[tex]K_c=4.77[/tex]
[tex][A]=0.30-x[/tex]
[tex][B]=0.40-x[/tex]
[tex][C]=x[/tex]
Putting values in above expression, we get:
[tex]4.77=\frac{x}{(0.30-x)\times (0.40-x)}\\\\x=0.16,0.75[/tex]
Neglecting the value of x = 0.75 because the equilibrium concentration cannot be greater than initial concentration.
So, concentration of A = (0.30 - x) = (0.30 - 0.16) = 0.14 M
Concentration of B = (0.40 - x) = (0.40 - 0.16) = 0.24 M
Concentration of C = x = 0.16 M
Hence, the concentration of A, B and C is 0.14 M, 0.24 M and 0.16 M respectively.
