In: Chemistry
A reaction: A (aq) + B (aq) <-----> C (aq) has a standard free energy change of -3.05 kJ/mol at 25 C. What are the concentrations of A, B, and C at equilibrium if, at the beginning of the reaction, their concentrations are 0.30 M, 0.40 M, and 0 M, respectively?
A = ? M
B= ? M
C= ? M
How would your answer above change if the reaction had a standard free energy change of +3.05 kJ/mol?
A.) There would be no change to the answers.
B.) All concentrations would be higher.
C.) All concentrations would be lower.
D.) There would be more A and B, but less C.
E.) There would be less A and B, but more C.
Answer – In this question there are given, standard free energy change ∆Go = -3.05 kJ
Reaction - A(aq) + B (aq) <-----> C (aq)
[A] = 0.3 M , [B]= 0.40 M, T = 25+273 = 298 K
First we need to calculate equilibrium constant from the standard free energy change
We know formula
∆Go = -RTlnK
-3.05*103 J = - 8.314 J/mol.K * 298 K * ln K
-3.05*103 J / - 8.314 J/mol.K * 298 K = ln K
So, ln K = 1.23
Taking antiln from both side
K = 3.43
Now we need to write the ICE table –
A(aq) + B (aq) <-----> C (aq)
I 0.30 0.40 0.0
C -x -x +x
E 0.30-x 0.40-x +x
We know
K = [C] / [A] [B]
3.43 = x / (0.30-x)(0.40-x)
3.43 [(0.30-x)(0.40-x)] = x
3.43x2 -2.401x+0.412 = x
3.43x2-3.401x+0.412 = 0
So using the quadratic equation
x = 0.162 M
so, at equilibrium
[A] = 0.30-x = 0.30-0.162 = 0.138 M
[B]= 0.40-x = 0.40-0.162 = 0.238 M
[C] = x = 0.162 M
If the reaction had a standard free energy change of +3.05 kJ/mol then equilibrium constant gets decreased and hence there is product formed less and reactant remaining more
So answer is - D.) There would be more A and B, but less C.