Question

A reaction A(aq)+B(aq)↽−−⇀C(aq) has a standard free‑energy change of −4.51 kJ/mol at 25 °C.

Answer 1

Answer:

(a) [A] = 0.13 M, [B]= 0.23 M and [C] = 0.17 M.

(b) Option B.

Explanation:

The reaction given:

                     A(aq)  +  B(aq)  ⇄  C(aq)      (1)

Initial:            0.30M   0.40M      0M         (2)                

Equilibrium:  0.3 - x     0.4 - x       x           (3)

The equation of Gibbs free energy of the reaction (1) is the following:

$\Delta G^{\circ} = - RTLn(K_{eq})$    (4)

where ΔG°: is the Gibbs free energy change at standard conditions, R: is the gas constant, T: is the temperature and $K_{eq}$: is the equilibrium constant

(a) To calculate the concentrations of A, B, and C at equilibrium, we need first determinate the equilibrium constant using equation (4), with ΔG°=-4.51x10³J/mol, T=25 + 273 = 298 K, R=8.314 J/K.mol:

$K_{eq} = e^{-\frac{\Delta G^{\circ}}{RT}} = e^{-\frac{-4.51\cdot 10^{3} J/mol}{8.314 J/K.mol \cdot 298 K}} = 6.17$      (5)

Now, we can calculate the concentrations of A, B, and C at equilibrium using the equilibrium constant calculated (5):

$K_{eq} = \frac{[C]}{[A][B]} = \frac{x}{(0.3 - x)(0.4 - x)}$     (6)    

Solving equation (6) for x, we have two solutions x₁=0.69 and x₂=0.17, and by introducing the solution x₂ into equation (3) we can get the concentrations of A, B, and C at equilibrium:                          

$[A] = 0.3 - x_{2} = 0.3 - 0.17 = 0.13 M$

$[B] = 0.4 - x_{2} = 0.4 - 0.17 = 0.23 M$

$[C] = x = 0.17 M$

Notice that the solution x₁=0.69 would have given negative values of the A and B concentrations.  

(b) If the reaction had a standard free-energy change of +4.51x10³J/mol, the equilibrium constant would be:

$K_{eq} = e^{-\frac{\Delta G^{\circ}}{RT}} = e^{-\frac{4.51\cdot 10^{3} J/mol}{8.314 J/K.mol \cdot 298 K}} = 0.16$

By solving the equation (6) for x, with the equilibrium constant calculated, we can get again two solutions x₁ = 6.9 and x₂= 0.017, and by introducing the solution x₂ into equation (3) we can get the concentrations of A, B, and C at equilibrium:

$[A] = 0.3 - x_{2} = 0.3 - 0.017 = 0.28 M$

$[B] = 0.4 - x_{2} = 0.4 - 0.017 = 0.38 M$

$[C] = x = 0.017 M$        

Again, the solution x₁=6.9 would have given negative values of the A and B concentrations.

Hence, the correct answer is option B: there would be more A and B but less C.

I hope it helps you!