Question

The standard Gibbs energy change at $300K$ for the reaction $2A\leftrightharpoons B+C$ is $2494.2J$. At a given time, the composition of the reaction mixture is [A] = $\frac{1}{2}$, [B] = $2$ and [C] $=\frac{1}{2}$. The reaction proceeds in the : [$R=8.314J/K/mol,e=2.718$]

• A. forward direction because $Q>$ $K_e$
• B. reverse direction because $Q>$ $K_e$
• C. forward direction because $Q<$ $K_e$
• D. reverse direction because $Q<$ $K_e$

Answer 1

The correct option is B reverse direction because $Q>$ $K_e$

The expression for the reaction quotient $Q$ is $Q=\frac{\left[B\right]\left[C\right]}{[A{]}^2}$
Substitute values in the above expression.

$Q=\frac{2\times \frac{1}{2}}{(\frac{1}{2}{)}^2}=4$

The relationship between the standard Gibbs free energy change and the equilibrium constant is $\Delta G=-2.303RTlogK$

Substitute values in the above expression.

$2494.2=-2.303\times 8.314\times 300logK$

$-0.4342=logK$

$K=0.37$

Thus, the value of the reaction quotient $Q$ (4) is greater than the value of the equilibrium constant, $K$.

Hence, the equilibrium will shift in the reverse direction and more reactants will be obtained.