The Gibbs free energy change (ΔG) determines the direction of a reaction. The relationship is given by:

$\mathrm{\Delta }G=\mathrm{\Delta }{G}^{°}+RT\ln Q$

where ΔG° is the standard Gibbs energy change, R is the gas constant, T is the temperature in Kelvin, and Q is the reaction quotient.

For the reaction $2A\rightleftharpoons B+C$, the reaction quotient Q is calculated as:

$Q=\frac{\left[B\right]\left[C\right]}{[A{]}^2}$

Given concentrations: [A] = 1/2, [B] = 2, [C] = 1/2. Substituting these values:

$Q=\frac{\left(2\right)(1/2)}{(1/2{)}^2}=\frac{1}{1/4}=4$

The equilibrium constant K_c is related to ΔG° by:

$\mathrm{\Delta }{G}^{°}=-RT\ln K$

Given ΔG° = 2494.2 J, R = 8.314 J/K/mol, T = 300 K. Solving for K:

$2494.2=-8.314\times 300\times \ln K$

$\ln K=-\frac{2494.2}{8.314\times 300}=-\frac{2494.2}{2494.2}=-1$

Thus, K = e^-1 = 1/2.718 ≈ 0.3679

Now, compare Q and K. Q = 4 and K ≈ 0.3679, so Q > K.

When Q > K, the reaction proceeds in the reverse direction to reach equilibrium.

Therefore, the correct option is: reverse direction because Q > K_C.

Related Topics

Gibbs Free Energy and Spontaneity: Gibbs free energy (ΔG) indicates whether a reaction is spontaneous (ΔG < 0) or non-spontaneous (ΔG > 0). The standard Gibbs energy change (ΔG°) relates to the equilibrium constant.

Reaction Quotient (Q) and Equilibrium Constant (K): Q is calculated using current concentrations, while K is the value at equilibrium. Comparing Q and K determines the reaction direction: if Q < K, reaction proceeds forward; if Q > K, reaction proceeds reverse; if Q = K, the system is at equilibrium.

Formulae

$\mathrm{\Delta }G=\mathrm{\Delta }{G}^{°}+RT\ln Q$

$\mathrm{\Delta }{G}^{°}=-RT\ln K$

For a reaction aA + bB ⇌ cC + dD, $Q=\frac{\left[C{]}^c\right[D{]}^d}{\left[A{]}^a\right[B{]}^b}$