For the reaction PCl5(g) → PCl3(g) + Cl2(g) at298 K, Keq = 1.87 × 10-7, what is ΔrG ° and isthe reaction spontaneous?

To find the ΔrG° (standard Gibbs free energy change) for the reaction, we can use the equation:

ΔrG° = -RT ln K

where: R is the universal gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin (298 K in this case), and K is the equilibrium constant (Keq = 1.87 × 10^-7).

Substituting the given values into the equation, we get:

ΔrG° = - (8.314 J/(mol·K)) * (298 K) * ln (1.87 × 10^-7) = 54.6 kJ/mol

The sign of ΔrG° determines whether the reaction is spontaneous. If ΔrG° is negative, the reaction is spontaneous. If ΔrG° is positive, the reaction is non-spontaneous. In this case, since ΔrG° is positive, the reaction is non-spontaneous at 298 K.