Question

Which of the following statements are correct about equilibrium constant for a gaseous phase reaction?

• A. Equilibrium constant expressed in terms of partial pressures has the unit of (pressure unit)${}^{\Delta n}$
• B. Equilibrium constant expressed in terms of concentrations has the unit of (concentration)${}^{\Delta n}$
• C. Equilibrium constant expressed in terms of relative activity (i.e., the activity of substance relative to its activity in standard state) has no unit
• D. Equilibrium constant is written simply as $K^0$ in terms of relative activity $=K_p\times P^0$ where, $P^0=100kPa$ in standard state for gases

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Equilibrium constant expressed in terms of partial pressures has the unit of (pressure unit)${}^{\Delta n}$
B Equilibrium constant expressed in terms of concentrations has the unit of (concentration)${}^{\Delta n}$
C Equilibrium constant is written simply as $K^0$ in terms of relative activity $=K_p\times P^0$ where, $P^0=100kPa$ in standard state for gases
D Equilibrium constant expressed in terms of relative activity (i.e., the activity of substance relative to its activity in standard state) has no unit

Equilibrium constant is the ratio of the product of the active masses of products to the ratio of the product of the active masses of reactants. The active masses are raised to appropriate stoichiometric coefficients.

All the four statements are correct about equilibrium constant for a gaseous phase reaction.

(A) Equilibrium constant expressed in terms of partial pressures has the unit of (pressure unit)${}^{\Delta n}$

Here, $\Delta n$ is the difference in the total number of gaseous products to total number of gaseous reactants. When $\Delta n=0$, the equilibrium constant expressed in terms of partial pressures becomes unitless.

(B) Equilibrium constant expressed in terms of concentrations has the unit of (concentration)${}^{\Delta n}$

Here, $\Delta n$ is the difference in the total number of gaseous products to total number of gaseous reactants. When $\Delta n=0$, the equilibrium constant expressed in terms of concentrations becomes unitless.

(C) Equilibrium constant expressed in terms of relative activity (i.e., the activity of substance relative to its activity in standard state) has no unit

This is because relative activity is the ratio of two quantities having same units. Hence, relative activity is dimensionless.

(D) Equilibrium constant is written simply as $K^0$ in terms of relative activity $=K_p\times P^0$ where, $P^0=100kPa$ in standard state for gases.

Here 100 kPa equals approx. 1 atm.