What is the Equilibrium Constant for the Reaction 2 NH3 (g) ? 1/2 N2 (g) 3/2 H2 (g) and How to Calculate It?

The equilibrium constant, denoted as K_c, is a measure of the extent to which a chemical reaction proceeds towards completion. For the specific reaction:

2 NH3 (g) ? 1/2 N2 (g) 3/2 H2 (g)

the equilibrium constant can be determined using the concentrations of the reactants and products. For a general reaction:

aA bB ? cC dD

the equilibrium constant expression is given by:

K_c [C]^c [D]^d / [A]^a [B]^b

Expressing the Equilibrium Constant for the Reaction

For the reaction 2 NH3 (g) ? 1/2 N2 (g) 3/2 H2 (g), the equilibrium constant expression is:

K_c [N2]^1/2 [H2]^3/2 / [NH3]^2

The coefficients in this expression are derived directly from the reaction equation, taking into account that the stoichiometric coefficients represent the molar concentrations of the species involved.

Numerical Value of the Equilibrium Constant

However, the specific numerical value of the equilibrium constant depends on the temperature. At 298 K (25 °C), the equilibrium constant for the typical ammonia synthesis reaction:

N2 (g) 3 H2 (g) ? 2 NH3 (g)

is reported as 6.8 × 10^5. For the reaction 1/2 N2 (g) 3/2 H2 (g) ? NH3 (g), the constant is the square root of the previous value, approximately 8.2 × 10^2. Conversely, for the decomposition reaction:

NH3 (g) ? 1/2 N2 (g) 3/2 H2 (g)

the equilibrium constant would be the reciprocal of the previous value, approximately 1.2 × 10^-3.

Factors Influencing the Equilibrium Constant

It is important to note that the equilibrium constant varies with temperature. The relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant (K) is given by:

ΔGo -RT ln K

where R is the gas constant, T is the temperature in Kelvin, and ΔGo is the standard Gibbs free energy change of the reaction.

For the reverse reaction (decomposition of NH3), the equilibrium constant is the reciprocal of the equilibrium constant for the forward reaction (synthesis of NH3), adjusted for the temperature.

Conclusion

Understanding the equilibrium constant for a specific reaction is crucial in chemical kinetics and thermodynamics. For the reaction 2 NH3 (g) ? 1/2 N2 (g) 3/2 H2 (g), the equilibrium constant expression is:

K_c [N2]^1/2 [H2]^3/2 / [NH3]^2

The numerical value, which varies with temperature, can be determined using thermodynamic data. This knowledge is essential for predicting the behavior of a reaction at equilibrium and for optimizing industrial processes like the Haber process for ammonia synthesis.