Question

If \(\mathrm{K}_{\mathrm{C}}\) for the formation of ammonia is \(2 \mathrm{moles}^{-2} \ell^{2}\), \(\mathrm{K}_{\mathrm{c}}\) for decomposition of ammonia is ___________.

Short answer

Answer: The equilibrium constant for the decomposition of ammonia is 0.5 moles²L⁻².

Step-by-step solution

Write the balanced equation for the formation of ammonia.

The balanced equation for the formation of ammonia is: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Calculate the equilibrium constant for the decomposition of ammonia.

The decomposition of ammonia is the reverse reaction of its formation, so the balanced equation for the decomposition of ammonia is: 2NH₃(g) ⇌ N₂(g) + 3H₂(g) Since the decomposition of ammonia is the reverse reaction of its formation, the equilibrium constants are inversely related. If we denote the equilibrium constant for the formation of ammonia as \(\mathrm{K_{C_{formation}}}\) and the equilibrium constant for the decomposition of ammonia as \(\mathrm{K_{C_{decomposition}}}\), then: \(\mathrm{K_{C_{decomposition}}} = \frac{1}{\mathrm{K_{C_{formation}}}}\) Given, \(\mathrm{K_{C_{formation}}} = 2 \, \mathrm{moles}^{-2}\ell^{2}\). Substituting the value in the equation above, we get: \(\mathrm{K_{C_{decomposition}}} = \frac{1}{2 \, \mathrm{moles}^{-2}\ell^{2}}\)

Simplify the expression for the equilibrium constant for the decomposition of ammonia

To find \(\mathrm{K_{C_{decomposition}}}\), simplify the expression: \(\mathrm{K_{C_{decomposition}}} = \frac{1}{2 \, \mathrm{moles}^{-2}\ell^{2}}\) \(\mathrm{K_{C_{decomposition}}} = 0.5 \, \mathrm{moles}^{2}\ell^{-2}\) So, the equilibrium constant for the decomposition of ammonia is \(0.5 \, \mathrm{moles}^{2}\ell^{-2}\).

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate. This dynamic equilibrium means that the concentrations of reactants and products remain constant over time. At equilibrium, reactions are still occurring, but there is no net change in concentrations.
For a given reaction, the equilibrium constant, represented as \( K_C \), quantifies the ratio of the concentrations of products to reactants, each raised to the power of their coefficients in the balanced equation. A large \( K_C \) indicates more products are present at equilibrium, while a small \( K_C \) suggests more reactants remain.
Understanding chemical equilibrium helps chemists predict the outcome of reactions and optimize conditions in industrial processes.

Reversible Reactions

Reversible reactions are those that can proceed in both directions: from reactants to products and vice versa. Such reactions often reach a state of equilibrium, where the forward and reverse reactions occur at equal rates.
These reactions are denoted with a double arrow symbol (⇌) in chemical equations. For example, the formation of ammonia from nitrogen and hydrogen is a reversible reaction: \( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \).
Reversible reactions play a crucial role in various natural and industrial processes because they offer flexibility in synthetically manipulating conditions to achieve desired product yields by shifting the equilibrium position either towards products or reactants.

Ammonia Synthesis

Ammonia synthesis is a chemical process where nitrogen and hydrogen gases react to form ammonia, represented by the equation \( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \). This process is fundamental in producing fertilizers essential for agriculture.
The synthesis of ammonia is typically carried out under high pressure and temperature using a catalyst in the Haber-Bosch process. This increases the reaction rate and shifts equilibrium towards ammonia production.
Understanding the equilibrium dynamics of this reaction allows chemists to adjust conditions like pressure and temperature to maximize ammonia yield, offering economic and environmental benefits.

Reaction Kinetics

Reaction kinetics refers to the study of the rates at which chemical processes occur and the factors that influence these rates. Knowing how fast a reaction proceeds can help in understanding and controlling reactions in both laboratory and industrial settings.
Several factors affect reaction rates, including temperature, concentration of reactants, surface area, and the presence of catalysts. For example, increasing temperature typically increases the rate of a reaction.
In the context of ammonia synthesis, reaction kinetics is crucial because it helps determine optimal conditions for both rate and yield. The use of catalysts can lower activation energy, significantly speeding up the reaction and making the industrial synthesis of ammonia viable at a commercial scale.