Question

Ammonia is produced by the Haber process, in which nitrogen and hydrogen are reacted directly using an iron mesh impregnated with oxides as a catalyst. For the reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ equilibrium constants ( \(K_{\mathrm{p}}\) values) as a function of temperature are \(300^{\circ} \mathrm{C}, \quad 4.34 \times 10^{-3}\) \(500^{\circ} \mathrm{C}, \quad 1.45 \times 10^{-5}\) \(600^{\circ} \mathrm{C}, \quad 2.25 \times 10^{-6}\) Is the reaction exothermic or endothermic?

Short answer

The Haber process is an exothermic reaction, as the value of the equilibrium constant Kp decreases with an increase in temperature.

Step-by-step solution

Analyze the given data

We are given three sets of temperature and Kp values for the Haber process: \(300^{\circ} \mathrm{C}\), \(K_{\mathrm{p}} = 4.34 \times 10^{-3}\) \(500^{\circ} \mathrm{C}\), \(K_{\mathrm{p}} = 1.45 \times 10^{-5}\) \(600^{\circ} \mathrm{C}\), \(K_{\mathrm{p}} = 2.25 \times 10^{-6}\) From the data, we can observe that as the temperature increases, the value of the equilibrium constant Kp decreases.

Determine if the reaction is exothermic or endothermic

Based on our observation in Step 1, we conclude that as the temperature increases, the value of Kp decreases, which indicates that the reaction is favoured at lower temperatures. This behaviour is characteristic of an exothermic reaction. Therefore, the Haber process in which ammonia is produced is an exothermic reaction.

Key concepts

Equilibrium Constants

The equilibrium constant, represented as \( K_{\mathrm{p}} \), is a vital aspect of the Haber process.
It provides a numerical measure of the position of equilibrium in the reaction between nitrogen \(( N_{2} )\) and hydrogen \(( H_{2} )\) to form ammonia \(( NH_{3} )\).
Simply put, \( K_{\mathrm{p}} \) expresses the ratio of the concentration of products to reactants at equilibrium, with each raised to the power of their respective coefficients in the balanced equation.

In the case of the Haber process:- \[ N_{2}(g) + 3 H_{2}(g) \rightleftharpoons 2 NH_{3}(g) \]- The equilibrium expression in terms of partial pressures is \( K_{\mathrm{p}} = \frac{(P_{\mathrm{NH}_{3}})^2}{(P_{\mathrm{N}_{2}})(P_{\mathrm{H}_{2}})^3} \).

At different temperatures, the value of \( K_{\mathrm{p}} \) will change, reflecting the dynamics of the system. A higher \( K_{\mathrm{p}} \) value implies that the equilibrium position favors the formation of products. Conversely, a lower \( K_{\mathrm{p}} \) indicates more of the reactants are present at equilibrium.
In the Haber process, adjustments in temperature significantly influence \( K_{\mathrm{p}} \), highlighting the reaction's specific temperature dependency.

Exothermic Reaction

An exothermic reaction is one where heat is released as the reaction occurs.
This implies that the chemical energy of the reactants is higher than that of the products, and the excess energy is given off, typically as heat.

For the Haber process, the observed decrease in \( K_{\mathrm{p}} \) values with increasing temperature is characteristic of an exothermic reaction. - If a reaction is exothermic, equilibrium shifts in favor of the products at lower temperatures because the system releases heat. - If the temperature is increased, the position of equilibrium will shift to absorb the added heat, favoring the reactants, hence the decrease in \( K_{\mathrm{p}} \).

This effect is explained by Le Chatelier's Principle, which states that a system in equilibrium will adjust to counteract the effects of a change in its conditions, such as temperature.

Ammonia Production

The Haber process is the predominant method for industrial ammonia production, fundamentally crucial for fertilizers.
Ammonia itself is a simple compound of nitrogen and hydrogen, but its synthesis on a large scale was a major achievement in chemistry.

The reaction is carried out under high pressures and moderate temperatures, with an iron catalyst to increase the rate of reaction. - Typically, pressures are around 150-200 atm, while temperatures are set between 400-500°C. - The catalyst used often includes iron infused with small amounts of oxides to enhance its activity.

The principles of chemical equilibrium and reaction kinetics are essential in optimizing the conditions for ammonia synthesis. While lower temperatures favor a higher yield of ammonia due to the exothermic nature of the reaction, temperatures must be sufficiently high to ensure a suitable rate of production. Thus, the Haber process represents a delicate balance between achieving high efficiency and maintaining effective reaction conditions.