Problem 70 - Chemistry An Atoms First Approach

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 \(\mathbf{r}_{\mathbf{p}}\).\(300^{\circ} \mathrm{C}, \quad 4.34 \times 10^{-3}\) \(500^{\circ} \mathrm{C}, \quad 1.45 \times 10^{-5}\) \(600^{\circ} \mathrm{C}, \quad 2.25 \times 10^{-6}\) Is the reaction exothermic or endothermic?

Step-by-Step Solution

Answer

The reaction is exothermic because the equilibrium constant decreases with an increase in temperature, indicating a negative enthalpy change (ΔH).

Step 1: Observe the equilibrium constants' behavior at different temperatures

Observe the given equilibrium constants (K) and their corresponding temperatures (T): - \(300^{\circ} \mathrm{C}\) and K = \(4.34 \times 10^{-3}\) - \(500^{\circ} \mathrm{C}\) and K = \(1.45 \times 10^{-5}\) - \(600^{\circ} \mathrm{C}\) and K = \(2.25 \times 10^{-6}\) As the temperature increases from \(300^{\circ} \mathrm{C}\) to \(500^{\circ} \mathrm{C}\) and further to \(600^{\circ} \mathrm{C}\), the equilibrium constant decreases.

Step 2: Determine the nature of the reaction

Since the equilibrium constant decreases with an increase in temperature, the reaction is exothermic. The negative enthalpy change (ΔH) causes the decrease in equilibrium constant as the temperature increases. So, the given reaction is exothermic.

Key Concepts

Chemical Equilibrium

The behavior of chemical reactions can be quite complex, especially when they reach a state called chemical equilibrium. Imagine a busy downtown where traffic is coming from different directions, and at some point, the number of cars entering is equal to the number leaving – that's a simple way of looking at equilibrium in a reaction.

When a reaction reaches chemical equilibrium, the rates of the forward and reverse reactions are equal. This means that the concentrations of the reactants and products remain constant over time, but not necessarily equal, because the system is balanced. It's important to note that equilibrium represents a dynamic balance; even though concentrations remain constant, the reactants are still converting into products and vice versa, but at identical rates.

In the case of the Haber process for producing ammonia, nitrogen and hydrogen gases react to form ammonia, and this reaction can also reverse – ammonia can decompose back into nitrogen and hydrogen. Equilibrium is reached when the rate of formation of ammonia equals the rate of its decomposition.

Equilibrium Constant

The equilibrium constant, represented by the symbol K, is a number that provides a lot of information about a chemical reaction at equilibrium. It's like a scorecard that tells you which team is 'winning' in a sports game where the teams are the reactants and products in a chemical reaction.

Mathematically, it's determined by the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their respective coefficients from the balanced chemical equation. For the Haber process the equation looks like this: \( K = \frac{[NH_3]^2}{[N_2][H_2]^3} \).

The magnitude of the equilibrium constant gives us insight into the position of the equilibrium: a larger value, much greater than 1, means there's more product than reactant, while a smaller value, much less than 1, suggests there's more reactant. The given equilibrium constants for the Haber process at different temperatures show this 'score' changes with temperature, implying the position of equilibrium shifts with temperature changes.

Exothermic Reaction

An exothermic reaction is one that releases heat; it's like a natural hand warmer providing toasty warmth on a cold day. In other words, it's a chemical reaction that results in a net release of energy to the surroundings - think of it as the chemical formula for a miniature sun.

The heat released during these reactions can often be felt or measured with a thermometer. In the context of the Haber process, we can infer that it is exothermic because as the temperature is increased, the equilibrium constant decreases. It's like the reaction doesn't 'want' to form as much product at higher temperatures because it's already getting heat from the surroundings, which is enough to satisfy its energy release 'needs'.

Physically, this decrease in the equilibrium constant with increasing temperature supports the idea that heat is a product of the reaction – and according to Le Chatelier's principle, adding more of a product, in this case heat, will shift the equilibrium to favor the reactants, hence the decrease in equilibrium constant values.