Problem 107 - Chemistry

Question

Consider the following exothermic reaction at equilibrium: $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$ Predict how the following changes affect the number of moles of each component of the system after equilibrium is reestablished by completing the table below. Complete the table with the terms increase, decrease, or no change.

Step-by-Step Solution

Answer

In summary, applying Le Chatelier's Principle to the given exothermic reaction and analyzing different disturbances yields the following changes in the number of moles for each case: 1. Increasing moles of N2: - N2: Increase - H2: Decrease - NH3: Increase 2. Decreasing moles of H2: - N2: Increase - H2: Decrease - NH3: Decrease 3. Increasing moles of NH3: - N2: Increase - H2: Increase - NH3: Increase 4. Decreasing moles of NH3: - N2: Decrease - H2: Decrease - NH3: Decrease

Step 1: Le Chatelier's Principle

Le Chatelier's principle states that when a chemical system at equilibrium is disturbed, the system will adjust itself to counteract the change and restore the equilibrium. In this case, we will apply this principle to predict how the changes in the system will affect the number of moles of each component. We have the following equilibrium reaction: \[\mathrm{N}_{2}(g) + 3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\] Now, let's examine each row in the given table. 1. Increasing the moles of N2:

Step 2: Forward reaction

Adding more N2 will shift the equilibrium towards the forward reaction, increasing the formation of NH3. Consequently, the moles of H2 will decrease as they are being consumed in the reaction. - N2: Increase - H2: Decrease - NH3: Increase 2. Decreasing the moles of H2:

Step 3: Reverse reaction

Removing H2 will shift the equilibrium towards the reverse reaction to compensate for the loss, leading to decreased formation of NH3. The backward reaction will produce more N2. - N2: Increase - H2: Decrease - NH3: Decrease 3. Increasing the moles of NH3:

Step 4: Reverse reaction

Adding more NH3 will shift the equilibrium towards the reverse reaction. Consequently, the moles of N2 and H2 will increase as NH3 is being consumed in the backward reaction. - N2: Increase - H2: Increase - NH3: Increase 4. Decreasing the moles of NH3:

Step 5: Forward reaction

Removing NH3 will shift the equilibrium towards the forward reaction to compensate for the loss, leading to increased formation of NH3. The forward reaction will consume more N2 and H2. - N2: Decrease - H2: Decrease - NH3: Decrease These are the predicted changes in the number of moles for each component in the reaction based on Le Chatelier's Principle.

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs in a reversible reaction when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time, although they are not necessarily equal. For a chemical reaction, such as the one between nitrogen gas (\(\mathrm{N}_2\)) and hydrogen gas (\(\mathrm{H}_2\)), forming ammonia (\(\mathrm{NH}_3\)), equilibrium is dynamic. This means that reactions continue to occur, but there is no net change in the concentrations of products and reactants.

An important aspect of chemical equilibrium is the equilibrium constant, \(K\). This can be expressed as the ratio of the concentration of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced chemical equation. In the case of our reaction, it is:

• \(K = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3}\)

Factors like temperature, pressure, and concentration can shift the equilibrium position, causing changes in \(K\). When these changes occur, the system will attempt to restore equilibrium by adjusting the rates of the forward and reverse reactions according to Le Chatelier's Principle.

Exothermic Reactions

Exothermic reactions are processes that release energy in the form of heat or light. In these reactions, the energy of the products is lower than the energy of the reactants. This means energy is released as the chemical bonds are formed in the products. In the reaction \(\mathrm{N}_2(g) + 3 \mathrm{H}_2(g) \rightarrow 2 \mathrm{NH}_3(g)\), it is exothermic because forming ammonia releases energy, typically in heat form, to the surroundings.

A distinct feature of exothermic reactions is that increasing the temperature typically shifts the equilibrium toward the reactants. This is because, according to Le Chatelier’s Principle, the system will attempt to absorb the added heat by favoring the endothermic direction (in this case, the reverse reaction). This behavior can impact how much product is formed or how much reactants are consumed when temperature changes. In practical terms, for processes like ammonia synthesis, adjusting temperature and other conditions can optimize yield and efficiency.

Reaction Kinetics

Reaction kinetics examines the rate at which chemical reactions occur and the factors affecting these rates. The reaction rate depends on the concentration of reactants, temperature, presence of catalysts, and the nature of the reactants.

In the given reaction between nitrogen and hydrogen to form ammonia, kinetics is important to understand how fast the equilibrium is reached. Reaction rates increase with higher temperatures due to increased molecular collisions and energy levels; however, this comes with the trade-off of altering the equilibrium position for exothermic reactions.

• Higher temperature speeds up reaction rates but may shift the equilibrium towards the reactants, reducing ammonia yield.
• Using a catalyst, like iron in the Haber process, helps overcome activation energy barriers, speeding up both forward and reverse reactions without affecting the equilibrium position.

Understanding the reaction kinetics allows chemists and engineers to design processes that maximize efficiency while achieving desired product concentrations. Mitigating these factors aids in practical and economical industrial applications, such as ammonia production for fertilizers.