Problem 68 - Chemistry The Central Science In Si Units

Question

Bromine and hydrogen react in the gas phase to form hydrogen bromide: \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)\). The reaction enthalpy is \(\Delta H^{\circ}=-6 \mathrm{~kJ} .(\mathbf{a})\) To increase the equilibrium yield of hydrogen bromide would you use high or low temperature? (b) Could you increase the equilibrium yield of hydrogen bromide by controlling the pressure of this reaction? If so, would high or low pressure favor formation of \(\mathrm{HBr}(g)\) ?

Step-by-Step Solution

Answer

Low temperature increases HBr yield; pressure has no effect.

Step 1: Analyze Reaction Enthalpy

The reaction enthalpy \(\Delta H^{\circ} = -6 \, \text{kJ/mol}\) shows that the formation of hydrogen bromide is exothermic since it is negative. An exothermic reaction releases heat.

Step 2: Applying Le Châtelier’s Principle to Temperature

According to Le Châtelier's principle, when the temperature of an exothermic reaction is increased, the equilibrium will shift to favor the reactants to absorb the extra heat. Conversely, lowering the temperature will shift the equilibrium to the right, favoring the formation of products. Therefore, to increase the yield of hydrogen bromide, a low temperature should be used.

Step 3: Analyze Pressure Change

Count the moles of gases on each side of the reaction: \( 1 \, \text{mol} \, \text{H}_2 + 1 \, \text{mol} \, \text{Br}_2 \) (total \(= 2 \, \text{mol}\)) on the reactant side, and \( 2 \, \text{mol} \, \text{HBr} \) on the product side. The total number of moles is equal on both sides: there is no net change in the number of moles of gas.

Step 4: Apply Pressure Effect Analysis

Since there is no change in the number of moles of gases from reactants to products, changing the pressure does not have an effect on the position of equilibrium according to Le Châtelier’s principle. Therefore, changing the pressure will not favor the formation of more hydrogen bromide.

Key Concepts

Reaction Enthalpy

When discussing chemical reactions, reaction enthalpy (\(\Delta H\)) is a crucial concept. It represents the heat change during a reaction, measured under constant pressure. For the reaction of bromine and hydrogen to form hydrogen bromide, the reaction enthalpy is given as \(-6 \, \text{kJ/mol}\). This negative value indicates that the reaction is exothermic. In simple terms, an exothermic reaction releases heat as it progresses.

• Positive \(\Delta H\) indicates endothermic reactions (heat absorbed).
• Negative \(\Delta H\) indicates exothermic reactions (heat released).

This concept is fundamental as it directly relates to how energy flows within a chemical system. Understanding whether a reaction is exothermic or endothermic gives insights into how temperature changes might affect the system.

Le Châtelier's Principle

In the world of chemical equilibrium, Le Châtelier's principle is a guiding star. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the change. For exothermic reactions like the one between bromine and hydrogen, temperature changes play a significant role.
When the temperature is increased, the system tends to shift towards the reactants to absorb the added heat. On the other hand, decreasing the temperature favors the products, as the system releases heat. Thus, for exothermic reactions, lowering the temperature can increase the yield of the desired product, such as hydrogen bromide.
This principle helps chemists predict how changes in conditions can affect reaction outcomes, making it essential for optimizing chemical processes.

Gas Phase Reactions

Gas phase reactions like the formation of hydrogen bromide occur entirely in the gaseous state. Understanding these reactions involves looking at factors like pressure and volume, which can affect the equilibrium. In the case of our reaction, the number of moles of gas on the reactant side equals the number of moles on the product side (\(1 \, \text{mol} \, \text{H}_2 \) + \(1 \, \text{mol} \, \text{Br}_2 \) versus \(2 \, \text{mol} \, \text{HBr}\)).

• Since there is no net change in the number of gas moles, pressure changes do not affect the equilibrium.
• Often in gas phase reactions, changes in pressure can shift equilibrium if there's a change in mole count.

In scenarios where mole counts differ, increased pressure typically shifts equilibrium towards the side with fewer moles, and vice versa. This characteristic is pivotal in designing reactions where pressure can be a tool for steering the equilibrium.

Exothermic Reactions

Exothermic reactions are characteristically heat-releasing processes. In the context of chemical equilibrium, recognizing a reaction as exothermic allows for predictions about how temperature shifts might alter equilibrium. When an exothermic reaction, such as the one forming hydrogen bromide from bromine and hydrogen, releases heat, it can be thought of as having heat as one of its products. Thus, in cold conditions, the equilibrium will favor product formation to "release" heat. - This inherent property makes exothermic reactions sensitive to temperature changes.
Understanding the nature of exothermic reactions helps in applications ranging from industrial chemical synthesis to environmental science, where managing heat release is critical.