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 \(\Delta H^{\circ}=-6 \mathrm{~kJ} .\) (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 \(\mathrm{HBr}(g) ?\)

Short answer

(a) To increase the equilibrium yield of hydrogen bromide, we should use a low temperature since the reaction is exothermic. (b) Controlling the pressure of this reaction is not a suitable way to increase the equilibrium yield of hydrogen bromide, as the number of moles of gas on both sides of the reaction is equal.

Step-by-step solution

(a) Determine the effect of temperature on the yield of HBr using Le Chatelier's principle.

Since the reaction is exothermic (\(\Delta H^\circ < 0\)), using Le Chatelier's principle, we know that increasing the temperature will shift the reaction towards the side with more energy (the reactants) and decreasing the temperature will shift the reaction towards the side with less energy (the products). Therefore, to increase the equilibrium yield of hydrogen bromide, we should use a low temperature.

(b) Determine if pressure can be used to control the equilibrium yield of HBr.

To examine the effect of pressure on the equilibrium yield of HBr, we need to compare the number of moles of reactant gases (H2 and Br2) with the number of moles of product gas (HBr). In this reaction, we have: \[\mathrm{H}_2(g) + \mathrm{Br}_2(g) \rightleftharpoons 2 \mathrm{HBr}(g)\] There are initially 1 mole of H2 and 1 mole of Br2, making a total of 2 moles of reactant gases. After the reaction, there are 2 moles of HBr gas. Since the number of moles of gas on both sides of the reaction is equal (2 moles in both cases), changing the pressure will not significantly affect the position of the equilibrium. Thus, controlling the pressure of this reaction is not a suitable way to increase the equilibrium yield of hydrogen bromide.

Key concepts

Equilibrium Yield

The term "equilibrium yield" refers to the amount of product that is formed when a chemical reaction reaches equilibrium. At equilibrium, the forward and reverse reactions occur at the same rate, meaning the concentrations of reactants and products remain constant. In the case of the reaction between bromine (\(\mathrm{Br}_2\)) and hydrogen (\(\mathrm{H}_2\)) to form hydrogen bromide (\(\mathrm{HBr}\)), the goal is to maximize the production of \(\mathrm{HBr}\). Applying Le Chatelier's Principle can help shift the equilibrium to favor the products and thus increase the yield.

For the given reaction, the enthalpy change (\(\Delta H^{\circ}\)) is negative, indicating it is exothermic. According to Le Chatelier's Principle, if you decrease the temperature, the equilibrium will shift to partly offset this change by producing more heat. This compensatory effect shifts the equilibrium toward the side of the reaction that releases heat—the product side (hydrogen bromide) in an exothermic reaction. Therefore, reducing the temperature should increase the equilibrium yield of \(\mathrm{HBr}\).

Reaction Enthalpy

Reaction enthalpy (\(\Delta H\)) quantifies the heat change during a chemical reaction. It is a crucial factor for understanding how different conditions alter the equilibrium position of a reaction. A reaction can either absorb heat (endothermic) or release heat (exothermic). In the provided reaction, the negative enthalpy change (\(\Delta H^{\circ} = -6 \text{ kJ/mol}\)) signifies that the reaction is exothermic, meaning it releases heat.

When considering adjustments to a reaction, enthalpy provides guidance on how temperature changes can affect equilibrium. In an exothermic reaction, like this one, raising the temperature will favor the reverse reaction: shifting equilibrium towards the formation of reactants. This is because the system absorbs the additional heat by favoring the endothermic direction, which supplies more energy. Therefore, for an exothermic reaction, lowering the temperature will enhance the production of \(\mathrm{HBr}\), thereby increasing the equilibrium yield.

Effect of Pressure on Equilibrium

The effect of pressure on equilibrium is determined by the number of gas molecules on either side of a balanced chemical equation. Le Chatelier’s Principle indicates that a system at equilibrium will adjust to counteract changes imposed on it. However, if the number of gas moles on each side is the same, changing the pressure will not affect the equilibrium position.

In the reaction between \(\mathrm{H}_2\) and \(\mathrm{Br}_2\) to form \(\mathrm{HBr}\), the equation is:

• 1 mole of \(\mathrm{H}_2\)
• 1 mole of \(\mathrm{Br}_2\)
• equilibrium with 2 moles of \(\mathrm{HBr}\)

This indicates that the total amount of gas does not change—2 moles of gaseous reactants become 2 moles of gaseous products.

Thus, altering the pressure does not significantly shift the equilibrium. Pressure changes primarily affect reactions where the number of gas moles on one side is different from the other. Consequently, in this specific reaction, adjusting pressure is not an effective means to increase the equilibrium yield of \(\mathrm{HBr}\).