Question

The water-gas shift reaction \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons\) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) is used industrially to produce hydrogen. The reaction enthalpy is \(\Delta H^{\circ}=-41 \mathrm{kJ}\) . (a) To increase the equilibrium yield of hydrogen would you use high or low temperature? ( b) Could you increase the equilibrium yield of hydrogen by controlling the pressure of this reaction? If so would high or low pressure favor formation of \(\mathrm{H}_{2}(g) ?\)

Short answer

To increase the equilibrium yield of hydrogen in the water-gas shift reaction, a low temperature should be used. Controlling the pressure will have no effect on the equilibrium yield of hydrogen in this reaction since the number of moles of gas on both sides of the reaction is equal.

Step-by-step solution

(a) Impact of Temperature on Equilibrium Yield of Hydrogen

Le Chatelier's principle states that if a dynamic equilibrium system is subjected to some change, the system will adjust itself to minimize the effect of that change. In this case, the reaction is exothermic, which means it releases heat. An exothermic reaction can be represented as: \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) + Heat\) To increase the equilibrium yield of hydrogen, we need to shift the equilibrium towards the products. According to Le Chatelier's principle, we should consider the following changes: 1. If we increase the temperature, the system will try to minimize the effect of increased heat by shifting the equilibrium towards the reactants (where heat is absorbed and less heat is produced). This would result in a lower yield of hydrogen. 2. If we decrease the temperature, the system will try to minimize the effect of decreased heat by shifting the equilibrium towards the products (where heat is released). This would result in a higher yield of hydrogen. So, to increase the equilibrium yield of hydrogen, we should use a low temperature.

(b) Impact of Pressure on Equilibrium Yield of Hydrogen

To analyze the effect of pressure on equilibrium, we should look at the number of moles of gas on both sides of the reaction: Reactants: 1 mole CO + 1 mole H2O Products: 1 mole CO2 + 1 mole H2 The number of moles of gas on both sides of the reaction is equal. According to Le Chatelier's principle, changing the pressure will have no effect on the position of the equilibrium if there are no differences in the number of moles of gas between the reactants and products. So, we cannot increase the equilibrium yield of hydrogen by controlling the pressure in this reaction.

Key concepts

Water-Gas Shift Reaction

The water-gas shift reaction is a vital industrial process used to produce hydrogen. The reaction takes place between carbon monoxide (CO) and water vapor (H₂O), resulting in carbon dioxide (CO₂) and hydrogen gas (H₂). It is represented by the equation:
\( \mathrm{CO}(g) + \mathrm{H}_2 \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_2(g) + \mathrm{H}_2(g) \).
This reaction is important because hydrogen is a crucial component in various industrial applications, including the production of ammonia and fuel cells. By shifting the equilibrium towards the products, we can increase the yield of hydrogen, which is the primary goal of optimizing this reaction.

Exothermic Reaction

An exothermic reaction is one that releases heat into the surroundings during the process. In the case of the water-gas shift reaction, it has a negative enthalpy change (\( \Delta H^{\circ}=-41 \mathrm{kJ} \)), indicating it releases heat.

• This release of heat can be thought of as a product of the reaction.
• Exothermic reactions generally result in a temperature increase of the surroundings.

Understanding whether a reaction is exothermic helps in predicting how changes in temperature will affect the equilibrium position, which is crucial for manufacturing processes.

Equilibrium Yield

The equilibrium yield refers to the amount of products formed when a reaction reaches a state of dynamic equilibrium.
This is the point where the forward and reverse reaction rates are equal.

• In the water-gas shift reaction, the equilibrium yield of hydrogen is influenced by various factors, including temperature and pressure.
• Optimizing conditions can maximize the production of hydrogen.

Reaching an optimal equilibrium yield is essential for efficiency and cost-effectiveness in industrial settings.

Impact of Temperature on Equilibrium

Temperature changes can significantly affect reaction equilibrium. Using Le Chatelier's Principle, we can predict reactions to temperature changes.

• In exothermic reactions like the water-gas shift reaction, increasing the temperature shifts the equilibrium towards the reactants, reducing hydrogen yield.
• Conversely, decreasing the temperature shifts the equilibrium towards the products, thus increasing the yield of hydrogen.

Therefore, to maximize hydrogen production in an exothermic reaction, a lower temperature is generally more favorable.

Impact of Pressure on Equilibrium

Pressure changes influence reactions involving gases, depending on the difference in the number of gas moles on each side of the equation. For the water-gas shift reaction:

• The number of gas moles on both sides is equal (2 moles each).
• According to Le Chatelier's principle, this means that changes in pressure have no effect on the equilibrium position.

Thus, modifying the pressure does not change the equilibrium yield of hydrogen in this particular reaction. Understanding these dynamics helps in designing efficient industrial processes.