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

(a) A low temperature would increase the equilibrium yield of hydrogen in the water-gas shift reaction. (b) The equilibrium yield of hydrogen cannot be influenced by controlling the pressure of this reaction.

Step-by-step solution

Analyze the effect of temperature on equilibrium yield of hydrogen

To determine whether a high or low temperature would increase the equilibrium yield of hydrogen, we will use the reaction enthalpy (∆H°). The given reaction is exothermic since ∆H° = -41 kJ (negative value). According to Le Chatelier's principle, to increase the yield of an exothermic reaction, you should decrease the temperature. Likewise, if the reaction is endothermic (positive ∆H°), the equilibrium yield would increase with increasing temperature. Therefore, for this water-gas shift reaction, a low temperature would increase the equilibrium yield of hydrogen.

Analyze the effect of pressure on equilibrium yield of hydrogen

To determine the effect of pressure on the equilibrium yield of hydrogen, we need to identify the number of moles of gas on both sides of the equation. For the given reaction: CO (g) + H2O (g) ⇌ CO2 (g) + H2 (g) There are a total of 2 moles of gas on both sides of the equation (1 mole of CO + 1 mole of H2O ⇌ 1 mole of CO2 + 1 mole of H2). According to Le Chatelier's principle, if the number of moles of gas is the same on both sides of the equation, changing the pressure will not affect the position of the equilibrium. Thus, pressure will not influence the equilibrium yield of hydrogen in this reaction. In conclusion, (a) to increase the equilibrium yield of hydrogen, it is recommended to use a low temperature, and (b) the equilibrium yield of hydrogen cannot be influenced by controlling the pressure of this reaction.

Key concepts

Equilibrium Yield of Hydrogen

The equilibrium yield of hydrogen in the water-gas shift reaction is of paramount interest in industrial applications, especially when the aim is to maximize hydrogen production. Understanding how temperature affects this yield is crucial.
To put it simply, the equilibrium position of a reaction indicates the relative amounts of reactants and products present when the reaction has stabilized and no further changes occur without external influence. Lower temperatures generally favor the production of more hydrogen in exothermic reactions, like the water-gas shift reaction, due to the release of heat as part of the products' formation.

In industrial settings, fine-tuning the temperature to optimize hydrogen production involves a delicate balance. Too low of a temperature might slow the reaction rate significantly, whereas too high of a temperature could shift the equilibrium unfavorably. Despite these considerations, it's important to note that achieving high yield is not solely a factor of temperature but involves the entire reactor design, catalyst selection, and other operational parameters.

Reaction Enthalpy

The term 'reaction enthalpy' refers to the heat absorbed or released during a chemical reaction at constant pressure, labeled as \( \Delta H^\circ \).
In the water-gas shift reaction, \( \Delta H^\circ \) is negative, meaning it is an exothermic process—the system releases heat to its surroundings.

The value of \( \Delta H^\circ = -41 \mathrm{kJ} \) gives a direct insight into the nature of the reaction, which is also a determinant in applying Le Chatelier's principle. Knowing whether a reaction is endothermic or exothermic helps us predict and control the conditions favorable for a desired equilibrium state, which can be particularly handy in industrial optimizations where energy efficiency and product yield are critical.

Le Chatelier's Principle

Le Chatelier's principle is a foundational concept in chemistry that details how a dynamic equilibrium adjusts to counteract any changes in conditions.
When a reaction at equilibrium is disturbed by altering concentration, pressure, or temperature, the system will shift its equilibrium position to counteract the change — effectively trying to 'rebalance' itself. For the water-gas shift reaction, lowering the temperature encourages the system to produce more heat to compensate for the heat loss, shifting the equilibrium toward more product formation (hydrogen and carbon dioxide in this case).

As for pressure, if we had varying amounts of gas on each side of the reaction, changing the pressure would cause a shift in the equilibrium in the direction towards fewer gas molecules. However, in our case, since the reaction involves equal moles of gas on both sides, pressure changes do not affect the equilibrium yield of hydrogen.

Exothermic Reaction

An exothermic reaction, such as the water-gas shift reaction, releases energy in the form of heat. This is reflected by a negative \( \Delta H^\circ \) value.
During an exothermic reaction, the enthalpy of the products is lower than the enthalpy of the reactants because energy has been emitted to the surroundings. This release of energy is essential in many industrial processes, as it can reduce the energy required from external sources and improve overall efficiency.

In the context of the water-gas shift reaction, the exothermic nature implies that conducting the reaction at lower temperatures not only shifts the equilibrium towards a higher yield of hydrogen but also presents an energy-saving advantage, as less heat needs to be supplied to the system. The balance between reaction kinetics and thermodynamics is key to achieving optimal results in such exothermic processes.