Question

An important reaction in the commercial production of hydrogen is $$\mathrm{CO}(g)+{\mathrm{H}}_2\mathrm{O}(g)\rightleftharpoons {\mathrm{H}}_2(g)+{\mathrm{CO}}_2(g)$$ How will this system at equilibrium shift in each of the five following cases? a. Gaseous carbon dioxide is removed. b. Water vapor is added. c. In a rigid reaction container, the pressure is increased by adding helium gas. d. The temperature is increased (the reaction is exothermic). e. The pressure is increased by decreasing the volume of the reaction container.

Short answer

Case (a): The system shifts to the right as more CO and H2O react to produce H2 and CO2. Case (b): The system shifts to the right, increasing H2 and CO2 concentration while decreasing CO concentration. Case (c): No shift in equilibrium as adding helium gas doesn't affect the number of moles of reactants or products. Case (d): The system shifts to the left, increasing CO and H2O concentration and decreasing H2 and CO2 concentration. Case (e): No significant shift in equilibrium, as the number of moles of gas on each side is the same.

Step-by-step solution

Case (a): Gaseous carbon dioxide is removed.

If we remove CO2 from the system, the reaction will shift towards the right side to make up for the loss and reestablish the equilibrium. This means more CO (g) and H2O (g) will react to produce H2 (g) and CO2 (g). In this case, the concentration of CO2 will increase, and the concentration of CO and H2O will decrease.

Case (b): Water vapor is added.

If we add more water vapor (H2O) to the system, the reaction will shift towards the right side to consume the excess reactant and reestablish the equilibrium. This means more CO (g) and H2O (g) will react to produce H2 (g) and CO2 (g). In this case, the concentration of H2 and CO2 will increase, and the concentration of CO will decrease.

Case (c): Pressure is increased by adding helium gas in a rigid container.

Adding helium gas does not directly involve the reaction, so it will not affect the number of moles of reactants or products. However, adding helium gas increases the total pressure in the container. Since all the substances involved in the reaction are gases, their concentrations will be affected by the change in pressure, but because the number of moles of gases is the same on both sides of the equation, the reaction will remain at equilibrium. As a result, there will be no shift in equilibrium in this case.

Case (d): Temperature is increased (the reaction is exothermic).

An exothermic reaction is one that releases heat. When we increase the temperature of this system, the reaction will shift to the left to counteract the change, thereby absorbing the extra heat and reestablishing the equilibrium. In this case, the concentration of H2 (g) and CO2 (g) will decrease, and the concentration of CO (g) and H2O (g) will increase.

Case (e): Pressure is increased by decreasing the volume of the reaction container.

When the pressure is increased by decreasing the volume of the container, the reaction will shift to the side with a lesser number of moles of gas to counteract the change in pressure, which in this case is the right side. Both sides of the balanced equation have the same number of moles of gas (one mole each), so the system will not shift significantly in either direction. As a result, the equilibrium will remain relatively unchanged.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept used to predict how a change in conditions affects a chemical equilibrium. Essentially, it states that if an external change is applied to a system at equilibrium, the system will adjust itself to counteract that change and restore a new equilibrium.

For example, if you increase the concentration of a reactant, the equilibrium shifts to produce more product in order to reduce the reactant's excess. This principle is not only applicable to changes in concentration but also to changes in pressure and temperature.

• An increase in pressure will shift the equilibrium towards the side of the reaction with fewer moles of gas.
• For temperature changes, the system will behave differently depending on whether the reaction is exothermic or endothermic.

Le Chatelier's Principle helps us predict the direction of the shift but doesn't provide information on the speed at which equilibrium is reestablished, which is determined by reaction kinetics.

Equilibrium Shift

An equilibrium shift occurs when a chemical reaction at equilibrium experiences a disturbance such as changes in concentration, pressure, or temperature. When such changes are introduced, the system shifts in a direction that attempts to minimize the disturbance and restore equilibrium.

In the reaction involving carbon monoxide and water vapor to produce hydrogen and carbon dioxide, any of the following can cause a shift:

• Removing carbon dioxide shifts the equilibrium to the right to produce more CO₂, thus countering the removal.
• Conversely, adding water vapor causes a shift to the right, as well, to use up the added water vapor by producing more product.

Shifts are not always dramatic; for instance, adding a non-reactive gas like helium does not typically result in an equilibrium shift as it does not change the balance of reactant or product concentrations.

Endothermic vs Exothermic Reactions

Understanding endothermic and exothermic reactions is key to predicting how temperature changes will affect equilibrium. An endothermic reaction absorbs heat from its surroundings, whereas an exothermic reaction releases heat.

In the context of Le Chatelier's Principle:

• For an exothermic reaction, increasing temperature adds heat, which causes the equilibrium to shift to the left to absorb that extra heat, reducing the amount of product formed.
• For an endothermic reaction, increasing temperature makes the equilibrium shift to the right, as more heat allows the reaction to proceed forward, producing more product.

In the case of our reaction with CO and H₂O, since it's exothermic, an increase in temperature will push the reaction to the left, favoring the reactants.

Reaction Kinetics

While equilibrium is about the balance between forward and reverse reactions, reaction kinetics deals with the rate at which these reactions occur. This concept is important because even if a particular condition implies a shift in equilibrium, the rate at which the system reaches the new equilibrium is determined by how proficiently the reactants can convert into products—and vice versa.

Factors influencing reaction kinetics include:

• The presence of a catalyst, which can lower the activation energy required for the reaction, speeding up both the forward and reverse processes without affecting equilibrium position.
• Temperature, as higher temperatures increase the kinetic energy of molecules, often increasing reaction rates.

Understanding kinetics allows us to optimize reaction conditions in industrial applications, ensuring processes run efficiently and economically while maintaining necessary equilibrium conditions.