Question

The reaction $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) $$ has \(\Delta H^{\circ}=-18 \mathrm{~kJ} .\) How will the amount of \(\mathrm{CH}_{3} \mathrm{OH}\) present at equilibrium be affected by the following changes? (a) Adding \(\mathrm{CO}(g)\) (b) Removing \(\mathrm{H}_{2}(g)\) (c) Decreasing the volume of the container (d) Adding a catalyst (e) Increasing the temperature

Short answer

(a) Increases CH3OH, (b) Decreases CH3OH, (c) Increases CH3OH, (d) No change in CH3OH, (e) Decreases CH3OH.

Step-by-step solution

- Le Chatelier’s Principle

Understand Le Chatelier's Principle which states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.

- Assess Impact of Adding CO(g)

According to Le Chatelier's Principle, adding more reactant (CO(g)) to the system will cause the equilibrium to shift to the right, producing more CH3OH(g) to re-establish equilibrium.

- Assess Impact of Removing H2(g)

Removing a reactant (H2(g)) from the system will cause the equilibrium to shift to the left in an attempt to produce more H2(g), which means there will be a decrease in CH3OH(g) at equilibrium.

- Assess Impact of Adding a Catalyst

Adding a catalyst will not affect the position of equilibrium. It will only increase the rate at which equilibrium is achieved.

- Assess Impact of Increasing the Temperature

Increasing the temperature of an exothermic reaction (negative ΔH°) will cause the equilibrium to shift to the left as the system tries to absorb excess heat by favoring the endothermic direction. This will result in a decrease in CH3OH(g) at equilibrium.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the backward reaction, resulting in no net change in the concentration of reactants and products over time. It's important to note that this balance does not mean the reactants and products are in equal amounts but that they are in a fixed ratio.

To visualize this concept, imagine a scale in perfect balance—one side with reactants and the other with products. While molecules are constantly switching sides (reacting), the scale remains balanced. However, when we add more weight (reactants or products) to one side, the scale will tip until it finds a new point of balance.

In the given exercise, we see this principle in action: when additional CO(g) is added, the reaction shifts to produce more CH₃OH(g), tipping the scale back to equilibrium. Conversely, removing H₂(g) shifts the balance in the opposite direction, reducing CH₃OH(g) as the system seeks a new equilibrium point.

Exothermic Reactions

Exothermic reactions are chemical reactions that release energy, usually in the form of heat, to their surroundings. The value of \( \Delta H^\circ \) is negative for exothermic reactions, indicating that energy is being released. This heat release is crucial to understanding how temperature changes affect equilibrium.

Because exothermic reactions like the formation of CH₃OH(g) are favorable at lower temperatures (where they can release heat), increasing the temperature supplies additional heat to the system. According to Le Chatelier's Principle, the system will shift to absorb this extra heat—which, in this case, is by favoring the reverse reaction. Hence, more reactants are formed, and less CH₃OH(g) is present at equilibrium, as observed in the solution to part (e) of the exercise.

Understanding exothermic reactions helps in grasping why changes in temperature can have a significant effect on the position of chemical equilibria, guiding industrial processes and laboratory conditions to optimize yield.

Impact of Catalysts on Equilibrium

Catalysts are substances that increase the rate of reaction without being consumed in the process, allowing chemical reactions to reach equilibrium faster. However, a common misconception is that they can alter the final amounts of reactants and products at equilibrium.

In the exercise, adding a catalyst was suggested as a change. But according to Step 5 of the solution, adding a catalyst does not affect the position of equilibrium; it merely speeds up the process of reaching that equilibrium from any given starting point. Catalysts work by providing an alternative reaction pathway with a lower activation energy, effectively speeding up both the forward and reverse reactions equally. Hence, while a catalyst is invaluable for industrial processes where time is of the essence, it won't change the established ratio of CH₃OH(g) at equilibrium.

For students visualizing this, think of a catalyst as an escalator in a two-story building. Whether you take the stairs or the escalator, your start and end points remain the same; the escalator simply gets you there quicker. Thus, the addition of a catalyst is impactful in terms of efficiency but neutral in terms of chemical equilibrium composition.