Question

Coal, which is primarily carbon, can be converted to natural gas, primari- ly \(\mathrm{CH}_{4, \text { by the exothermic reaction: }}\) $$\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)$$ Which disturbance favors \(\mathrm{CH}_{4}\) at equilibrium? \begin{equation}\begin{array}{l}{\text { a. adding more } \mathrm{C} \text { to the reaction mixture }} \\ {\text { b. adding more } \mathrm{H}_{2} \text { to the reaction mixture }} \\ {\text { c. raising the temperature of the reaction mixture }} \\ {\text { d. } \text { lowering the volume of the reaction mixture }} \\ {\text { e. adding a catalyst to the reaction mixture }} \\ {\text { f. adding neon gas to the reaction mixture }}\end{array}\end{equation}

Short answer

Lowering the volume of the reaction mixture favors the formation of CH4 at equilibrium.

Step-by-step solution

Understand the Principle of Le Chatelier

Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. This helps predict the effect of changes in concentration, pressure, or temperature.

Analyze the Given Options

Evaluate each option (a to f) to determine how they would affect the equilibrium of the reaction \(\mathrm{C}(s)+2\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)\), keeping in mind the principle from Step 1.

Assess the Effect of Adding Reactants

Adding more \(\mathrm{C}\) or \(\mathrm{H}_{2}\) would increase the concentration of reactants, which would shift the equilibrium to the right, favoring the formation of \(\mathrm{CH}_{4}\).

Consider the Effect of Temperature Change

Raising the temperature of an exothermic reaction would shift the equilibrium to the left, favoring the reactants. Therefore, this would not favor \(\mathrm{CH}_{4}\) production.

Understand the Impact of Volume Change

Lowering the volume of the reaction will increase the pressure, and according to Le Chatelier's principle, the system will favor the side with fewer moles of gas to decrease pressure. Since the products side has fewer gas moles, this will favor \(\mathrm{CH}_{4}\) production.

Evaluate the Role of a Catalyst

Adding a catalyst to a reaction mixture only speeds up the reaction and does not affect the position of equilibrium. Thus, it does not favor either side of the equilibrium.

Determine the Effect of an Inert Gas

Adding an inert gas such as neon to the reaction mixture at constant volume does not affect the partial pressures of the reacting gases and, therefore, does not shift the equilibrium position.

Identify the Correct Disturbance Favoring CH4

From the analysis above, options a (adding more \(\mathrm{C}\)), b (adding more \(\mathrm{H}_{2}\)), and d (lowering the volume) could potentially favor \(\mathrm{CH}_{4}\) at equilibrium. Since the question specifies a singular 'disturbance', the best answer is the one that most directly favors \(\mathrm{CH}_{4}\) production. Lowering the volume directly affects the pressure, which has a more significant impact in shifting the equilibrium toward the side with fewer moles of gas, which is the product side in this case, and therefore, option d is the best answer.

Key concepts

Chemical Equilibrium

Understanding chemical equilibrium is fundamental in chemistry. It's a state where the rate of the forward reaction equals the rate of the reverse reaction, so the concentrations of reactants and products remain constant over time. This doesn't mean the reactants and products are in equal concentrations, but that they've reached a balance.

Imagine a busy downtown where people are constantly entering and leaving at the same rate. Just as the number of people in the downtown stays the same, the amounts of reactants and products in a chemical equilibrium remain unchanged. The important thing to remember is that even though the macroscopic properties remain constant, at the molecular level, reactions are still occurring; it's a dynamic process.

Equilibrium Shift

An equilibrium shift occurs when external conditions are modified, and the system responds to re-establish equilibrium according to Le Chatelier's Principle. This principle is a cornerstone in understanding how a chemical system adapts to changes.

For instance, if we add more reactants to a system in equilibrium, it's like adding more people to the downtown area; the balance is disrupted. The system will respond by shifting the equilibrium to produce more product, essentially trying to 'thin out the crowd' by moving some of the extra people (reactants) into shops (products).

This dynamic dance allows chemists to manipulate conditions to increase the yield of desired products. It’s essential for industries, from pharmaceuticals to manufacturing, ensuring that they can maximize production efficiency.

Reaction Mixture Disturbances

When a reaction mixture is disturbed, the system will adjust the equilibrium position to oppose the disturbance, that's Le Chatelier's principle in action. Think of it as a self-correcting mechanism within a chemical reaction.

Here are common ways to disturb the mixture:

• Changing concentrations of reactants or products, which can shift the equilibrium to the opposite side.
• Altering the temperature; for exothermic reactions, an increase in temperature shifts the balance towards reactants. Conversely, cooling an endothermic reaction favors the formation of products.
• Modifying the pressure by changing the volume of the system affects gaseous equilibria, shifting toward the side with fewer gas molecules to relieve the pressure.
• Adding an inert gas at constant volume has no effect since it doesn't change the system's total pressure or concentration of reactants/products.

Understanding these disturbances and how they impact chemical equilibrium is crucial for controlling reactions in research and industrial settings. The goal is to maintain the desired level of reactants and products, optimizing for various outcomes.