Question

Coal, which is primarily carbon, can be converted to natural gas, primarily \(\mathrm{CH}_{4}\), by this exothermic reaction. $$ \mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g) $$ If this reaction mixture is at equilibrium, predict the effect (shift right, shift left, or no effect) of these changes. (a) adding more \(C\) to the reaction mixture (b) adding more \(\mathrm{H}_{2}\) to the reaction mixture (c) raising the temperature of the reaction mixture (d) lowering the volume of the reaction mixture (e) adding a catalyst to the reaction mixture

Short answer

Predicted effects: (a) Shift right, (b) Shift right, (c) Shift left, (d) Shift right, (e) No effect.

Step-by-step solution

Understanding Le Châtelier's Principle

Le Châtelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. We will use this principle to predict the effects of various changes to the reaction mixture.

Determining the Effect of Adding More Carbon (C)

Adding more carbon (C) to the reaction mixture increases the concentration of a reactant. According to Le Châtelier's Principle, the system will respond by shifting the equilibrium to the right to decrease the concentration of added carbon. This results in the production of more methane (CH_4).

Determining the Effect of Adding More Hydrogen Gas (H2)

Adding more hydrogen gas (H_2) increases the concentration of a reactant. Le Châtelier's Principle predicts that the equilibrium will shift to the right to use up the excess H_2 by producing more methane (CH_4).

Determining the Effect of Raising the Temperature

Since the reaction is exothermic, heat is a product. Increasing the temperature adds more heat to the system, essentially increasing the concentration of a product. According to Le Châtelier's Principle, the equilibrium will shift to the left to absorb the added heat and counter the change, resulting in less methane (CH_4).

Determining the Effect of Lowering the Volume of the Reaction Mixture

Lowering the volume of the reaction mixture increases the pressure of the system. The equilibrium will shift towards the side with fewer moles of gas to decrease the pressure. In this case, the products side has one mole of gas (CH_4) while the reactants side has two moles of gases (one mole of solid C and two moles of H_2 gas). Therefore, the equilibrium will shift to the right to reduce the pressure.

Determining the Effect of Adding a Catalyst to the Reaction Mixture

The presence of a catalyst lowers the activation energy of a reaction but does not alter the equilibrium position. It only speeds up the rate at which equilibrium is achieved. Thus, adding a catalyst to the reaction mixture has no effect on the equilibrium position.

Key concepts

Chemical Equilibrium

Imagine a busy market where people are constantly buying and selling goods. Now, imagine this market reaching a state where the rate of buying equals the rate of selling. In the world of chemistry, this is what we call chemical equilibrium. At equilibrium, the rate of the forward reaction, the process of reactants turning into products, is equal to the rate of the reverse reaction, where products revert back to reactants. It's important to note that even though the rates are equal, the amounts of reactants and products do not have to be equal - equilibrium is about the rate of change, not the amounts of substances.

This concept is beautifully demonstrated in the conversion of carbon to methane in the presence of hydrogen gas. The equilibrium can be disturbed by altering concentrations of reactants or products, pressure, volume, or temperature. However, the system will strive to achieve a new equilibrium by adjusting the rates of the forward and reverse reactions.

Reaction Shift

So what happens when you shake things up, like adding more carbon or hydrogen to our carbon-to-methane reaction? This is where reaction shift comes into play. Le Châtelier's Principle is like a recipe for equilibrium that tells us how the system reacts to disturbances. In the case of adding more carbon, the system reacts by shifting the reaction to the right, which means more methane will be produced to reduce the extra carbon added.

Shift Right or Shift Left?

If we increase the concentration of a reactant, the shift is towards the products, or to the right. Conversely, increasing the concentration of a product or adding heat (in an exothermic reaction) will cause the equilibrium to shift towards the reactants, or to the left. This dance of shifting left and right continues until the system settles at a new equilibrium - the market's new normal.

Exothermic Reactions

Think of exothermic reactions as benevolent creatures that give you warmth. They literally exhale energy, usually as heat, as they transform reactants into products. The conversion of carbon and hydrogen gas into methane is an example of such a reaction. It releases heat into the surroundings, making it exothermic.

Heat as a Product

An intriguing way to look at exothermic reactions is to consider heat as one of the products. So when we increase the temperature, we're effectively adding more 'product' into the system. Le Châtelier's Principle tells us that to counter this change, the equilibrium will shift to the left, towards the reactants, to absorb the extra heat. It's like our reaction is saying, 'It's too hot! Let's cool down by making less methane and more carbon and hydrogen.' This intuitive approach to understanding exothermic reactions helps us predict the behavior of a system when it's pushed out of balance by temperature changes.