Question

Predict the direction in which each of the following equilibria will shift if the pressure on the system is decreased by expansion. (a) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \rightleftharpoons \mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(2 \mathrm{CH}_{4}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g)\) (c) \(\mathrm{I}_{2}(s)+\mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)\)

Short answer

Question: Predict the direction in which each of the given equilibria will shift if the pressure on the system is decreased by expansion. (a) 2 H₂O₂(l) ⇌ O₂(g) + 2 H₂O(l) (b) 2 CH₄(g) ⇌ C₂H₂(g) + 3 H₂(g) (c) I₂(s) + H₂(g) ⇌ 2 HI(g) Answer: (a) The equilibrium will shift to the right (towards the products side). (b) There will be no significant shift in the equilibrium. (c) The equilibrium will shift to the right (towards the products side).

Step-by-step solution

(a) Analyze the given equilibrium

For the equilibrium \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \rightleftharpoons \mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\), there is 1 mole of gas in the products side, and no gas on the reactants side.

(a) Predict the direction of the shift

Since there are more moles of gas on the products side, the equilibrium will shift to the right (towards the products side) when the pressure is decreased.

(b) Analyze the given equilibrium

For the equilibrium \(2 \mathrm{CH}_{4}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g)\), there are 4 moles of gas on the reactants side and 4 moles of gas on the products side.

(b) Predict the direction of the shift

Since the number of moles of gas on both sides of the reaction is equal, there will be no significant shift in the equilibrium when the pressure is decreased.

(c) Analyze the given equilibrium

For the equilibrium \(\mathrm{I}_{2}(s)+\mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)\), there is 1 mole of gas on the reactants side and 2 moles of gas on the products side.

(c) Predict the direction of the shift

Since there are more moles of gas on the products side, the equilibrium will shift to the right (towards the products side) when the pressure is decreased.

Key concepts

Le Chatelier's Principle

When we look at a chemical reaction at equilibrium, the conditions can often play a crucial role in determining the direction in which the reaction tends to proceed. This is where Le Chatelier's Principle comes into play. This principle posits that if an external change is applied to a reaction at equilibrium, the system will adjust to minimize that change.

Consider the act of decreasing pressure, as in the exercise given. In a system at equilibrium that involves gases, reducing the pressure effectively means providing more volume. The system will 'want' to counteract this by increasing the pressure again. This is often achieved by shifting the equilibrium towards the side with more gas moles, which would take up more space and increase the pressure.

For instance, if we look at an equilibrium where adding or removing heat is involved, the equilibrium would shift to absorb the added heat if the temperature is increased. Conversely, it would produce more heat if the temperature is decreased. The beautiful simplicity of Le Chatelier's Principle helps predict how equilibria react to various stresses, keeping in mind that the reaction seeks to maintain a state of balance.

Equilibrium Shift

Talking about shifts, let's focus on how a change in conditions causes an equilibrium shift. When a dynamic equilibrium is disturbed, it doesn't just stay put; instead, it shifts in one direction or another. A shift to the right, toward products, suggests that more products are being formed, while a shift to the left, toward reactants, means that the reactants are being favored.

Using the exercise as an example, when the pressure is decreased in reaction (a), the system tries to counter the reduction by shifting towards the product side, where there are more gas particles. However, in reaction (b), no shift occurs because the number of gas molecules remains the same, regardless of a decrease in pressure. For reaction (c), we again see a shift to the right as the system seeks to balance out the lowered pressure by producing more gas molecules in the form of HI.

It's important to note that these shifts do not change the actual equilibrium constant of the reaction but merely adjust the concentrations of reactants and products until equilibrium is re-established under the new conditions.

Reaction Quotient

Let's delve into the reaction quotient, often denoted as Q. This is a measure that tells us the direction in which a reaction at non-equilibrium conditions is likely to proceed to reach equilibrium. It is calculated in the same way as the equilibrium constant (K), but uses the current or initial concentrations instead of the equilibrium concentrations.

If we have Q < K, the reaction proceeds to the right, making more products to attain equilibrium. In contrast, if Q > K, the reaction shifts to the left, using up products to form reactants until equilibrium is reached. And when Q = K, the system is at equilibrium, and no shift occurs.

Understanding the reaction quotient can help predict and explain shifts like the ones in our textbook exercise. For instance, if after a change like a decrease in pressure Q was found to be less than K, this would predict a rightward shift toward the production of more gas molecules, which is aligned with the conclusions drawn based on Le Chatelier's Principle.