Question

For a certain gas-phase reaction, the fraction of products in an equilibrium mixture is increased by increasing the temperature and increasing the volume of the reaction vessel. (a) What can you conclude about the reaction from the influence of temperature on the equilibrium? (b) What can you conclude from the influence of increasing the volume?

Short answer

(a) Since increasing the temperature increases the fraction of products in equilibrium, the reaction is endothermic. This is because an increase in temperature favors the forward reaction in endothermic processes. (b) The equilibrium shifts to increase the fraction of products when the volume is increased, implying that the number of moles of gas is greater on the product side than on the reactant side.

Step-by-step solution

(a) Influence of Temperature on Equilibrium

Le Chatelier's principle states that if a change in conditions is applied to a system at equilibrium, the system will respond by adjusting its position to counteract the imposed change. When temperature is increased in an exothermic reaction, the equilibrium constant (K) decreases, and when temperature is increased in an endothermic reaction, K increases. In this case, increasing the temperature increases the fraction of products in equilibrium, which implies that K also increases. This further suggests that the reaction is endothermic, as the increase in temperature favors the forward reaction which leads to more products.

(b) Influence of Increasing Volume on Equilibrium

When the volume of the reaction vessel is increased, the pressure is generally reduced. According to Le Chatelier's principle, if pressure is decreased, the equilibrium will shift to the side with a greater number of moles of gas, because this will counteract the pressure reduction. In this case, the equilibrium shifts to increase the fraction of products when the volume is increased. This implies that the number of moles of gas is greater on the product side than on the reactant side. So, from (a) and (b), we can conclude that the given reaction is an endothermic reaction with a greater number of moles of gas in products than reactants.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle serves as a guide for predicting how a change in conditions impacts a chemical system at equilibrium. It states that if a dynamic equilibrium system is subjected to a change in concentration, temperature, or pressure, the system will adjust itself to partially counteract the effect of the change, ultimately reaching a new equilibrium position.

For instance, in the provided exercise, increasing the temperature caused more products to be formed, indicating that the system shifted to absorb the extra heat. Think of it like an invisible seesaw; when one side is disturbed, the other side adjusts to bring things back into balance. In essence, it's the chemical world's way of saying 'keep calm and carry on.'

Endothermic Reactions

Endothermic reactions absorb heat from their surroundings. This means that as you add heat to the system, such as increasing the temperature, the reaction shifts to consume that heat, producing more product and fewer reactants.

In our exercise, the observation that increasing temperature increases the production of the reaction's products tells us that heat is being used up in the process to form those products, hence confirming that the reaction is endothermic. Unlike their exothermic counterparts, which release heat, endothermic reactions essentially 'soak up' warmth, making them the 'sponges' of the chemical reaction world.

Equilibrium Constant

The equilibrium constant (K) is a number that expresses the ratio of products to reactants at equilibrium, and it varies with temperature. In an endothermic reaction, increasing the temperature increases K, because heat is a reactant. It's similar to saying that more heat 'tips the scales' in favor of the products for endothermic reactions.

The increase in the fraction of products, as mentioned in the exercise, therefore suggests an increase in K, solidifying the notion that the reaction harnesses heat from its surroundings (heat acts as a reactant) to move forward. The value of K provides a snapshot of the reaction's preferred state at a given temperature—a higher K value favors products, hinting at the reaction's cozy relationship with heat.

Reaction Vessel Volume

Changing the volume of the reaction vessel affects the concentration and pressure of the gaseous components in an equilibrium system. An increase in volume leads to a decrease in pressure, causing the reaction to favor the production of more moles of gas, should it be able to, to balance the change.

In our specific scenario, the fact that increasing the volume also increases the fraction of products suggests that there are more gas molecules among the products compared to the reactants. This is akin to opening up a room to allow more party guests (gas molecules) on one side—the system expands to make everyone comfortable, thereby shifting the equilibrium. Always remember, the reaction will shift towards the side with more gas particles when the 'party room' (volume) gets bigger.