Problem 12 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

The following gas phase reaction is exothermic \\[ \mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g}) \\] What will be the effect of (a) increasing the pressure, (b) increasing the temperature, and (c) adding a catalyst on (i) the equilibrium constant, \(K\), and (ii) the yield of \(\mathrm{CO}_{2}\) ? (Section 15.5 )

Step-by-Step Solution

Answer

(a) Increasing pressure increases \(\mathrm{CO}_{2}\) yield, \(K\) unchanged. (b) Increasing temperature decreases \(\mathrm{CO}_{2}\) yield and \(K\). (c) Catalyst does not affect \(\mathrm{CO}_{2}\) yield or \(K\).

Step 1: Understanding the Reaction Conditions

The reaction is exothermic, meaning it releases heat. It proceeds according to \(\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})\). We need to consider the effects of pressure, temperature, and catalysis on this equilibrium.

Step 1: Effect of Increasing Pressure

The pressure of a gaseous reaction is related to the number of moles of gas on either side of the equation. Here, on the reactants side, there are \(1 + \frac{1}{2} = 1.5\) moles of gas and on the products side, there is 1 mole of gas. Increasing pressure will shift equilibrium toward the side with fewer moles of gas, which is the product side (forming more \(\mathrm{CO}_{2}\)). However, this shift does not alter the equilibrium constant \(K\), as \(K\) is dependent only on temperature.

Step 2: Effect of Increasing Temperature

An exothermic reaction releases heat; therefore, increasing the temperature adds heat to the system. According to Le Chatelier's Principle, the system will shift in the direction that absorbs heat, which is the endothermic direction (backwards towards reactants). This will decrease the yield of \(\mathrm{CO}_{2}\) and also decrease the equilibrium constant \(K\) as more reactants are formed.

Step 3: Effect of Adding a Catalyst

A catalyst speeds up the rate of both the forward and reverse reactions equally, allowing the equilibrium position to be reached faster. However, adding a catalyst does not change the position of the equilibrium, the yield of \(\mathrm{CO}_{2}\), or the equilibrium constant \(K\).

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is crucial in understanding how a system at equilibrium responds to changes. The principle essentially states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change.
For instance, if you increase the pressure in a system with gases, the equilibrium will shift toward the side with fewer moles of gas. This happens because systems will try to relieve the added pressure. In the context of the given chemical reaction, increasing the pressure shifts the equilibrium towards the formation of more carbon dioxide, as there are fewer moles on the product side. However, this shift does not change the equilibrium constant, as the value of the constant is only affected by temperature changes.
Temperature changes impact equilibrium significantly since exothermic and endothermic reactions absorb or release heat. According to Le Chatelier's Principle, increasing temperature for an exothermic reaction will shift the equilibrium towards the reactants, as the system attempts to absorb the excess heat.

Exothermic Reactions

In an exothermic reaction, energy is released, usually in the form of heat, during the conversion of reactants to products. This is important to understand in equilibrium reactions.
Whenever you increase the temperature of an exothermic reaction, it can be visualized as adding a product (heat). The system will respond by shifting the equilibrium to favor the reactants, thereby decreasing the yield of products such as \( \mathrm{CO}_2 \).
Also, increasing the temperature of an exothermic reaction decreases the equilibrium constant, \(K\), because there's a greater tendency for the reverse (endothermic) reaction, consuming more products and forming more reactants. Thus, while intuitively it might seem that more heat allows for more reaction, in exothermic systems, it's the balance of conditions that directs the reaction's progress.

Equilibrium Constant

The equilibrium constant, denoted as \( K \), provides a quantifiable measure of a chemical reaction's position at equilibrium under a given temperature. It expresses the ratio of product concentrations to reactant concentrations, raised to the power of their stoichiometric coefficients.
For the given reaction, any change in temperature influences \( K \). Specifically, in exothermic reactions like the conversion of carbon monoxide and oxygen to carbon dioxide, increasing the temperature decreases the value of \( K \). This is because the forward reaction is exothermic, and increasing temperature favors the reverse reaction, reducing the concentration of products at equilibrium.
It's critical to remember that \( K \) is unaffected by changes in pressure or the addition of catalysts. These factors only influence how quickly equilibrium is reached, not the equilibrium position itself.

Catalysis

Catalysts play an essential role in chemical reactions by increasing the rate at which equilibrium is achieved, without being consumed in the process. They do so by providing an alternative reaction pathway with a lower activation energy.
In the context of a chemical equilibrium, adding a catalyst accelerates both the forward and reverse reactions equally. It efficiently brings the system to equilibrium faster but does not alter the balance of reactants and products at equilibrium.
This means the yield of \(\mathrm{CO}_2\) or the equilibrium constant, \( K \), remains unchanged. The sole function of the catalyst is to speed up the attainment of equilibrium without impacting the position of the equilibrium or the inherent tendencies of the reaction to proceed toward either direction.