Problem 83 - Chemistry: The Central Science in SI Units, Global Edition

Question

Nitric oxide (NO) reacts readily with chlorine gas as follows: $$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)$$ At \(700 \mathrm{~K},\) the equilibrium constant \(K_{p}\) for this reaction is \(2.6 \times 10^{-3}\). Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium. (a) \(P_{\mathrm{NO}}=20.3 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=20.3 \mathrm{kPa}, R_{\mathrm{NOCl}}=20.3 \mathrm{kPa}\) (b) \(P_{\mathrm{NO}}=25.33 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=15.2 \mathrm{kPa}, R_{\mathrm{NOCl}}=2.03 \mathrm{kPa}\) (c) \(P_{\mathrm{NO}}=15.2 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=42.6 \mathrm{kPa}, P_{\mathrm{NOCl}}=5.07 \mathrm{kPa}\)

Step-by-Step Solution

Answer

(a) The reaction will proceed to the left, towards reactants, to reach equilibrium. (b) The reaction will proceed to the right, towards the products, to reach equilibrium. (c) The reaction mixture is at equilibrium.

Step 1: Calculate Qp for the given mixture(a)

Now, we will use the values provided to calculate the reaction quotient \(Q_p\): \(Q_p = \frac{(20.3)^2}{(20.3)^2 \times 20.3} = \frac{1}{20.3} = 0.049\)

Step 2: Compare Qp with Kp for mixture(a)

Since \(Q_p = 0.049\) and \(K_p = 2.6 \times 10^{-3}\), we have \(Q_p > K_p\) indicating that the reaction will proceed to the left, towards reactants to reach equilibrium. (b) \(P_{NO} = 25.33 kPa\), \(P_{Cl_2} = 15.2 kPa\), \(P_{NOCl} = 2.03 kPa\)

Step 1: Calculate Qp for the given mixture(b)

Now, we will use the values provided to calculate the reaction quotient \(Q_p\): \(Q_p = \frac{(2.03)^2}{(25.33)^2 \times 15.2} = \frac{4.1209}{9743.908} = 0.0004228\)

Step 2: Compare Qp with Kp for mixture(b)

Since \(Q_p = 0.0004228\) and \(K_p = 2.6 \times 10^{-3}\), we have \(Q_p < K_p\), indicating that the reaction will proceed to the right, towards the products to reach equilibrium. (c) \(P_{NO} = 15.2 kPa\), \(P_{Cl_2} = 42.6 kPa\), \(P_{NOCl} = 5.07 kPa\)

Step 1: Calculate Qp for the given mixture(c)

Now, we will use the values provided to calculate the reaction quotient \(Q_p\): \(Q_p = \frac{(5.07)^2}{(15.2)^2 \times 42.6} = \frac{25.7049}{9868.32} = 0.002605\)

Step 2: Compare Qp with Kp for mixture(c)

Since \(Q_p = 0.002605\) and \(K_p = 2.6 \times 10^{-3}\), we have \(Q_p \approx K_p\), indicating that the reaction mixture is at equilibrium.

Key Concepts

Reaction Quotient

The reaction quotient, denoted as \(Q\), is a crucial concept that helps us determine whether a chemical reaction is at equilibrium. It involves the same mathematical expression as the equilibrium constant but uses the current concentrations or pressures of the reactants and products, rather than their equilibrium values.

To calculate \(Q_p\), which is the reaction quotient in terms of partial pressures, we utilize the formula that mirrors the equilibrium expression. For the given reaction:

• \(2\mathrm{NO}(g) + \mathrm{Cl}_2(g) \rightleftharpoons 2\mathrm{NOCl}(g)\),

\(Q_p\) is calculated as: \[Q_p = \frac{(P_{\mathrm{NOCl}})^2}{(P_{\mathrm{NO}})^2 \times P_{\mathrm{Cl_2}}}\]
The values of \(Q\) can be compared to \(K\) to predict the direction of the reaction:

• If \(Q < K\), the reaction will shift to the right, producing more products.
• If \(Q > K\), the reaction will shift to the left, producing more reactants.
• If \(Q = K\), the system is already at equilibrium, and no shift will occur.

Understanding and calculating the reaction quotient helps in predicting how a reaction will proceed.

Equilibrium Constant

The equilibrium constant, represented as \(K\), is key to understanding chemical equilibrium. It is defined for a balanced chemical equation and is a measure of the extent to which reactants are converted into products.

For reactions involving gases, we often use \(K_p\), which is calculated using the partial pressures of the gases. For our reaction:

• \(2\mathrm{NO}(g) + \mathrm{Cl}_2(g) \rightleftharpoons 2\mathrm{NOCl}(g)\),

the equilibrium constant \(K_p\) is determined by the formula: \[K_p = \frac{(P_{\mathrm{NOCl}})^2}{(P_{\mathrm{NO}})^2 \times P_{\mathrm{Cl}_2}}\]
The value of \(K_p\) for this reaction tells us about the position of equilibrium. A larger \(K\) signifies that, at equilibrium, the system contains a higher concentration of products relative to reactants, whereas a smaller \(K\) indicates the opposite.\(K\) is always constant at a given temperature and provides a benchmark for the reaction quotient \(Q\), allowing us to predict the shift required to achieve equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental guideline describing how a chemical system at equilibrium responds to changes imposed upon it. It asserts that if a system at equilibrium is subjected to a change in conditions, such as concentration, temperature, or pressure, the system will adjust itself to counteract that change and a new equilibrium will be established.

When applied to our reaction:

• \(2\mathrm{NO}(g) + \mathrm{Cl}_2(g) \rightleftharpoons 2\mathrm{NOCl}(g)\),

we can predict how these changes affect the equilibrium position:

• If the concentration of \(\mathrm{NO}\) or \(\mathrm{Cl}_2\) is increased, the system will shift to the right, producing more \(\mathrm{NOCl}\) to reduce the stress.
• If the pressure is increased by reducing the volume, the system will favor the side with fewer moles of gas, thus shifting toward \(\mathrm{NOCl}\).
• If the temperature is increased, the direction of the shift depends on whether the reaction is exothermic or endothermic. If exothermic, it will shift to the left; if endothermic, it will shift to the right.

Le Chatelier's Principle provides invaluable insight into how external factors can influence the behavior and balance of a chemical reaction.