Question

A reaction chamber contains a mixture of \(\mathrm{CO}_{2}, \mathrm{CO},\) and \(\mathrm{O}_{2}\) in equilibrium at a specified temperature and pressure. Now some \(\mathrm{N}_{2}\) is added to the mixture while the mixture temperature and pressure are kept constant. Will this affect the number of moles of \(\mathrm{O}_{2} ?\) How?

Short answer

Answer: The addition of N₂ gas will not affect the number of moles of O₂ in the reaction chamber, as N₂ is an inert gas and does not disrupt the stoichiometry nor the equilibrium of the reaction. The equilibrium composition of the reacting gases remains the same.

Step-by-step solution

Write down the balanced equation for the reaction

For this exercise, we need to consider the reaction between CO₂ and CO, which can be represented by the balanced equation: \begin{equation} \mathrm{CO} + \frac{1}{2}\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2} \end{equation}

Identify the effect of adding N₂

Since N₂ is an inert gas (does not participate in the reaction), its addition to the reaction chamber will not disrupt the stoichiometry of the balanced equation. Therefore, the reaction will remain balanced even after the addition of N₂ gas.

Analyze the effect on equilibrium and partial pressures

The addition of N₂ will increase the total pressure in the chamber without directly affecting the partial pressures of the reacting gases. As a result, the reaction will remain at equilibrium, and the composition of the reacting gases (CO, O₂, and CO₂) will not be affected by adding N₂.

Conclusion

In conclusion, the addition of N₂ to the reaction chamber will not affect the number of moles of O₂, since it is an inert gas and does not disrupt the stoichiometry nor the equilibrium of the reaction. The equilibrium composition of the reacting gases remains the same.

Key concepts

Understanding Reaction Stoichiometry

Reaction stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves balancing chemical equations to ensure that the number of atoms for each element is preserved throughout the reaction. For instance, let's take the provided example:

Step 1: A balanced chemical equation is written, detailing the reaction between carbon monoxide (CO) and oxygen (O₂) to form carbon dioxide (CO₂), which is crucial for understanding the stoichiometry of the process:

\[\mathrm{CO} + \frac{1}{2}\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\]

The coefficients in the equation represent the mole ratios between reactants and products. In this equation, one mole of CO reacts with half a mole of O₂ to produce one mole of CO₂. When analyzing changes in a reaction system, understanding stoichiometry helps us predict how alterations, such as adding a substance like nitrogen gas (N₂), might affect the reaction. However, since N₂ does not appear in the stoichiometric equation, we can infer that its presence will not change the mole ratios of the reactants and products.

How the Equilibrium Constant Relates to Reactants and Products

The equilibrium constant, symbolized as K, is a number that provides a measure of the relative concentrations of reactants and products at equilibrium in a reversible reaction. For the given exercise:

Step 2 and Step 3: Assessing the effect of adding an inert gas such as N₂ to the reaction mixture is simpler when we consider the equilibrium constant. The value of the equilibrium constant is determined by the specific reaction conditions and does not change unless the temperature alters. It is expressed for the reaction as:

\[K = \frac{[\mathrm{CO}_{2}]}{[\mathrm{CO}][\mathrm{O}_{2}]^{1/2}}\]

Adding N₂ does not affect the concentrations of the reacting gases directly, hence the position of the equilibrium remains unchanged. While the total pressure of the system increases, the ratio of reactant and product concentrations, and thus the equilibrium constant, remains the same.

The Influence of Partial Pressure in Chemical Equilibrium

Partial pressure is the pressure exerted by a single type of gas in a mixture of gases. It's a critical factor in the equilibrium of gases in a reaction, as chemical reactions that involve gases are affected by changes in pressure. Let's consider its role in our problem:

Step 3: Initially, it may seem that adding N₂ would alter the equilibrium by changing the pressure. However, the partial pressure of a gas is proportional to its mole fraction in the gas mixture, which is not altered by the addition of an inert gas at constant volume and temperature. Therefore, the partial pressure of the reacting gases (CO, O₂, CO₂) remains constant even with the extra N₂. This is why the existing reaction equilibrium is maintained, and the moles of oxygen (O₂) involved in the reaction are unaffected by the introduction of nitrogen (N₂) into the system.