Problem 60 - Chemistry

Question

In the uncatalyzed reaction $$\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ the pressure of the gases at equilibrium are \(P_{\mathrm{N}_{2} \mathrm{O}_{4}}=\) 0.377 and \(P_{\mathrm{NO}_{2}}=1.56 \mathrm{~atm}\) at \(100^{\circ} \mathrm{C} .\) What would happen to these pressures if a catalyst were added to the mixture?

Step-by-Step Solution

Answer

The addition of a catalyst in the reaction mixture would not have any effect on the equilibrium pressures. It only helps the system to reach equilibrium more quickly, but does not change the equilibrium concentrations.

Step 1: Understanding the role of a catalyst in a chemical reaction

A catalyst is a substance that speeds up a chemical reaction by lowering the activation energy barrier, helping reactants to reach the transition state more easily. However, it does not change the equilibrium position nor the equilibrium concentrations of the reactants and products.

Step 2: Interpretation of equilibrium pressures

The given equilibrium pressures of the gases, \(P_{N_{2}O_{4}}=0.377 ~atm\) and \(P_{NO_{2}}=1.56 ~atm\) are the pressures when the system has reached equilibrium at \(100^{\circ} C\). This means the forward and reverse reactions are happening at the same rate, and the concentrations of the reactants and products are stable.

Step 3: Effect of adding a catalyst

If a catalyst were added to the mixture, it would speed up both the forward and reverse reactions, which means the system would reach equilibrium more quickly. However, it would not change the equilibrium pressures \(P_{N_{2}O_{4}}\) and \(P_{NO_{2}}\), because it does not change the equilibrium position or the equilibrium concentrations.

Key Concepts

Catalyst in Chemical Reactions

Understanding the role of a catalyst in chemical reactions is crucial for grasping the essentials of chemical kinetics and equilibrium.

A catalyst is a substance that accelerates the rate of a reaction without being consumed in the process. It accomplishes this by providing an alternative reaction pathway with a lower activation energy. Think of it like a shortcut that allows reactants to convert into products more efficiently.

However, a common misconception is that a catalyst merely speeds up the attainment of equilibrium but does not affect the equilibrium position itself. The equilibrium constant, which is dependent on temperature but not on the presence of a catalyst, remains unchanged. Thus, while a catalyst makes a reaction reach equilibrium faster, the concentrations of reactants and products at equilibrium are unaffected. In the exercise, the addition of a catalyst to the N₂O₄ and NO₂ reaction would not alter the equilibrium pressures provided.

Equilibrium Pressure

When discussing equilibrium pressure, we are often referring to the pressure exerted by a gas in a closed system at equilibrium.

In a closed system where gases react, the equilibrium state is reached when the rates of the forward and reverse reactions equalize, resulting in constant pressures of the reactants and products. The ratio of these pressures, raised to the power of their stoichiometric coefficients, gives the reaction's equilibrium constant (K_p) at a given temperature.

In the given exercise, the equilibrium pressures for N₂O₄ and NO₂ are specific numerical values indicating the point at which both the production and decomposition of these gases occur at the same rate. It's important to note that changing the amount of substances or adding a catalyst won't alter the equilibrium pressures unless there is a corresponding temperature change.

Activation Energy

Every chemical reaction requires a certain amount of energy to proceed, known as the activation energy. This is the energy barrier that reactants must overcome to transform into products.

Activation energy can be visualized as the height of a hill that reactants must climb to react with one another. Once over the hill, they can roll down into the valley of products. The lower the hill (activation energy), the easier it is for the reaction to happen. Catalysts play a pivotal role here by reducing the activation energy required, analogous to building a tunnel through the hill, thereby speeding up the reaction.

Despite lowering the activation energy, catalysts do not influence the inherent energy of the reactants or products nor the overall energy change of the reaction; they only make it easier for the reaction to start. In our textbook example, a catalyst would not modify the equilibrium pressures; instead, it facilitates the reaction to reach those pressures quicker.