Problem 70 - Chemistry The Science in Context

Question

Ammonia is added to a gaseous reaction mixture containing \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) that is at chemical equilibrium. How will the addition of ammonia affect the relative concentrations of \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) if the equilibrium constant of reaction 2 is much greater than the equilibrium constant of reaction \(1 ?\) (1) \(\quad \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) (2) \(\quad \mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(s)\)

Step-by-Step Solution

Answer

The addition of ammonia will cause a decrease in the concentrations of H2 and Cl2, and a significant decrease in the concentration of HCl in the system. This is because the reaction consuming HCl (and forming NH4Cl) will have a dominant effect due to the larger equilibrium constant, K2.

Step 1: Write the reactions and equilibrium constants

We know the two reactions and their equilibrium constants: (1) H2(g) + Cl2(g) <=> 2HCl(g), with equilibrium constant K1 (2) HCl(g) + NH3(g) <=> NH4Cl(s), with equilibrium constant K2 We are given that K2 >> K1.

Step 2: The Le Châtelier's principle

Le Châtelier's principle states that when a change is made to a system in chemical equilibrium, the system will shift its equilibrium position to counteract the imposed change, and regain a new equilibrium state. In this case, we are adding NH3 to the reaction mixture.

Step 3: Determine the effect of adding ammonia on reaction 2

As we add NH3 to the system, the concentration of NH3 increases. According to Le Châtelier's principle, the system will counteract this change by trying to reduce the concentration of NH3. Thus, reaction 2 will shift to the right, leading to the formation of more NH4Cl(s) and the consumption of HCl(g).

Step 4: Determine the effect of the decrease in HCl concentration on reaction 1

When the concentration of HCl decreases due to reaction 2, reaction 1 will shift to the right, according to Le Châtelier's principle. This will lead to the formation of more HCl(g) and the consumption of H2(g) and Cl2(g).

Step 5: Determine the overall effect of adding ammonia on the relative concentrations of H2, Cl2, and HCl

Since K2 >> K1, reaction 2 shifting right will have a dominant effect on the overall system. The overall effect of adding ammonia will be: - A decrease in H2 and Cl2 concentrations as reaction 1 shifts to the right to counteract the decrease in HCl concentration due to reaction 2. - A significant decrease in HCl concentration, as it is consumed in reaction 2 to form NH4Cl(s) at a much greater rate than it is being formed in reaction 1. In conclusion, the relative concentrations after the addition of ammonia will be lower for H2 and Cl2, and significantly lower for HCl.

Key Concepts

Chemical Equilibrium

Understanding chemical equilibrium is fundamental when studying reactions. Imagine a busy city intersection where the number of cars entering equals the number of cars leaving; the traffic 'flows' yet remains 'steady'. Similarly, in a chemical reaction at equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, thus the concentrations of reactants and products remain constant over time.

However, equilibrium doesn't mean the reactants and products are present in equal amounts, but rather their rates of formation are balanced. The equilibrium state is dynamic because the reactions continue to occur, yet no net change is observed. It's like the hustle of the city—always moving, but consistently busy.

Reaction Shift

Responding to Change: Reaction Shifts

When a chemical system at equilibrium faces a disturbance, such as change in concentration, temperature, or pressure, it reacts in a way to counteract this change, as described by Le Châtelier's Principle. Think of it as a comfort-loving person adjusting their sitting position to maintain comfort; the chemical system 'adjusts' itself to regain equilibrium.

For example, adding more of a reactant typically causes the reaction to shift towards the products to 'use up' the excess reactant. Conversely, removing a product from the system would shift the reaction towards producing more of that product. This 'shifting' process is crucial in industrial chemical processes to maximize yields and is also integral to the self-regulation of many biological systems.

Equilibrium Constants

Quantifying Equilibrium: The Equilibrium Constant (K)

Each chemical reaction at equilibrium has an associated equilibrium constant, represented by K, which provides a ratio of product concentrations to reactant concentrations, raised to the power of their stoichiometric coefficients. This constant is crucial because it indicates the extent to which a reaction proceeds before reaching equilibrium.

A larger K value (K2 >> K1) implies a greater extent of product formation. When K is small, reactants are favored. So, if you're cooking a stew (the reaction), think of K as the recipe that dictates the balance of ingredients (reactants and products) for the perfect flavor (equilibrium).

In the given exercise, K2 is much larger than K1, indicating that reaction 2 will dominate the equilibrium shift when ammonia is added, leading to a significant change in the concentrations of the reactants and products involved.