Problem 35 - Chemistry: Principles and Reactions

Question

At a certain temperature, \(K\) is \(1.3 \times 10^{5}\) for the reaction $$2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g)$$ What is the equilibrium pressure of hydrogen sulfide if those of hydrogen and sulfur gases are \(0.103\) atm and \(0.417\) atm, respectively?

Step-by-Step Solution

Answer

Question: Given the reaction H2(g) + S2(g) ⇌ 2H2S(g) with an equilibrium constant K = 1.3 x 10^5, find the equilibrium pressure of H2S if the equilibrium pressures of H2 and S2 are 0.103 atm and 0.417 atm, respectively. Answer: The equilibrium pressure of hydrogen sulfide (H2S) is approximately 0.449 atm.

Step 1: Write down the expression for the equilibrium constant (K)

According to the given balanced chemical equation, the expression for the equilibrium constant (K) can be written as follows: $$K = \frac{P_{H_2S}^2}{P_{H_2}^2 \times P_{S_2}}$$ Here, \(P_{H_2S}\) is the equilibrium pressure of hydrogen sulfide, \(P_{H_2}\) is the equilibrium pressure of hydrogen, and \(P_{S_2}\) is the equilibrium pressure of sulfur.

Step 2: Insert the given values into the expression for K

We have K = \(1.3 \times 10^{5}\), \(P_{H_2} = 0.103\) atm, and \(P_{S_2} = 0.417\) atm. Plugging these values into the expression for K, we get: $$1.3 \times 10^{5} = \frac{P_{H_2S}^2}{(0.103)^2 \times 0.417}$$

Step 3: Solve for the equilibrium pressure of hydrogen sulfide (\(P_{H_2S}\))

Now, we just need to solve for \(P_{H_2S}\): $$P_{H_2S}^2 = 1.3 \times 10^{5} \times (0.103)^2 \times 0.417$$ $$P_{H_2S} = \sqrt{1.3 \times 10^{5} \times (0.103)^2 \times 0.417}$$ $$P_{H_2S} \approx 0.449 \text{ atm}$$ So, the equilibrium pressure of hydrogen sulfide is approximately 0.449 atm.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is an essential concept in chemical equilibrium, helping us predict how changes in conditions affect the system's equilibrium position. It's all about maintaining equilibrium when a "disturbance" occurs. Think of it like a scale that tips one side if you add weight to it, trying to return to a balanced state.
When a change in concentration, temperature, or pressure is applied to a reaction at equilibrium:

• The system adjusts to partially counteract that change.
• If you increase the concentration of reactants, the system will shift to produce more products to reduce the added reactants.
• Increasing pressure favors the side of the reaction with the fewer moles of gas.
• Temperature changes require considering whether the reaction is exothermic or endothermic.

By grasping this principle, you understand how different factors can influence an equilibrium system, allowing better control over chemical reactions. You can think of it as nature's way of "fighting back" to stabilize the changes imposed on it.

Chemical Equilibrium

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction in a chemical system. At this point in a closed container, the concentrations of all species remain constant over time, even though both reactions continue to occur.
In the reaction involving hydrogen, sulfur, and hydrogen sulfide, equilibrium is reached when:

• The substance conversion rates into each other stay constant.
• There is no further observable change in the concentration of any participant in the reaction.

Achieving equilibrium doesn't mean that reactants and products are in equal amounts. Instead, it reflects a stable ratio governed by the equilibrium constant (\( K \)), which provides the proportions of products to reactants at equilibrium for a given temperature.
Understanding chemical equilibrium helps in predicting the direction of a reaction and the concentrations of various species at any point in time.

Reaction Quotient

The reaction quotient (\( Q \)) is a snapshot of a reaction at any given moment and helps determine the direction it needs to go to reach equilibrium. It's like taking a peek into the reaction at any point, and it serves as a tool to predict the reaction's shift.
To calculate \( Q \), you use the same formula as for the equilibrium constant (\( K \)), but with the current concentrations or pressures instead of equilibrium values:

• \( Q = \frac{{[\text{products}]}}{{[\text{reactants}]}} \)

Comparing \( Q \) and \( K \) helps in deciding which way the reaction will proceed:

• If \( Q < K \), the reaction moves forward to produce more products.
• If \( Q > K \), the reaction shifts in reverse to generate more reactants.
• If \( Q = K \), the system is at equilibrium, with no net change in the reaction direction.

By using the reaction quotient, you can anticipate shifts in a reaction, guiding adjustments to reach or maintain equilibrium.