Problem 17 - Chemistry The Central Science In Si Units

Question

When the following reactions come to equilibrium, does the equilibrium mixture contain mostly reactants or mostly products? (a) \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) at \(900 \mathrm{~K} K_{c}=2.24\) (b) \(\left.2 \mathrm{CO}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{C}(s)\right)\) at \(1300 \mathrm{~K} K_{p}=5.27 \times 10^{-5}\)

Step-by-Step Solution

Answer

(a) Mostly products, (b) Mostly reactants.

Step 1: Understand Equilibrium Constants

Equilibrium constants (\(K_c\) and \(K_p\)) provide a measure of the ratio of product concentrations to reactant concentrations at equilibrium. A \(K\) value greater than 1 indicates more products, whereas a \(K\) value less than 1 indicates more reactants.

Step 2: Analyze Reaction (a)

For reaction (a), \(K_c = 2.24\). Since \(K_c > 1\), this suggests that, at equilibrium, the concentration of products \(\text{CO}_2\) and \(\text{H}_2\) is greater than the concentration of reactants \(\text{H}_2\text{O}\) and \(\text{CO}\). Thus, the equilibrium mixture contains mostly products.

Step 3: Analyze Reaction (b)

For reaction (b), \(K_p = 5.27 \times 10^{-5}\). This is much less than 1, indicating that at equilibrium, the concentration of reactants \(2 \text{CO}(g)\) is significantly higher than the concentration of products \(\text{CO}_2(g)\) and \(\text{C}(s)\). Thus, the equilibrium mixture contains mostly reactants.

Key Concepts

Equilibrium Constant (Kc and Kp)

In chemical reactions, the equilibrium constant symbolizes the balance between products and reactants in a system that has reached equilibrium. There are two primary types of equilibrium constants:

• K_c: This is used for reactions in solutions and expressed in terms of concentration (mol/L).
• K_p: This indicates the equilibrium constant when dealing with gases, expressed in terms of partial pressures.

Both constants serve the same purpose of defining the position of equilibrium in a reaction. A value for either K greater than 1 suggests the reaction favors the formation of products at equilibrium. Conversely, a value less than 1 indicates that the reactants are favored in the equilibrium state.
These constants are crucial measures and allow chemists to predict the direction and extent of chemical reactions under given conditions. They provide insight into how shifts in conditions like temperature and pressure could alter the equilibrium state.

Reactants and Products

Understanding reactants and products is essential in any chemical process. Reactants are the original substances that undergo a reaction to form new products. In the equilibrium context, both reactants and products are present, but their concentrations do not change with time when equilibrium is achieved.

Let's examine the reactions provided:

• For reaction (a): The reactants are H₂O(g) and CO(g), and the products are CO₂(g) and H₂(g).
• In reaction (b): The reactant is 2 CO(g), and the products include CO₂(g) and elemental carbon C(s).

This distinction is key in calculating the equilibrium constant since it represents the ratio of the concentrations of the products to the reactants raised to the power of their stoichiometric coefficients from the balanced reaction equation. Only reactants and products in their gaseous or aqueous states are considered in these calculations.

Chemical Reaction Analysis

In analyzing chemical reactions to understand their equilibrium positions, we study how initial reactants convert into products over time until the system reaches dynamic balance.
In our examples, the analysis starts with assessing the equilibrium constants:

• **Reaction (a)**: With K_c = 2.24 > 1, this reaction at 900 K suggests products CO₂ and H₂ are more prevalent than reactants at equilibrium.
• **Reaction (b)**: Having K_p = 5.27 × 10^-5 < 1 implies a predominance of reactants at equilibrium at 1300 K.

Such assessments guide the understanding of how the mixture will behave under specific conditions without altering the initial amounts of substances. It allows prediction of how much product forms or how much reactant remains, which is crucial for industrial applications and laboratory settings for efficiency and yield.