Problem 110 - General Chemistry: Principles and Modern Applications

Question

In the reaction \(\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}), K=1.0 \times\) \(10^{5}\) at \(25^{\circ} \mathrm{C} .\) Would you expect a greater amount of product or reactant?

Step-by-Step Solution

Answer

There will be a greater amount of product (\(H_{2}O_{2}(aq)\)) at equilibrium.

Step 1: Understand the reaction

In this reaction, hydrogen peroxide gas, \( H_{2}O_{2}(g) \), is converted into aqueous hydrogen peroxide, \( H_{2}O_{2}(aq) \). This reaction can go both ways, meaning the gas can become aqueous, or the aqueous form can become a gas.

Step 2: Understand the implications of K

The equilibrium constant, K, is a measure of the ratio of concentrations of products to reactants at equilibrium. If K > 1, there are more products than reactants at equilibrium, since the numerator (products) would be larger than the denominator (reactants). If K < 1, there are more reactants than products.

Step 3: Apply K to this reaction

In this case, K=1.0x\(10^{5}\), which is much larger than 1. Therefore, at equilibrium, there would be more product (\(H_{2}O_{2}(aq)\)) than reactant (\(H_{2}O_{2}(g)\)).

Key Concepts

Equilibrium Constant

The equilibrium constant, often denoted as \( K \), provides insight into the balance of a chemical reaction at equilibrium. It depicts the ratio of the concentrations of products to the concentrations of reactants. The formula for \( K \) is:

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

If \( K \) is greater than 1, this suggests that the products are favored, meaning the concentration of products is higher than that of reactants at equilibrium.If \( K \) is less than 1, the reactants are favored instead.

In our example reaction, \( K = 1.0 \times 10^{5} \), a very large number, indicating a significant presence of products in comparison to reactants.This means the equilibrium position is shifted towards the formation of aqueous hydrogen peroxide over its gaseous form.

Hydrogen Peroxide

Hydrogen Peroxide, with the chemical formula \( H_2O_2 \), is a compound well-known for its bleaching and disinfecting properties.It exists in different phases, including liquid, gas, and aqueous solution.

🔍 **Characteristics:**

• In Gas Phase: At higher temperatures or low pressures, hydrogen peroxide can transition into a gas, indicated by \( H_{2}O_{2}(g) \).
• In Aqueous Solution: When mixed with water, it is represented as \( H_{2}O_{2}(aq) \), typically seen at lower pressures or room temperatures.

In chemical reactions such as the provided one, hydrogen peroxide can transition between phases, indicating its dynamic nature and dependency on conditions like temperature and pressure.This flexibility is crucial in applications like medical sterilization and environmental bleaching.

Phase Equilibrium

Phase equilibrium occurs when different physical states or phases of a substance exist together without changing over time.In our reaction, it involves the equilibrium between gaseous hydrogen peroxide \( H_{2}O_{2}(g) \) and its aqueous form \( H_{2}O_{2}(aq) \).

At phase equilibrium, each phase maintains a stable concentration relative to the amount of energy available at a given temperature. The equilibrium constant \( K \), as derived from the reaction's conditions, helps determine how these concentrations relate.For example, a large \( K \) here suggests that maintaining a dynamic yet stable state is more reactive towards forming the aqueous phase.
🔍 **Key Takeaways:**

• It's a balance without net change over time, despite ongoing molecular exchanges between phases.
• Dependent on pressure and temperature, these conditions influence which phase will predominantly form or dissolve.

Understanding phase equilibrium is crucial in industries where specific states of substances need to be maintained, e.g., pharmaceuticals and chemical manufacturing.