A mixture of H2(g) and O2(g) is prepared by electrolyzing...

A mixture of $\mathrm{H}_{2}(\mathrm{g})$ and $\mathrm{O}_{2}(\mathrm{g})$ is prepared by electrolyzing $1.32 \mathrm{g}$ water, and the mixture of gases is collected over water at $30^{\circ} \mathrm{C}$ and $748 \mathrm{mmHg}$. The volume of "wet" gas obtained is 2.90 L. What must be the vapor pressure of water at $30^{\circ} \mathrm{C} ?$ $$2 \mathrm{H}_{2} \mathrm{O}(1) \stackrel{\text { electrolysis }}{\longrightarrow} 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$

A mixture of $\mathrm{H}_{2}(\mathrm{g})$ and $\mathrm{O}_{2}(\mathrm{g})$ is prepared by electrolyzing $1.32 \mathrm{g}$ water, and the mixture of gases is collected over water at $30^{\circ} \mathrm{C}$ and $748 \mathrm{mmHg}$. The volume of "wet" gas obtained is 2.90 L. What must be the vapor pressure of water at $30^{\circ} \mathrm{C} ?$
$$2 \mathrm{H}_{2} \mathrm{O}(1) \stackrel{\text { electrolysis }}{\longrightarrow} 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$

Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. It is a fundamental principle used to calculate unknown parameters in gas mixtures, particularly when corrections for water vapor pressure are needed.

Gas Collection over Water

When gases are collected over water, the collected gas is saturated with water vapor. This method necessitates accounting for the water vapor's pressure when applying gas laws, as the measured pressure includes both the gas of interest and the water vapor.

Stoichiometry of Electrolysis

Stoichiometry in the context of electrolysis involves using balanced chemical equations to determine the mole ratios of reactants and products. It is essential for calculating the amounts of gases produced during the electrolysis of water and understanding the underlying quantitative relationships.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature. It is important when gases are collected over water because the water vapor contributes to the total observed pressure, requiring a correction to obtain the pressure of the dry gas.

Partial Pressure

Partial pressure refers to the individual pressure contributed by each component in a gas mixture. In gas collections involving water vapor, the total pressure is the sum of the partial pressures of both the collected gases and the water vapor, making it a critical concept for correct analysis.

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