A sample of \(\mathrm{CH}_{4}\) gas was collected over water at \(29^{\circ} \mathrm{C}\) and 749 \(\mathrm{mm} \mathrm{Hg}\). What is the partial pressure of the \(\mathrm{CH}_{4}\) ? (Refer to Appendix 5 for the vapor pressure of water.)

Understanding the concept of vapor pressure is crucial when dealing with mixtures of gases, especially when collected over water. Vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. In simpler terms, it's the pressure created by the evaporation of liquid or solid into a gas.

For water, this pressure will vary depending on the temperature. Typically, tables or appendices, such as Appendix 5 mentioned in the exercise, provide this information. At 29°C, the vapor pressure of water can be found listed in such references. This vapor pressure is important to consider because it contributes to the total pressure in the container where a gas is collected over water. To determine the partial pressure of just the gas of interest, like methane (CH4), one must subtract the vapor pressure of water from the total pressure measured.

When working with gas mixtures, like a sample of gas collected over water, the total pressure measured is the sum of pressures exerted by each individual component in the mixture. This total pressure is the result of all the gas particles colliding with the walls of the container. Each component, including water vapor, contributes to the overall pressure depending on its concentration and the temperature.

It's key to realize that gases do not react with each other under these circumstances; they act independently. Therefore, to find the pressure of a specific gas within the mixture, we must understand the distribution of total pressure among the individual gases, which brings us to Dalton's law of partial pressures.

Dalton's law of partial pressures is essential when separating the pressure contributions of various gases in a mixture. It states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. The partial pressure of each gas is proportionate to its mole fraction in the mixture.

Applying this law to the textbook question, once we have the vapor pressure of water at 29°C, Dalton's law directs us to subtract it from the total pressure (749 mm Hg) to isolate the partial pressure of methane (CH4). This can be seen as the gas having its own ‘space’ or share of the pressure in the container, separate from the water vapor and any other gasses present. Using this law allows students to understand and calculate the behaviors of gases in a mixture with greater precision.