To solve this problem, we need to determine the partial pressure of hydrogen gas when it is collected over water. Follow these steps:
1. Understand the problem: We know that the total pressure in the collecting bottle is a combination of the partial pressure of hydrogen gas and the vapor pressure of water. The total pressure given is 97.1 kPa, and the vapor pressure of water is 3.2 kPa.
2. Set up the equation: According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. Mathematically, this is represented as:
[tex]\[
P_{\text{total}} = P_{\text{hydrogen}} + P_{\text{water vapor}}
\][/tex]
We need to solve for [tex]\( P_{\text{hydrogen}} \)[/tex], the partial pressure of hydrogen gas.
3. Substitute the known values into the equation: The total pressure [tex]\( P_{\text{total}} \)[/tex] is 97.1 kPa and the vapor pressure of water [tex]\( P_{\text{water vapor}} \)[/tex] is 3.2 kPa. Plug these values into the equation:
[tex]\[
97.1 \, \text{kPa} = P_{\text{hydrogen}} + 3.2 \, \text{kPa}
\][/tex]
4. Solve for [tex]\( P_{\text{hydrogen}} \)[/tex]: To find the partial pressure of hydrogen, subtract the vapor pressure of water from the total pressure:
[tex]\[
P_{\text{hydrogen}} = 97.1 \, \text{kPa} - 3.2 \, \text{kPa} = 93.9 \, \text{kPa}
\][/tex]
5. Conclusion: The partial pressure of the hydrogen gas in the collecting bottle is 93.9 kPa.
Therefore, the correct answer is:
[tex]\[
\boxed{93.9 \, \text{kPa}}
\][/tex]
