When a chemist collects hydrogen gas over water, she ends up with a mixture of hydrogen and water vapor in her collecting bottle. If the pressure in the collecting bottle is 97.1 kilopascals and the vapor pressure of the water is 3.2 kilopascals, what is the partial pressure of the hydrogen?

A. 93.9 kPa
B. 98.1 kPa
C. 100.3 kPa
D. 104.5 kPa

Note: Standard atmospheric pressure: [tex]R=0.0821 \frac{L \cdot atm}{mol \cdot K}[/tex]

To determine the partial pressure of hydrogen gas in the collecting bottle, we need to use Dalton's Law of Partial Pressures. This law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas in the mixture.

Here's the step-by-step solution:

1. Identify Known Values:
- Total Pressure in the Collecting Bottle: This is given as 97.1 kilopascals (kPa).
- Vapor Pressure of Water: This is given as 3.2 kilopascals (kPa).

2. Apply Dalton's Law of Partial Pressures:
- According to Dalton’s Law, the total pressure is the sum of the partial pressures of the hydrogen gas and the water vapor in the bottle. Mathematically, it can be represented as:
[tex]\[
\text{Total Pressure} = \text{Partial Pressure of Hydrogen} + \text{Vapor Pressure of Water}
\][/tex]

3. Calculate the Partial Pressure of Hydrogen:
- Rearrange the formula to solve for the partial pressure of hydrogen:
[tex]\[
\text{Partial Pressure of Hydrogen} = \text{Total Pressure} - \text{Vapor Pressure of Water}
\][/tex]
- Substitute the known values into the equation:
[tex]\[
\text{Partial Pressure of Hydrogen} = 97.1 \, \text{kPa} - 3.2 \, \text{kPa}
\][/tex]
- Calculate the result:
[tex]\[
\text{Partial Pressure of Hydrogen} = 93.9 \, \text{kPa}
\][/tex]

Therefore, the partial pressure of the hydrogen gas is 93.9 kPa, which corresponds to option A.