Gas Laws Fact Sheet

\[
\begin{array}{|l|l|}
\hline
\text{Ideal gas law} & PV = nRT \\
\hline
\text{Ideal gas constant} & R = 8.314 \\
& R = 0.0821 \frac{L \cdot kPa}{mol \cdot K} \\
\hline
\end{array}
\]

Select the correct answer.

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. [tex]\( 93.9 \, \text{kPa} \)[/tex]
B. [tex]\( 98.1 \, \text{kPa} \)[/tex]
C. [tex]\( 100.3 \, \text{kPa} \)[/tex]
D. [tex]\( 104.5 \, \text{kPa} \)[/tex]

To find the partial pressure of the hydrogen gas, we can use Dalton's Law of Partial Pressures. According to this law, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture.

Here's how you can solve the problem step-by-step:

1. Identify the total pressure: The total pressure in the collecting bottle is given as 97.1 kilopascals (kPa).

2. Identify the vapor pressure of water: The vapor pressure of the water in the bottle is given as 3.2 kilopascals (kPa).

3. Apply Dalton's Law of Partial Pressures: According to Dalton's Law, the total pressure is the sum of the partial pressure of hydrogen and the partial pressure of water vapor. Therefore, you can express this relationship as:

[tex]\[
\text{Total Pressure} = \text{Partial Pressure of Hydrogen} + \text{Vapor Pressure of Water}
\][/tex]

4. Solve for the partial pressure of hydrogen: Rearrange the equation to find the partial pressure of the hydrogen gas:

[tex]\[
\text{Partial Pressure of Hydrogen} = \text{Total Pressure} - \text{Vapor Pressure of Water}
\][/tex]

5. Substitute the known values:

[tex]\[
\text{Partial Pressure of Hydrogen} = 97.1 \text{ kPa} - 3.2 \text{ kPa} = 93.9 \text{ kPa}
\][/tex]

So, the partial pressure of the hydrogen gas is 93.9 kPa. Therefore, the correct answer is A. [tex]\( 93.9 \text{ kPa} \)[/tex].