Gas Laws Fact Sheet

[tex]
\[
\begin{array}{|l|l|}
\hline
\text{Ideal gas law} & P V = n R T \\
\hline
\text{Ideal gas constant} & R = 0.0821 \frac{L \cdot atm}{mol \cdot K} \\
\hline
\text{Standard atmospheric pressure} & 1 \, atm = 101.3 \, kPa \\
\hline
\text{Celsius to Kelvin conversion} & K = ^{\circ}C + 273.15 \\
\hline
\end{array}
\]
[/tex]

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

To determine the partial pressure of hydrogen in the bottle, we use the fact that the total pressure in the bottle is the sum of the partial pressures of hydrogen and water vapor. This can be written as:

[tex]$$
P_{\text{total}} = P_{\text{H}_2} + P_{\text{H}_2O}
$$[/tex]

In this problem, the total pressure in the bottle is given as [tex]$97.1\ \text{kPa}$[/tex], and the vapor pressure of the water is [tex]$3.2\ \text{kPa}$[/tex]. We want to find the partial pressure of hydrogen, [tex]$P_{\text{H}_2}$[/tex]. Rearranging the equation, we have:

[tex]$$
P_{\text{H}_2} = P_{\text{total}} - P_{\text{H}_2O}
$$[/tex]

Substitute in the given values:

[tex]$$
P_{\text{H}_2} = 97.1\ \text{kPa} - 3.2\ \text{kPa} = 93.9\ \text{kPa}
$$[/tex]

Thus, the partial pressure of hydrogen is [tex]$93.9\ \text{kPa}$[/tex].

The correct answer is:

A. [tex]$\quad 93.9\ \text{kPa}$[/tex]