Gas Laws Fact Sheet

[tex]
\[
\begin{array}{|l|l|}
\hline \text{Ideal gas law} & P V = n R T \\
\hline \text{Ideal gas constant} & \begin{array}{l}
R = 8.314 \frac{L \cdot kPa}{mol \cdot K} \\
\text{or} \\
R = 0.0821 \frac{L \cdot atm}{mol \cdot K}
\end{array} \\
\hline \text{Standard atmospheric pressure} & 1 \, atm = 101.3 \, kPa \\
\hline \text{Celsius to Kelvin conversion} & K = { }^{\circ} C + 273.15 \\
\hline
\end{array}
\]
[/tex]

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

Here's a step-by-step solution:

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

2. Identify the Vapor Pressure of Water:
The vapor pressure of water at the moment is 3.2 kilopascals (kPa).

3. Apply Dalton's Law of Partial Pressures:
According to Dalton's Law:
[tex]\[
\text{Total Pressure} = \text{Partial Pressure of Hydrogen} + \text{Vapor Pressure of Water}
\][/tex]

4. Rearrange the Equation to Solve for the Partial Pressure of Hydrogen:
[tex]\[
\text{Partial Pressure of Hydrogen} = \text{Total Pressure} - \text{Vapor Pressure of Water}
\][/tex]
[tex]\[
\text{Partial Pressure of Hydrogen} = 97.1 \, \text{kPa} - 3.2 \, \text{kPa}
\][/tex]

5. Calculate the Partial Pressure of Hydrogen:
[tex]\[
\text{Partial Pressure of Hydrogen} = 93.9 \, \text{kPa}
\][/tex]

Hence, the partial pressure of the hydrogen is 93.9 kPa, which corresponds to answer choice A.