Sure, let's solve this step-by-step.
1. Determine the moles of hydrogen gas:
Given:
- Total moles of gas in the container: [tex]\( n_T = 6.4 \)[/tex] moles
- Percentage of hydrogen gas: [tex]\( 25\% \)[/tex]
To find the moles of hydrogen gas ([tex]\( n_H \)[/tex]):
[tex]\[
n_H = \text{total moles} \times \text{percentage of hydrogen}
\][/tex]
[tex]\[
n_H = 6.4 \times 0.25 = 1.6 \text{ moles}
\][/tex]
2. Determine the partial pressure of hydrogen gas:
Given:
- Total pressure in the container: [tex]\( P_T = 1.24 \)[/tex] atm
Using the relationship between partial pressure and moles:
[tex]\[
\frac{P_H}{P_T} = \frac{n_H}{n_T}
\][/tex]
Rearrange to solve for [tex]\( P_H \)[/tex] (the partial pressure of hydrogen):
[tex]\[
P_H = P_T \times \frac{n_H}{n_T}
\][/tex]
[tex]\[
P_H = 1.24 \times \frac{1.6}{6.4}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{1.6}{6.4} = 0.25
\][/tex]
Therefore:
[tex]\[
P_H = 1.24 \times 0.25 = 0.31 \text{ atm}
\][/tex]
So, the partial pressure of hydrogen in the container is [tex]\( 0.31 \)[/tex] atm.
