To answer the question of finding the partial pressure of hydrogen in the container, follow these steps:
1. Identify the given values:
- Total moles of gas in the container, \( n_T = 6.4 \) moles.
- Fraction of hydrogen gas in the container, \( \text{Hydrogen fraction} = 0.25 \).
- Total pressure of the gas mixture, \( P_T = 1.24 \) atm.
2. Calculate the moles of hydrogen gas:
The fraction of hydrogen gas is \( 0.25 \) (or 25%), so the moles of hydrogen, \( n_H \), can be calculated as:
[tex]\[
n_H = \text{Hydrogen fraction} \times n_T = 0.25 \times 6.4 = 1.6 \text{ moles}
\][/tex]
3. Use the formula for partial pressure:
The partial pressure of a gas in a mixture can be found using the relation:
[tex]\[
\frac{P_a}{P_T} = \frac{n_a}{n_T}
\][/tex]
Where:
- \( P_a \) is the partial pressure of the gas (hydrogen in this case).
- \( P_T \) is the total pressure of the gas mixture.
- \( n_a \) is the moles of the gas (hydrogen in this case).
- \( n_T \) is the total moles of gas in the mixture.
4. Rearrange the formula to solve for \( P_a \):
[tex]\[
P_a = P_T \times \frac{n_a}{n_T}
\][/tex]
5. Substitute the known values into the equation:
[tex]\[
P_H = 1.24 \times \frac{1.6}{6.4}
\][/tex]
6. Simplify the fraction:
[tex]\[
\frac{1.6}{6.4} = 0.25
\][/tex]
7. Calculate the partial pressure:
[tex]\[
P_H = 1.24 \times 0.25 = 0.31 \text{ atm}
\][/tex]
Therefore, the partial pressure of hydrogen in the container is \( 0.31 \) atm.
Among the given options:
- \( 0.31 \) atm
- \( 0.93 \) atm
- \( 5.2 \) atm
- \( 31 \) atm
The correct option is [tex]\( \boxed{0.31 \text{ atm}} \)[/tex].
