Answer :
To determine the partial pressure of hydrogen gas, we need to follow a systematic approach. We will use the given data and apply Dalton's Law of Partial Pressures, which states that the partial pressure of a gas in a mixture is proportional to its mole fraction in the mixture.
### Step-by-step Solution:
1. Identify the total moles of gas:
[tex]\[ n_{\text{total}} = 6.4 \text{ moles} \][/tex]
2. Determine the moles of hydrogen gas:
Hydrogen makes up [tex]\( 25\% \)[/tex] of the total moles.
[tex]\[ n_{\text{hydrogen}} = 0.25 \times 6.4 = 1.6 \text{ moles} \][/tex]
3. Identify the total pressure in the container:
[tex]\[ P_T = 1.24 \text{ atm} \][/tex]
4. Use Dalton's Law of Partial Pressures:
The formula for the partial pressure of hydrogen is:
[tex]\[ \frac{P_{\text{hydrogen}}}{P_T} = \frac{n_{\text{hydrogen}}}{n_{\text{total}}} \][/tex]
5. Calculate the partial pressure of hydrogen:
[tex]\[ P_{\text{hydrogen}} = \frac{n_{\text{hydrogen}}}{n_{\text{total}}} \times P_T \][/tex]
Plugging in the known values:
[tex]\[ P_{\text{hydrogen}} = \frac{1.6}{6.4} \times 1.24 \text{ atm} \][/tex]
Simplifying the fraction:
[tex]\[ \frac{1.6}{6.4} = 0.25 \][/tex]
Therefore:
[tex]\[ P_{\text{hydrogen}} = 0.25 \times 1.24 = 0.31 \text{ atm} \][/tex]
### Conclusion:
The partial pressure of hydrogen in the container is [tex]\( 0.31 \text{ atm} \)[/tex].
So, the correct answer is:
[tex]\[ 0.31 \text{ atm} \][/tex]
From the given choices, the correct option is:
[tex]\[ 0.31 \text{ atm} \][/tex]
### Step-by-step Solution:
1. Identify the total moles of gas:
[tex]\[ n_{\text{total}} = 6.4 \text{ moles} \][/tex]
2. Determine the moles of hydrogen gas:
Hydrogen makes up [tex]\( 25\% \)[/tex] of the total moles.
[tex]\[ n_{\text{hydrogen}} = 0.25 \times 6.4 = 1.6 \text{ moles} \][/tex]
3. Identify the total pressure in the container:
[tex]\[ P_T = 1.24 \text{ atm} \][/tex]
4. Use Dalton's Law of Partial Pressures:
The formula for the partial pressure of hydrogen is:
[tex]\[ \frac{P_{\text{hydrogen}}}{P_T} = \frac{n_{\text{hydrogen}}}{n_{\text{total}}} \][/tex]
5. Calculate the partial pressure of hydrogen:
[tex]\[ P_{\text{hydrogen}} = \frac{n_{\text{hydrogen}}}{n_{\text{total}}} \times P_T \][/tex]
Plugging in the known values:
[tex]\[ P_{\text{hydrogen}} = \frac{1.6}{6.4} \times 1.24 \text{ atm} \][/tex]
Simplifying the fraction:
[tex]\[ \frac{1.6}{6.4} = 0.25 \][/tex]
Therefore:
[tex]\[ P_{\text{hydrogen}} = 0.25 \times 1.24 = 0.31 \text{ atm} \][/tex]
### Conclusion:
The partial pressure of hydrogen in the container is [tex]\( 0.31 \text{ atm} \)[/tex].
So, the correct answer is:
[tex]\[ 0.31 \text{ atm} \][/tex]
From the given choices, the correct option is:
[tex]\[ 0.31 \text{ atm} \][/tex]
