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A container holds 6.4 moles of gas. Hydrogen gas makes up [tex]25 \%[/tex] of the total moles in the container. If the total pressure is [tex]1.24 \, \text{atm}[/tex], what is the partial pressure of hydrogen?

Use [tex]\frac{p_2}{P_T}=\frac{n_2}{n_T}[/tex].

A. [tex]0.31 \, \text{atm}[/tex]
B. [tex]0.93 \, \text{atm}[/tex]
C. [tex]5.2 \, \text{atm}[/tex]
D. [tex]31 \, \text{atm}[/tex]



Answer :

GinnyAnswer
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]

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