Answer :
Sure, let's break this down step-by-step.
We begin with the given values:
- The total pressure of the gas mixture (hydrogen gas and water vapor) is [tex]\( 97.1 \)[/tex] kilopascals (kPa).
- The vapor pressure of water is [tex]\( 3.2 \)[/tex] kilopascals (kPa).
We need to determine the partial pressure of the hydrogen gas.
According to Dalton's Law of Partial Pressures:
[tex]\[ \text{Total pressure} = \text{Partial pressure of hydrogen} + \text{Partial pressure of water vapor} \][/tex]
Let's denote:
- [tex]\( P_{\text{total}} \)[/tex] as the total pressure,
- [tex]\( P_{\text{H}_2} \)[/tex] as the partial pressure of hydrogen,
- [tex]\( P_{\text{H}_2O} \)[/tex] as the partial pressure of water vapor.
Given:
[tex]\[ P_{\text{total}} = 97.1 \, \text{kPa} \][/tex]
[tex]\[ P_{\text{H}_2O} = 3.2 \, \text{kPa} \][/tex]
We need to solve for [tex]\( P_{\text{H}_2} \)[/tex]. To do this, we rearrange Dalton's Law to find the partial pressure of hydrogen:
[tex]\[ P_{\text{H}_2} = P_{\text{total}} - P_{\text{H}_2O} \][/tex]
Substitute the known values:
[tex]\[ P_{\text{H}_2} = 97.1 \, \text{kPa} - 3.2 \, \text{kPa} \][/tex]
Perform the subtraction:
[tex]\[ P_{\text{H}_2} = 93.9 \, \text{kPa} \][/tex]
Hence, the partial pressure of the hydrogen gas is [tex]\( 93.9 \, \text{kPa} \)[/tex]. None of the provided options (9 kPa, 98.1 kPa, 100.3 kPa, 1OA F kPn) match the correct answer.
We begin with the given values:
- The total pressure of the gas mixture (hydrogen gas and water vapor) is [tex]\( 97.1 \)[/tex] kilopascals (kPa).
- The vapor pressure of water is [tex]\( 3.2 \)[/tex] kilopascals (kPa).
We need to determine the partial pressure of the hydrogen gas.
According to Dalton's Law of Partial Pressures:
[tex]\[ \text{Total pressure} = \text{Partial pressure of hydrogen} + \text{Partial pressure of water vapor} \][/tex]
Let's denote:
- [tex]\( P_{\text{total}} \)[/tex] as the total pressure,
- [tex]\( P_{\text{H}_2} \)[/tex] as the partial pressure of hydrogen,
- [tex]\( P_{\text{H}_2O} \)[/tex] as the partial pressure of water vapor.
Given:
[tex]\[ P_{\text{total}} = 97.1 \, \text{kPa} \][/tex]
[tex]\[ P_{\text{H}_2O} = 3.2 \, \text{kPa} \][/tex]
We need to solve for [tex]\( P_{\text{H}_2} \)[/tex]. To do this, we rearrange Dalton's Law to find the partial pressure of hydrogen:
[tex]\[ P_{\text{H}_2} = P_{\text{total}} - P_{\text{H}_2O} \][/tex]
Substitute the known values:
[tex]\[ P_{\text{H}_2} = 97.1 \, \text{kPa} - 3.2 \, \text{kPa} \][/tex]
Perform the subtraction:
[tex]\[ P_{\text{H}_2} = 93.9 \, \text{kPa} \][/tex]
Hence, the partial pressure of the hydrogen gas is [tex]\( 93.9 \, \text{kPa} \)[/tex]. None of the provided options (9 kPa, 98.1 kPa, 100.3 kPa, 1OA F kPn) match the correct answer.
