Question
A mixture of oxygen, helium, and nitrogen gases exerts a total pressure of 287 kPa. If the partial pressures of the oxygen and the helium are 112 kPa and 11 kPa respectively, what would be the partial pressure exerted by the nitrogen?
276 kPa
101 kPa
175 kPa
164 kPa
276 kPa
101 kPa
175 kPa
164 kPa
Answers
GPT-4o mini
To find the partial pressure of nitrogen, you can use Dalton's law of partial pressures, which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas.
The formula can be expressed as:
\[
P_{\text{total}} = P_{\text{O}_2} + P_{\text{He}} + P_{\text{N}_2}
\]
Given:
- \( P_{\text{total}} = 287 \, \text{kPa} \)
- \( P_{\text{O}_2} = 112 \, \text{kPa} \)
- \( P_{\text{He}} = 11 \, \text{kPa} \)
We need to find \( P_{\text{N}_2} \):
\[
P_{\text{N}_2} = P_{\text{total}} - P_{\text{O}_2} - P_{\text{He}}
\]
Substituting in the given values:
\[
P_{\text{N}_2} = 287 \, \text{kPa} - 112 \, \text{kPa} - 11 \, \text{kPa}
\]
Calculating the right-hand side:
\[
P_{\text{N}_2} = 287 \, \text{kPa} - 123 \, \text{kPa} = 164 \, \text{kPa}
\]
Therefore, the partial pressure exerted by the nitrogen is \( \boxed{164 \, \text{kPa}} \).
The formula can be expressed as:
\[
P_{\text{total}} = P_{\text{O}_2} + P_{\text{He}} + P_{\text{N}_2}
\]
Given:
- \( P_{\text{total}} = 287 \, \text{kPa} \)
- \( P_{\text{O}_2} = 112 \, \text{kPa} \)
- \( P_{\text{He}} = 11 \, \text{kPa} \)
We need to find \( P_{\text{N}_2} \):
\[
P_{\text{N}_2} = P_{\text{total}} - P_{\text{O}_2} - P_{\text{He}}
\]
Substituting in the given values:
\[
P_{\text{N}_2} = 287 \, \text{kPa} - 112 \, \text{kPa} - 11 \, \text{kPa}
\]
Calculating the right-hand side:
\[
P_{\text{N}_2} = 287 \, \text{kPa} - 123 \, \text{kPa} = 164 \, \text{kPa}
\]
Therefore, the partial pressure exerted by the nitrogen is \( \boxed{164 \, \text{kPa}} \).