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 \( \boxed{164 , \text{kPa}} \).