To find the partial pressure of oxygen in the tank, we can use Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
Given:
- Total pressure, \( P_{total} = 150 , \text{kPa} \)
- Partial pressure of nitrogen, \( P_{N_2} = 90 , \text{kPa} \)
- Partial pressure of carbon dioxide, \( P_{CO_2} = 34 , \text{kPa} \)
We need to find the partial pressure of oxygen, \( P_{O_2} \).
Using the equation:
\[ P_{total} = P_{N_2} + P_{CO_2} + P_{O_2} \]
Substituting the known values:
\[ 150 , \text{kPa} = 90 , \text{kPa} + 34 , \text{kPa} + P_{O_2} \]
Now combine the pressures of nitrogen and carbon dioxide:
\[ 150 , \text{kPa} = 124 , \text{kPa} + P_{O_2} \]
Now, solve for \( P_{O_2} \):
\[ P_{O_2} = 150 , \text{kPa} - 124 , \text{kPa} \] \[ P_{O_2} = 26 , \text{kPa} \]
Thus, the partial pressure of oxygen is \( \boxed{26 , \text{kPa}} \).
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