To solve this problem, we'll need to make use of the concept of partial pressures in a gas mixture. The total pressure of a mixture of gases is the sum of the partial pressures of each individual gas. This concept is described by Dalton's Law of Partial Pressures.
Given in the problem:
- Total pressure in the tank: [tex]\( P_{total} = 205 \)[/tex] atmospheres
- Partial pressure of nitrogen: [tex]\( P_{N_2} = 143 \)[/tex] atmospheres
- Partial pressure of helium: [tex]\( P_{He} = 41 \)[/tex] atmospheres
We are asked to find the partial pressure of oxygen [tex]\( P_{O_2} \)[/tex].
According to Dalton's Law of Partial Pressures:
[tex]\[ P_{total} = P_{N_2} + P_{He} + P_{O_2} \][/tex]
Rearranging the equation to solve for [tex]\( P_{O_2} \)[/tex]:
[tex]\[ P_{O_2} = P_{total} - (P_{N_2} + P_{He}) \][/tex]
Substitute the given values:
[tex]\[ P_{O_2} = 205 \, \text{atm} - (143 \, \text{atm} + 41 \, \text{atm}) \][/tex]
[tex]\[ P_{O_2} = 205 \, \text{atm} - 184 \, \text{atm} \][/tex]
[tex]\[ P_{O_2} = 21 \, \text{atm} \][/tex]
Therefore, the partial pressure of oxygen in the tank is [tex]\( 21 \)[/tex] atmospheres. The correct answer is:
A. 21 atm
