To determine the partial pressure of oxygen in the scuba diver's air tank, we need to use the information given about the total pressure and the partial pressures of the other gases present (nitrogen and helium).
Let's break down the problem step-by-step:
1. Identify the total pressure in the tank:
The total pressure in the tank is given as 205 atmospheres (atm).
2. Identify the partial pressures of the other gases:
- The partial pressure of nitrogen ([tex]\(P_{N_2}\)[/tex]) is 143 atm.
- The partial pressure of helium ([tex]\(P_{He}\)[/tex]) is 41 atm.
3. Set up the relationship based on Dalton's Law of Partial Pressures:
According to Dalton's Law, the total pressure in a gas mixture is the sum of the partial pressures of each component gas. Therefore, we can express this relationship as:
[tex]\[
P_{total} = P_{N_2} + P_{He} + P_{O_2}
\][/tex]
where [tex]\(P_{O_2}\)[/tex] is the partial pressure of oxygen, which we need to find.
4. Substitute the known values into the equation:
[tex]\[
205 \, \text{atm} = 143 \, \text{atm} + 41 \, \text{atm} + P_{O_2}
\][/tex]
5. Solve for [tex]\(P_{O_2}\)[/tex]:
First, sum the partial pressures of nitrogen and helium:
[tex]\[
143 \, \text{atm} + 41 \, \text{atm} = 184 \, \text{atm}
\][/tex]
Next, subtract this sum from the total pressure to find the partial pressure of oxygen:
[tex]\[
205 \, \text{atm} - 184 \, \text{atm} = 21 \, \text{atm}
\][/tex]
Therefore, the partial pressure of oxygen in the tank is 21 atmospheres.
The correct answer is:
A. 21 atm.
