To find the partial pressure of oxygen in the scuba diver's air tank, we will use the concept of total pressure and partial pressures in a mixture of gases. According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
Given:
- The total pressure in the tank is 205 atmospheres.
- The partial pressure of nitrogen (P[tex]\(_{\text{N}_2}\)[/tex]) is 143 atmospheres.
- The partial pressure of helium (P[tex]\(_{\text{He}}\)[/tex]) is 41 atmospheres.
To find the partial pressure of oxygen (P[tex]\(_{\text{O}_2}\)[/tex]), we use the equation:
[tex]\[
P_{\text{total}} = P_{\text{N}_2} + P_{\text{He}} + P_{\text{O}_2}
\][/tex]
Rearranging to isolate P[tex]\(_{\text{O}_2}\)[/tex], we get:
[tex]\[
P_{\text{O}_2} = P_{\text{total}} - P_{\text{N}_2} - P_{\text{He}}
\][/tex]
Substitute the given values into the equation:
[tex]\[
P_{\text{O}_2} = 205 \text{ atm} - 143 \text{ atm} - 41 \text{ atm}
\][/tex]
Perform the subtraction:
[tex]\[
P_{\text{O}_2} = 205 \text{ atm} - 184 \text{ atm} = 21 \text{ atm}
\][/tex]
Therefore, the partial pressure of oxygen in the tank is 21 atmospheres.
The correct answer is:
A. [tex]\( 21 \)[/tex] atm
