To find the partial pressure of oxygen in the scuba diver's air tank, we can use Dalton’s Law of Partial Pressures. Dalton’s Law states that the total pressure exerted by a gaseous mixture is the sum of the partial pressures of each individual gas in the mixture. Mathematically, it can be expressed as:
[tex]\[ P_{\text{total}} = P_{\text{nitrogen}} + P_{\text{helium}} + P_{\text{oxygen}} \][/tex]
We are given:
- The total pressure ([tex]\(P_{\text{total}}\)[/tex]) is 205 atmospheres.
- The partial pressure of nitrogen ([tex]\(P_{\text{nitrogen}}\)[/tex]) is 143 atmospheres.
- The partial pressure of helium ([tex]\(P_{\text{helium}}\)[/tex]) is 41 atmospheres.
We need to find the partial pressure of oxygen ([tex]\(P_{\text{oxygen}}\)[/tex]).
We can rearrange Dalton’s Law to solve for [tex]\(P_{\text{oxygen}}\)[/tex]:
[tex]\[ P_{\text{oxygen}} = P_{\text{total}} - P_{\text{nitrogen}} - P_{\text{helium}} \][/tex]
Substituting the given values:
[tex]\[ P_{\text{oxygen}} = 205 \, \text{atm} - 143 \, \text{atm} - 41 \, \text{atm} \][/tex]
[tex]\[ P_{\text{oxygen}} = 205 - 143 - 41 \][/tex]
[tex]\[ P_{\text{oxygen}} = 21 \, \text{atm} \][/tex]
Therefore, the partial pressure of oxygen in the tank is [tex]\(21 \, \text{atm}\)[/tex].
The correct answer is:
A. 21 atm
