Gas Laws Fact Sheet
\begin{tabular}{|l|l|}
\hline Ideal gas law & [tex]$PV = nRT$[/tex] \\
\hline & [tex]$R = 8.314 \left( \frac{J}{mol \cdot K} \right)$[/tex] \\
\hline Ideal gas constant & or \\
& [tex]$R = 0.0821 \frac{L \cdot atm}{mol \cdot K}$[/tex] \\
\hline Standard atmospheric pressure & [tex]$1 \, atm = 101.3 \, kPa$[/tex] \\
\hline Celsius to Kelvin conversion & [tex]$K = {^\circ}C + 273.15$[/tex] \\
\hline
\end{tabular}

Select the correct answer.

A scuba diver's air tank contains oxygen, helium, and nitrogen at a total pressure of 205 atmospheres. The partial pressure of nitrogen is 143 atmospheres, and the partial pressure of helium is 41 atmospheres. What is the partial pressure of oxygen in the tank?

A. 21 atm
B. 103 atm
C. 307 atm
D. 389 atm



Answer :

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