Question

A scuba diver $60ft$below the ocean surface inhales $50.0mL$of compressed air from a ccuba tank at a pressure of $3.00atm$and a temperature of $8°C$. What is the final pressure of air, in atmospheres, in the lungs when the gas expands to $150.0mL$at a body temperature of $37°C$, if the amount of gas does not change?

Short answer

The final pressure of the gas is$1.1atm$.

Step-by-step solution

Given Information

We need to find the final pressure of gas.

Simplify

The combined gas law is:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

Consider:

initial pressure$P_1=3atm$

initial temperature$T_1=8°C=\left(8+273\right)K=281K$

initial volume$V_1=50mL$

final temperature$T_2=37°C=\left(37+273\right)K=310K$

final volume$V_2=150mL$

Now, calculating the final pressure $P_2$is:

$$\begin{gathered} P_2=\left(\frac{\left(P_1\times V_1\right)}{T_1}\right)\times \left(\frac{V_2}{T_2}\right) \\ {P}_2=\left(\frac{\left(3atm\times 50mL\right)}{281K}\right)\times \left(\frac{310K}{150mL}\right) \\ {P}_2=1.1atm \end{gathered}$$