Question

Whitney's lung capacity was measured as $3.2L$at a body temperature of $37°C$and a pressure of $745mmHg$. What is her lung capacity, in liters, at STP?

Short answer

Whitney's lung capacity at STP is$2.8L$.

Step-by-step solution

Given Information

We need to find Whitney's lung capacity at STP.

Simplify

Now,

STP conditions mean:

• Standard temperature is exactly $0°C\left(273K\right)$
• Standard pressure id exactly $1atm(760mmHg)$

Combined gas law :

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

Consider:

initial pressure$P_1=745mmHg$

final pressure$P_1=760mmHg$

initial volume$V_1=3.2L$

initial temperature$T_1=37°C=(37+273)K=310K$

final temperature $T_2=0°C=(0+273)K=273K$

Now, finding the final volume $V_2$:

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

$$\begin{gathered} V_2=\left(\frac{P_1\times V_1}{T_1}\right)\times \left(\frac{T_2}{P_2}\right) \\ {V}_2=\left(\frac{745mmHg\times 3.2L}{310K}\right)\times \left(\frac{273K}{760mmHg}\right) \\ {V}_2=\frac{650832L}{235600} \\ {V}_2=2.8L \end{gathered}$$