Q. 8.61 - An Introduction to General, Organic, and Biological Chemistry

Question

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

Step-by-Step Solution

Answer

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

Step 1: Given Information

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

Step 2: Simplify

Now,

 STP conditions mean:

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

Combined gas law :

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

Consider:

initial pressure $P_1=745 mmHg$

final pressure $P_1=760mmHg$

initial volume $V_1=3.2 L$

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 $V_2$:

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

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