Q. 8.72 - An Introduction to General, Organic, and Biological Chemistry

Question

In problem $8.71$, the balloon reached an altitude of  $1000m$, where the pressure was $658mmHg$ and the temperature was $-8°C$. What was the volume, in liters, of the balloon at these conditions?

Step-by-Step Solution

Answer

The volume of the balloon under given conditions is $34748.15L$.

Step 1: Given Information

We have given the altitude is $1000m$, the pressure is $658mmHg$ and the temperature is $-8°C$.

Step 2: Simplify

Using the ideal gas equation and deriving the volume from the equation

$$\begin{gathered} PV=nRT \\ V=\frac{nRT}{P} ... \left(1\right) \end{gathered}$$

Here we have the pressure $P=658mmHg=\frac{658}{760}atm=0.866atm$,

the temperature $T=-8°C=-8+273=265K$.

The number of moles of Hydrogen gas is $$\begin{gathered} n=\frac{m{H}_2}{M{M}_{H_2}}=\frac{2786.8g}{2.016g/mol} \\ n=1382.34mol \end{gathered}$$

Using all the values in equation $\left(1\right)$

$$\begin{gathered} V=\frac{1382.34mol\times 0.0821{\displaystyle \frac{atm-L}{mol-K}}\times 265K}{0.866atm}=\frac{30074.88}{0.866}L \\ V=34748.15L \end{gathered}$$