Q. 8.71 - An Introduction to General, Organic, and Biological Chemistry

Question

In $1783$, Jacques Charles launched his first balloon filled with hydrogen gas, which he chose because it was lighter than air. If the balloon had a volume of $31000 L$, how many kilograms of hydrogen were needed to fill the balloon at STP?

Step-by-Step Solution

Answer

The amount of Hydrogen needed is $32000L$.

Step 1: Given Information

We have given that the volume of the balloon is $31000 L$.

Step 2: Calculation

Considering the volume of the balloon $V_1=31000L$

Pressure of gas $p_1=\frac{755mmHg}{760}=0.99atm$

The temperature $T_1=22°C+273=295K$

$$\begin{gathered} p_2=658mmHg=0.87atm \\ {T}_2=-8°C+273=265K \end{gathered}$$

Using the gas law

$$\begin{gathered} \frac{p_1\times V_1}{T_1}=\frac{p_2\times V_2}{T_2} \\ {V}_2=\frac{p_1\times V_1\times T_2}{T_1} \\ =\frac{0.99atm\times 31000L\times 265K}{295K\times 0.87atm} \\ {V}_2=32000L \end{gathered}$$