Question

Three balloons are filled with different amounts of an ideal gas. One balloon is filled with 3 moles of the gas, filling the balloon to 30 L. The second balloon contains 2 moles of gas.

The third balloon occupies a volume of 45 L.

(i) What volume will the second balloon occupy?

(ii) How many moles of the gas does the third balloon contain?

• A. 30 L; 4 moles
• B. 40L; 1.5 moles
• C. 20 L; 4.5 moles
• D. 10L; 2 moles

Answer 1

The correct option is C

20 L; 4.5 moles

At constant pressure and temperature, the number of moles of a gas (n) is proportional to the volume (V) - this is Avogadro's law. Therefore, at fixed T and P -

$\left(\frac{n}{v}\right)$=CONSTANT.

For the gas and conditions in question, we can write this constant by looking at the first balloon -

$\left(\frac{n_1}{V_1}\right)=\left[\frac{3moles}{30L}\right]=0.1moles/L$

which gives us the constant molar density.

(i) For the second balloon,

$\left(\frac{n_2}{V_2}\right)=\left(\frac{n_1}{V_1}\right)=0.1mole/L$

$\Rightarrow V_2=\left(\frac{n_2}{0.1}\right)L$

$\Rightarrow V_2=20L$.

(ii) The third balloon occupies 45L. Thus,

$\left(\frac{n_3}{V_3}\right)=\left(\frac{n_1}{V_1}\right)=0.1mole/L$

$\Rightarrow n_3=V_3\times 0.1moles$

$\Rightarrow n_3=4.5moles.$