Question

A hot-air balloon is filled with air to a volume of 3000 m3 at 750 torr and 21°C. The air in the balloon is then heated to 60.°C, causing the balloon to expand to a volume of 5000. What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out. Thus the pressure in the balloon is always the same as that of the atmosphere.)

Answer 1

Answer: 1.47

Explanation:

The combined gas equation when pressure is constant:

$\frac{V_1}{n_1T_1}=\frac{V_2}{n_2T_2}$

where,

$n_1$ =original number of moles of air in the balloon = ?

$n_2$ =  number of moles of air in the heated balloon = ?

$V_1$ = initial volume of gas = $3000m^3$

$V_2$ = final volume of gas = $5000m^3$

$T_1$ = initial temperature of gas = $21^oC=273+21=294K$

$T_2$ = final temperature of gas = $60^oC=273+60=333K$

Now put all the given values in the above equation, we get the final pressure of gas.

$\frac{3000}{n_1\times 294K}=\frac{5000}{n_2\times 333K}$

$\frac{n_2}{n_1}=1.47$

Therefore, the  ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon is 1.47