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

Step-by-step explanation:

The combined gas equation when pressure is constant:

`(V_1)/(n_1T_1)=(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.

`(3000)/(n_1* 294K)=(5000)/(n_2* 333K)`

`(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