Question

An inflated balloon contains X air molecules.After some time the volume of the balloon is found to be the half at the same temperature and pressure when a few air molecules are expelled out. a)How many molecules will be there in the balloon now? b) Which is the gas law associated with this?

Answer 1

(a): The balloon will contain
`(X)/(2)` number of molecules now.

(b): The gas law associated with this is Avogadro's law.

Step-by-step explanation:

Avogadro's law states that the volume of the gas is directly proportional to the number of moles of the gas at constant pressure and temperature

Mathematically,

`V\propto n` (At constant pressure and temperature)

OR

`(V_1)/(n_1)=(V_2)/(n_2)` .....(1)

where,

`V_1\text{ and }n_1` = Initial volume and number of moles

`V_2\text{ and }n_2` = Final volume and number of moles

We are given:

`V_2=(V_1)/(2)`

Putting values in equation 1, we get:

`(V_1)/(n_1)=(V_1)/(2* n_2)\\\\n_2=(n_1)/(2)`

(a):

If
`n_1` number of moles of gas contains X number of molecules

So,
`(n_1)/(2)` number of moles of gas will contain =
`(X)/(n_1)* {n_1}{2}=(X)/(2)` number of molecules

Hence, the balloon will contain
`(X)/(2)` number of molecules now.

(b): The law used is Avogadro's law.