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

Answer:

(a): The balloon will contain $\frac{X}{2}$ number of molecules now.

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

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

$\frac{V_1}{n_1}=\frac{V_2}{n_2}$               .....(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:

$V_2=\frac{V_1}{2}$

Putting values in equation 1, we get:

$\frac{V_1}{n_1}=\frac{V_1}{2\times n_2}\\\\n_2=\frac{n_1}{2}$

(a):

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

So, $\frac{n_1}{2}$ number of moles of gas will contain = $\frac{X}{n_1}\times {n_1}{2}=\frac{X}{2}$ number of molecules

Hence, the balloon will contain $\frac{X}{2}$ number of molecules now.

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