Answer:
(a): The balloon will contain [tex]\frac{X}{2}[/tex] 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,
[tex]V\propto n[/tex] (At constant pressure and temperature)
OR
[tex]\frac{V_1}{n_1}=\frac{V_2}{n_2}[/tex] .....(1)
where,
[tex]V_1\text{ and }n_1[/tex] = Initial volume and number of moles
[tex]V_2\text{ and }n_2[/tex] = Final volume and number of moles
We are given:
[tex]V_2=\frac{V_1}{2}[/tex]
Putting values in equation 1, we get:
[tex]\frac{V_1}{n_1}=\frac{V_1}{2\times n_2}\\\\n_2=\frac{n_1}{2}[/tex]
(a):
If [tex]n_1[/tex] number of moles of gas contains X number of molecules
So, [tex]\frac{n_1}{2}[/tex] number of moles of gas will contain = [tex]\frac{X}{n_1}\times {n_1}{2}=\frac{X}{2}[/tex] number of molecules
Hence, the balloon will contain [tex]\frac{X}{2}[/tex] number of molecules now.
(b): The law used is Avogadro's law.
