Answer: 0.111 moles of [tex]CH_4[/tex] were added
Explanation:
According to the Avogadro's law, the volume of gas is directly proportional to the number of moles of gas at same pressure and temperature. That means,
[tex]V\propto n[/tex]
or,
[tex]\frac{V_1}{V_2}=\frac{n_1}{n_2}[/tex]
where,
[tex]V_1[/tex] = initial volume of gas = 7.00 L
[tex]V_2[/tex] = final volume of gas = 8.20 L
[tex]n_1[/tex] = initial moles of gas = 0.650 mole
[tex]n_2[/tex] = final moles of gas = ?
Now we put all the given values in this formula, we get
[tex]\frac{7.00}{8.20}=\frac{0.650}{n_2}[/tex]
[tex]n_2=0.761[/tex]
Thus moles added are (0.761-0.650) = 0.111 moles