Answer : The number of moles of gas added to the container will be, 20.89 mole
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 = 8.15 L
[tex]V_2[/tex] = final volume of gas = 17.9 L
[tex]n_1[/tex] = initial number of moles of gas = 9.51 mole
[tex]n_2[/tex] = final number of moles of gas = ?
Now we put all the given values in this formula, we get the final moles of gas.
[tex]\frac{8.15L}{17.9L}=\frac{9.51mole}{n_2}[/tex]
[tex]n_2=20.89mole[/tex]
Therefore, the number of moles of gas added to the container will be, 20.89 mole