Given :
A sample of gas occupies 200 L at 780 mm Hg and 280 K.
To Find :
The new volume, in liters, of the gas at 810 mm Hg and 300 K.
Solution :
We know, by ideal gas equation :
[tex]PV = nRT[/tex]
Since, every thing is constant except [tex]nR[/tex] .
So,
[tex]\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}[/tex]
Putting all given values we get :
[tex]V_2 = \dfrac{T_2}{T_1}\times \dfrac{P_1}{P_2}\times V_1\\\\V_2 = \dfrac{300}{280}\times \dfrac{780}{810}\times 200\ L\\\\V_2 = 206.35 \ L[/tex]
Therefore, the new volume is 206.35 L.
