Question

a gas is filled in a container of volume v at 121c. to what temperature should it be heated in order that one fourth of the gas may escape out of the vessel

Answer 1

Since gas is going to escape, i assume that the container is open. Hence, due to any increase in temperature, there will be no effect on pressure. So, P=constant. Also, whatever gas is going to be left in container, it's gonna take same volume. So, V = constant. But the number of molecules is gonna change as 1/3 of gas is not here. If initial no. of moles be N, then remaining no. of moles is 2/3 N. Then, through Ideal gas law, no. of moles is inversely proportional to Temperature. For initial temperature Ti and final Temperature Tf, and initial no. of moles Ni and final nno. of moles Nf, we get an equation Ni / Nf = Tf / Ti

Fot Ti = 300 K, Ni = N, Nf = 2/3 N , we get Tf = 450 K i.e. 177 °C which is the hike in temperature required.

Answer 2

Since gas is going to escape, i assume that the container is open. Hence, due to any increase in temperature, there will be no effect on pressure. So, P=constant. Also, whatever gas is going to be left in container, it's gonna take same volume. So, V = constant. But the number of molecules is gonna change as 1/3 of gas is not here. If initial no. of moles be N, then remaining no. of moles is 2/3 N. Then, through Ideal gas law, no. of moles is inversely proportional to Temperature. For initial temperature Ti and final Temperature Tf, and initial no. of moles Ni and final nno. of moles Nf, we get an equation Ni / Nf = Tf / Ti

Fot Ti = 300 K, Ni = N, Nf = 2/3 N , we get Tf = 450 K i.e. 177 °C which is the hike in temperature required.