Question

.If 17.99 mol of helium gas is at 13.0 ?C and a gauge pressure of 0.337 atm .

a)Calculate the volume of the helium gas under these conditions.

b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.05 atm .

Answer 1

a) Total pressure of gauge pressure = 0.337+1=1.337 atm=1.337*10⁵ Pa

number of moles of gas = 17.99

temperature of gas = 13+273=286 K

From ideal gas equation, PV=nRT

V=nRT/P=17.99*8.314*286/1.337*10⁵ = 0.32 m³

b) We know that PV/T=constant

initial pressure = 1.337*10⁵ Pa

initial volume =0.32 m³

initial temperature = 286 K

final pressure = 1.05+1 =2.05 atm=2.05*10⁵ Pa

final volume = 0.32/2=0.16 m³

Final temperature of gas = 2.05*10⁵*0.16*286/1.337*10⁵ = 70.16 K