054 mol of argon gas is admitted to an evacuated 80 cm3 cont

0.54 mol of argon gas is admitted to an evacuated 80 cm^3 container at 40 degree C. The gas then undergoes an isochoric heating to a temperature of 200 degreeC What is the final pressure of the gas?

Solution

Number of moles n = 0.54 mol

Initial volume V = 80 cm ³

                      = 80 x10 ^-6 m ³

Initial temprature T = 40 ^o C = 40 + 273 = 313 K

Initial pressure P = ?

from the relation PV = nRT

        P = nRT / V

            = (0.54)(8.314)(313)/(80x10 ^-6)

            = 17.565 x10 ⁶ Pa

Final temprature T \' = 200 ^o C = 200 + 273 = 473 K

At constant volume , P \' /P = T \' / T

From this final pressure P \' = (T \' / T ) P

P \' =(473 /313)(17.565x10 ⁶)

      = 26.544x10 ⁶ Pa

      = 2.7 x10 ⁷ Pa           ( two significant figures)