Question

a) A balloon is filled with 1000 liters of a gas on the ground at 1.000 bar pressure and 25.6 ^oC temperature. What is the number of moles of gas in the balloon? ( R= 0.08206 L.atm/mol. K). 1 atm = 1.01325 bar.

b) If the balloon ascends to an altitude where the pressure is 0.620 bar and the temperature is 260 K, what is the molar mass of the gas in the balloon if its densityis 0.8037 g/L?

c) The rms velocity of a gas is given by the equation u = sqrt(3RT/M). Calculate the rms velocity in m/s for molecular nitrogen gas at 600 K where R = 8.314 J/mol-K and M is in units of kg/mol. Units come out correctly since 1J=1kg-m²/s²

Answer 1

a) from ideal gas equation

   PV = nRT

n = no of mol of gas = PV/RT

                       = (1*1000/(0.0831*(25.6+273.15)))

           = 40.28 mol

b) from ideal gas equation

   PV = nRT

   n = w/M

PV = (w/M)RT

M = molarmass = wRT/PV

      d = density = w/v

M = molarmass = dRT/P

         = 0.8037*0.0831*260/0.62

         = 28 g/mol

c) u = sqrt(3RT/M)

       = sqrt(3*8.314*600/(28*10^-3))

       = 731.07 m/s