Question

a gas is filled in a container at certain temperature and pressure at the same temperature more gas is filled in the vessel calculate the percentage increase in the mass of the gas if the ratio of initial and final pressure is 1: 2

Answer 1

100% since by kinetic theory of gas we know that pressure is directly proportional to mass if the volume is constant.

Answer 2

This question is based on ideal gas theorem. That is,

            $PV = nRT$--------- (1)

Where P = pressure

           V = volume

          n = number of moles

          R = gas constant = 8.314 J/molK

          T = temperature

but we know, number of moles = mass/ molecular weight

                                                 $n = m/M$---------- (2)

substituting equation (2) for equation (1)

       $PV = mRT/M$

Volume (V), R, temperature(T) and molecular weight(M) are constants in this question.

Therefore, Pressure is directly proportional to the mass of the gas.

                  P ∝ m

• Let p = initial pressure

            m1= initial mass of the gas

                  p ∝ m1----- (3)

• Let 2p = final pressure

             m2= final mass of the gas

                 2p ∝ m2----- (4)

dividing equation (4) by (3),

                $2p/p = m2/m1$

                  $2m1 = m2$

Percentage increase in mass = (increasement of mass/initial mass)* 100%

                                                  =[(m2 - m1)/m1] *100%

                                                  =[(2m1-m1)/m1] * 100%

                                                  =100%