The volumes of gases A,B,C,D are in ratio 1:2:2:4 under the same conditions of temperature and pressure.
a) Which sample contains maximum number of molecules?
b) If the temperature and pressure of gas A are kept constant then what will happen to the volume of A when number of molecules is doubled?
c) Which gas law is being observed?
d) If the volume of A is actually 5.6dm^3 as S.T.P calculate the number of molecules in D at S.T.P
e) State the mass of D if the gas is N2O

Dear Student,
(a)  As we know,
      PV=nRT
    Since, P and T constant then V is directly proportional to n(no. of moles) so that V₂ /V₁ = n₂/n₁ 
      So, for D volume = 4V (given) is maximum
      So no . of moles is maximum for D.
(b) For gas A ,
       at constant T and P ,
           n₂ =2n₁ 
            so, V₂ = (n₂/n₁) x V₁ = 2V₁ (volume will also be doubled.)
     Volume odf A will get doubled.
(c)  The law followed is Gay Lussac's law which, is applied on ideal gases held at constant temperature and pressure.
(d) At STP , P = 1 atm, T = 273 K , V=5.6 L R= 0.082 L atm/Kmol
     So, n = PV/RT
              = 1 x 5.6 /273 x 0.082
              = 0.25 mol 
So, no. of mole of D = 4 x 0.25 = 1 mole at STP
Since, at STP 1 mole  = 6.022 x 10²³ molecules of D gas.
(e) As volume  of  A = 5.6 , then volume of D = 4 x 5.6=22.4 L, similarly moles of D = 4 x 0.25 = 1 mole
    ​So, mass of D (N₂O) = mass of 1 mole of N₂O = molar mass = 2 x 14+16 = 44 gm
Regards
​​​​​​