# 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 V/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 = 2V(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
​​​​​​

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