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Question

The volumes of gases A, B, C and D are in the ratio 1:2:2:4 under the same conditions of temperature and pressure.
(i) Which sample of gas contains the maximum number of molecules?
(ii) If the temperature and the pressure of gas A are kept constant, then what will happen to the volume of A when the number of molecules is doubled?
(iii) If this ratio of gas volume refers to the reactants and products for a reaction, which gas law is being observed?
(iv) If the volume of A is actually 5.6 dm^3 at STP, of D at STP (Avogadro's Number is 6×1023.
(v) Using your answer from (iv), state the mass of D if the gas is dinitrogen oxide(N2O).

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Solution

(i) D
We have, PV=nRT
Since, P and T constant then V is directly proportional to n (no. of moles) so that V1n1=V2n2
So, for D volume = 4V (given) is maximum so no . of moles is maximum for D.

(ii) For gas A , at constant. T and P , n2=2n1 so, V2=n2n1×V1=2V1 (volume will also be doubled.)

(iii)The law followed is Gay Lussac's law which, is applied on ideal gases held at constant temperature and pressure.

(iv) At STP , P = 1 atm, T = 273 K , V=5.6 L R= 0.082 L atm/Kmol
So, n=PVRT=1×5.6273×0.082=0.25mol
So, no. of moles of D = 4 × 0.25 = 1 mole at STP
Since, at STP 1mole = 6.023×1023 molecules of D gas.

(v) As volume of A = 5.6 , then volume of D = 4 × 5.6= 22.4 L, similalry moles of D = 4 × 0.25 = 1mole
So, mass of D (N2O = mass of 1 mole of N2O = molar mass = 2 × 14 + 16 = 44 gm


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