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 $6 \times 10^{23}$ .
(v) Using your answer from (iv), state the mass of D if the gas is dinitrogen oxide $(N_{2} O)$ .

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Solution

(i) D
We have, $P V = n R T$
Since, P and T constant then V is directly proportional to n (no. of moles) so that $\frac{V_{1}}{n_{1}} = \frac{V_{2}}{n_{2}}$
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 , $n_{2} = 2 n_{1} s o, V_{2} = \frac{n 2}{n 1} \times V_{1} = 2 V_{1}$ (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, $n = \frac{P V}{R T} = \frac{1 \times 5.6}{273 \times 0.082} = 0.25 m o l$
So, no. of moles of D = 4 $\times$ 0.25 = 1 mole at STP
Since, at STP 1mole = $6.023 \times 10^{23}$ molecules of D gas.

(v) As volume of A = 5.6 , then volume of D = 4 $\times$ 5.6= 22.4 L, similalry moles of D = 4 $\times$ 0.25 = 1mole
So, mass of D $(N_{2} O$ = mass of 1 mole of $N_{2} O$ = molar mass = 2 $\times$ 14 + 16 = 44 gm

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Similar questions

(a) 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 volumes refer to the reactants and products of a reaction, which gas law is being observed?
(iv) If the volume of A is actually 5.6 dm³ at STP, calculate the number of molecules in the actual volume 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).
(N = 14; O = 16)
(b) Calculate the percentage of nitrogen in aluminium nitride. (Al = 27, N = 14)

The volumes of gases A, B, C and D are in this ratio 1 : 2 : 2 : 4 under the same conditions of temperature and pressure.

Using your answer from (d), state the mass of D if the gas is dinitrogen oxide (N₂O). [N = 14, O = 16]

The volumes of gases A, B, C and D are in this ratio 1 : 2 : 2 : 4 under the same conditions of temperature and pressure.

If the volume of A is actually 5.6 dm³ at STP, calculate the number of molecules in the actual volume of D at STP (Avogadro's number is 6 x 10²³).

The volume of D is four times the volume of A as given.

According to Avogadro's Law, "Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules". But how is this statement correct? How do we know that equal number of molecules are present in two gases taken in equal volumes?

Even if we consider equal volumes of any two gases(let's consider two gases for example) contain equal number of molecules, if we have the two gases in two containers of same volumes, we can add more gas to any one container and increase the density of the gas inside the container. In that case, the volume of the gas remains equal to the volume of the container but the number of gas molecules inside the container has increased and there is no chage to the number of molecules of the other gas we took inside a similar container. So now we have equal volumes of two gases but we have increased the number of molecules of one gas so now how can we say that the equal volumes of these two gases contain equal number of molecules?

If we take equal number of molecules of two gases and contain one of the gas in a container of some volume and the other gas in a container of a different volume, we will have unequal volumes of two gases having equal number of particles.

So how is Avogadro's Law explained?

Following question refer to one mole of chlorine gas.
(a) What is the volume occupied by this gas at STP?
(b) What will happen to volume of gas, if pressure is double?
(c) What volume will it occupy at $273^{\circ} C$ ?
(d) If the relative atomic mass of chlorine is 35.5, what will be the mass of 1 mole of chlorine gas?

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