(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)

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Solution

(a)
(i) Ratio of volume of gas D is the highest. Hence, according to the Avogadro's law, gas D has maximum number of molecules.

(ii) According to the ideal gas equation,
PV = nRT
At constant pressure and temperature, volume of gas is directly proportional to the number of moles or number of molecules of the gas. Hence, if number of molecules of A is doubled, its volume will also be doubled.

(iii) Gay-Lussac's law is being observed in the given ratio. This law states that reacting volumes of the gases bears a simple ratio to another and also to the volumes of the gaseous products, under conditions of same temperature and pressure.

(iv) Volume of gas D is four times the volume of gas A. Hence, if volume of gas A is 5.6 dm³, then volume of gas D is 22.4 dm³.
Number of molecules of gas D = Number of moles $\times$ Avogadro's Number
= $\frac{Volume of gas D}{Molar volume of gas D at STP} \times 6.022 \times 10^{23}$
= $\frac{22.4}{22.4} \times 6.022 \times 10^{23}$
= 6.022 $\times$ 10²³
(v) Mass of one mole of gas D or (N₂O) = Number of moles $\times$ Molecular mass of N₂O
= 1 $\times$ [(14)2 + 16] = 44 g

(b) Molar mass of aluminium nitride (AlN) = 27 g + 14 g = 41 g
Mass of nitrogen in aluminium nitride = 14 g
$Percentage of N = \frac{Mass of N in compound}{Molecular mass of AlN} \times 100 = \frac{14}{41} \times 100 = 34.1 %$

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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 $(N_{2} O)$ .

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).

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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]

A, B

and

C

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and

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A, B

and

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molecules in

A

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(b) Calculate the number of molecules of

O_{2}

present in

B . (c) I f t h e v o l u m e o f

, p r e s e n t i n

i s d o u b l e d a t S T P, c a l c u l a t e t h e m a s s i n g r a m o f

N_2

g a s . [g i v e n : M o l a r v o l u m e a t S T P

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$2 K C l O_{3} M n O_{2} - --- \to 2 K C l + 3 O_{2}$

(i) Calculate the mass of $K C l O_{3}$ required to produce 6.72 litres of $O_{2}$ at STP.
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