(a) A gas cylinder contains 24 × 10²⁴ molecules of nitrogen gas. If Avogadro's number is 6 × 10²³ and the relative atomic mass of nitrogen is 14, calculate:
(i) Mass of nitrogen gas in the cylinder.
(ii) Volume of nitrogen at STP in dm³.

(b) Commercial sodium hydroxide weighing 30 g has some sodium chloride in it. The mixture on dissolving in water and subsequent treatment with excess silver nitrate solution formed a precipitate weighing 14.3 g.What is the percentage of sodium chloride in the commercial sample of sodium hydroxide? The equation for the reaction is
NaCl + AgNO₃ → AgCl + NaNO₃.
[Relative molecular mass of NaCl = 58; AgCl = 143]

(c) A certain gas 'X' occupies a volume of 100 cm³ at S.T.P. and weighs 0.5 g. Find its relative molecular mass.

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Solution

(a)
(i) Number of moles of nitrogen gas in 24 × 10²⁴ molecules = $\frac{24 \times 10^{24}}{6.023 \times 10^{23}} = 39.85 mol$
Mass of nitrogen gas = Moles of nitrogen gas $\times$ Molecular mass of nitrogen gas
= 39.85 $\times$ 28 = 1115.8 g

(ii) Volume of one mole of nitrogen at STP = 22.4 dm³
Volume of 39.84 moles of nitrogen at STP = (22.4 $\times$ 39.85) dm³ = 892.64 dm³

(b) According to the balanced chemical equation, one mole of NaCl gives one mole of AgCl.
Number of moles of AgCl in 14.3 g of precipitate = $\frac{Mass of AgCl}{Molecular mass of AgCl} = \frac{14.3}{143} = 0.1 mol$
Number of moles of NaCl in 30 g of sodium hydroxide = 0.1 mol
Mass of 0.1 moles of NaCl = 58(0.1) g = 5.8 g
Hence, 30 g of sample contains 5.8 g of NaCl.
$Percentage of NaCl = \frac{Mass of NaCl}{Mass of NaOH} \times 100 = \frac{5.8}{30} \times 100 = 19.3 %$

(c) Number of moles of gas X = $\frac{Volume occupied by X gas}{Molar volume} = \frac{100 \times (10^{- 1})^{3} {dm}^{3}}{22.4 {dm}^{3} / mol} = 4.46 \times 10^{- 3} mol$
Relative molecular mass of gas = $\frac{Mass of gas}{Number of moles} = \frac{0.5 g}{4.46 \times 10^{- 3} mol} = 0.1121 \times 10^{3} g / mol = 112.1 g / mol$

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Commercial sodium hydroxide weighing 30 g has some sodium chloride in it. The mixture on dissolving in water and subsequent treatment with excess silver nitrate solution formed a precipitate weighing 14.3 g. What is the percentage of sodium chloride in the commercial sample of sodium hydroxide? The equation for the reaction is

Nacl + AgNO₃→ AgCl + NaNO₃

A gas cylinder contains 24 x 10²⁴ molecules of nitrogen gas. If Avogadro’s number is 6 x 10²³ and the relative atomic mass of nitrogen is 14, calculate:

A certain gas ‘X’ occupies a volume of 100 $c m^{3}$ at STP and weighs 0.5 g.

Find its relative molecular mass.

Q. Given below are word equations. Convert them into chemical equations using symbols and valencies. Balance the equations. Use appropriate signs for gases and precipitates in the reaction.
i) Zinc Sulphide