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Ideal Gas Equation

A 2.0 g sam...

Question

$A$ $2.0$ g sample of a mixture containing sodium carbonate, sodium bicarbonate and sodium sulphate is gently heated till the evolution of $C O_{2}$ ceases. The volume of $C O_{2}$ at $750$ mm of Hg pressure and at $298$ K is measured to be $123.9$ mL. $A$ $1.5$ g of the same sample requires $150$ mL of $\frac{M}{10} H C l$ for complete neutralisation. The percentage composition of the components of the mixture will be :

N a_{2} C O_{3} = 53 %

N a_{2} S O_{4} = 31.5 %

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N a_{2} C O_{3} = 26.5 %

N a_{2} S O_{4} = 73.5 %

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N a_{2} C O_{3} = 50 %

N a_{2} S O_{4} = 50 %

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N a_{2} C O_{3} = 26.5 %

N a_{2} S O_{4} = 31.5 %

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Solution

The correct option is D $N a_{2} C O_{3} = 26.5 %$ , $N a_{2} S O_{4} = 31.5 %$
Only $N a H C O_{3}$ decomposes to give $C O_{2}$ .
The reaction is as follows:
$2 N a H C O_{3} Δ \to N a_{2} C O_{3} + C O_{2} + H_{2} O$

$P V = n R T$ is the ideal gas equation.

$\frac{750}{760} \times \frac{123.9}{1000} = n \times 0.0821 \times 298$ $⟹ n = 4.997 \times 10^{- 3} = 5 \times 10^{- 3}$ mol $C O_{2}$

Moles of $N a H C O_{3} = 5 \times 10^{- 3} \times 2 = 0.01$ mol
Mass of $N a H C O_{3} = 0.01 \times 84 = 0.84$ g

Percentage of $N a H C O_{3} = \frac{0.84}{2} \times 10 = 42 %$

Millimoles of $H C l = 150 \times \frac{1}{10} = 15$ mmol

$H C l$ reacts with $N a_{2} C O_{3}$ and $N a H C O_{3}$ .
$2$ g mixture has $0.01$ mol $N a H C O_{3}$ .

$1.5$ g mixture has $\frac{0.01}{2} \times 1.5 = 0.0075$ mol $N a H C O_{3}$ $= 7.5$ mmol of $N a H C O_{3}$

$N a H C O_{3} + H C l \to N a C l + C O_{2} + H_{2} O$

Millimoles of $H C l$ neutralization by $N a_{2} C O_{3} = 15 - 7.5 = 7.5$ mmol

$N a_{2} C O_{3} + 2 H C l \to 2 N a C l + C O_{2} + H_{2} O$

Millimoles of $N a_{2} C O_{3} = \frac{7.5}{2} = 3.75$ mmol

Mass of $N a_{2} C O_{3} = 3.75 \times 106 \times 10^{- 3} = 0.3975$ g

Percentage of $N a_{2} C O_{3} = \frac{0.3975}{1.5} \times 100 = 26.5 %$

Percentage of $N a_{2} S O_{4} = 100 - (42 + 26.5) = 31.5 %$

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Similar questions

100 g

112 %

H_{2} S O_{4}

5.3 g

N a_{2} C O_{3}

C O_{2}

300 K

H_{2} S O_{4} + N a_{2} C O_{3} \to N a_{2} S O_{4} + H_{2} O + C O_{2}

N a_{2} C O_{3}, N a_{2} S O_{4}

N a O H

H C l

B a C l_{2}

B a S O_{4}

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N a_{2} C O_{3} = 106 g, N a_{2} S O_{4} = 142 g, B a S O_{4} = 233 g, H C l = 36.5 g a n d N a O H = 40 g

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Complete the following reaction: $N a_{2} C O_{3} + H_{2} S O_{4} \to$ ___?

Complete the following reaction: $N a_{2} C O_{3} (s) + d i l . H C l (a q) \to$ ___?

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