A solution contains $N a_{2} C O_{3} and N a H C O_{3} .$ 10ml of this solution requires 2.5ml of $(\frac{1}{5}) M - H C l$ solution for the end point using phenolphthalein, as indicator. In another experiment, 10ml of the same original solution requires 7.5ml of $(\frac{1}{5}) M - H C l$ solution for the end point using methyl orange, as indicator. Which of the following statement is INCORRECT regarding the original solution? (Atomic weights of Na = 23, C= 12, O = 16)

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10 ml of original solution contains 0.053g $N a_{2} C O_{3}$ .

10ml of original solution contains 0.042g $N a H C O_{3}$ .

Concentration of $N a_{2} C O_{3}$ in original solution is 0.05M

Concentration of $N a H C O_{3}$ in original solution is 0.1M

answer is D.

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Detailed Solution

Using phenolphthalein,
$1 \times M_{N a_{2} C O_{3}} \times 10 = 2.5 \times \frac{1}{5} = 0.5 M_{N a_{2} C O_{3}} = 0.05 M$
Using methyl orange
$2 \times M_{N a_{2} C O_{3}} \times 10 + 1 \times M_{N a H C O_{3}} \times 10 = 7.5 \times \frac{1}{5} 2 \times 0.05 \times 10 + 10 M_{N a H C O_{3}} = 1.5 M_{N a H C O_{3}} = 0.05 M$
Mass of $M_{N a_{2} C O_{3}}$ in 10 ml solution $= 10 \times 0.05 \times 106 g m \times 10^{- 3} = 0.053 g m$
Mass of $N a H C O_{3}$ in 10 ml solution $= 10 \times 0.05 \times 84 \times 10^{- 3} g m = 0.042 g m$