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Preparations and Uses of Sodium Carbonate

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If $100$ mL of $S O_{2}$ solution requires $50$ mL of $0.01$ M ${C r_{2} O_{7}}^{2 -}$ in acidic medium, then $S O_{2}$ solution is __________ $10^{- 3}$ M.

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Solution

The reaction is as follows:
$K_{2} C r_{2} O_{7} + 3 S O_{2} + H_{2} S O_{4} \to K_{2} S O_{4} + C r_{2} (S O_{4})_{3} + H_{2} O$
Thus, $1$ mole of potassium dichromate reacts with $3$ moles of sulphur dioxide.
Number of millimoles of potassium dichromate $= 50 \times 0.01 = 0.5$ millimoles.
Number of millimoles of sulfur dioxide $3 \times 0.5 = 1.5$ millimoles.
The molarity of the sulphur dioxide solution $= \frac{1.5}{100} = 0.015$ M $= 15 \times 10^{- 3}$ M.

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