The density of 3 molal solution of NaOH is $1.110 g m L^{- 1}$ . Calculate the molarity of the solution.

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Solution

3 molal solutoin of NaOH means 3 moles of NaOH are dissolved in 1 kg solvent. So, the mass of solution = 1000 g solvent + 120. g NaOH = 1120 g solution

(Molar mass of NaOH = 23 + 16 + 1 = 40 g and 3 moles of NaOH $= 3 \times 40 = 120 g$ )

Volume of solution $= \frac{M a s s o f s o l u t i o n}{D e n s i t y o f s o l u t i o n}$ $(∵ d = \frac{m}{V})$

$V = \frac{1120 g}{1.110 g m L^{- 1}} = 1009 m L$

$M o l a r i t y = \frac{M o l e s o f s o l u t e \times 1000}{V o l u m e o f s o l u t i o n (m L)}$

$= \frac{3 \times 1000}{1009} = 2.973 M \approx 3 M$

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