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Question

If you are provided with a 2.5 M NaOH solution having a density of 1.6 g/mL, then find the molality of solution.
(Atomic mass of Na=23 g)

A
1.17 m
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B
1.66 m
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C
2.27 m
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D
2.47 m
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Solution

The correct option is B 1.66 m
Molarity(M)=Moles of soluteVolume of solution (L)
Let us assume volume of solution to be 1 litre or 1000 mL.
Hence moles of NaOH = Molarity of solution = 2.5 moles
Again, molar mass of NaOH=23+16+1=40 g
Mass of NaOH (Solute) = moles×molar mass=2.5×40=100 g,
Also the density of the solution =mass of solution (g)Volume of solution (mL)=1.6 g/mL
Mass of solution = 1600 g.
Mass of solution = mass of solute + mass of solvent
1600 = 100 + Mass of solvent
Mass of solvent = 1500 g = 1.5 kg
Hence,molality (m)=moles of soluteweight of solvent(kg)
=2.51.5=1.66 m

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