Question

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

• A. $1.17m$
• B. $1.66m$
• C. $2.27m$
• D. $2.47m$

Answer 1

The correct option is B $1.66m$

$Molarity\left(M\right)=\frac{\text{Moles of solute}}{\text{Volume of solution (L)}}$
Let us assume volume of solution to be 1 litre or $1000mL$.
Hence moles of $NaOH$ = Molarity of solution = $2.5moles$
Again, molar mass of $NaOH=23+16+1=40g$
Mass of $NaOH$ (Solute) = $moles\times molarmass=2.5\times 40=100g$,
Also the density of the solution $=\frac{\text{mass of solution (g)}}{\text{Volume of solution (mL)}}=1.6g/mL$
Mass of solution = $1600g$.
Mass of solution = mass of solute + mass of solvent
1600 = 100 + Mass of solvent
Mass of solvent = 1500 g = 1.5 kg
Hence,$molality\left(m\right)=\frac{\text{moles of solute}}{\text{weight of solvent(kg)}}$
$=\frac{2.5}{1.5}=1.66m$