Question

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

• A. 2.69 M
• B. 2.97 M
• C. 4.57 M
• D. 6.70 M

Answer 1

The correct option is B 2.97 M

Molality of $NaOH$ solution $=3$ m

Molality=number of moles of solute/mass of solvent(kg)

$3=\frac{n}{massofsolvent}$

mass of solvent $=\frac{1000n}{3}$ g

Also, number of moles=mass/molar mass

For $NaOH$ solution, $n=\frac{m}{40}$

Density of solution,$\rho =1.110g/mL$

Mass of 1 mL solution $=1.11g=m_{solute}+m_{solvent}$

$\frac{n\times 40+1000n}{3}=1.11$

$n=2.97\times {10}^{-3}$ mol

Molarity = number of moles of solute/ volume of solution(L)

$M=\frac{2.97\times {10}^{-3}}{0.001}=2.97M$

Hence, option $B$ is correct.