# Solve the following

Question:

Nalorphene (C19H21NO3), similar to morphine, is used to combat withdrawal symptoms in narcotic users. Dose of nalorphene generally given is 1.5 mg.

Calculate the mass of 1.5 × 10−3m aqueous solution required for the above dose.

Solution:

The molar mass of nalorphene $\left(\mathrm{C}_{19} \mathrm{H}_{21} \mathrm{NO}_{3}\right)$ is given as:

$19 \times 12+21 \times 1+1 \times 14+3 \times 16=311 \mathrm{~g} \mathrm{~mol}^{-1}$

In 1.5 × 10−3m aqueous solution of nalorphene,

$1 \mathrm{~kg}(1000 \mathrm{~g})$ of water contains $1.5 \times 10^{-3} \mathrm{~mol}=1.5 \times 10^{-3} \times 311 \mathrm{~g}$

$=0.4665 \mathrm{~g}$

Therefore, total mass of the solution $=(1000+0.4665) \mathrm{g}$

$=1000.4665 \mathrm{~g}$

This implies that the mass of the solution containing 0.4665 g of nalorphene is 1000.4665 g.

Therefore, mass of the solution containing 1.5 mg of nalorphene is:

$\frac{1000.4665 \times 1.5 \times 10^{-3}}{0.4665} \mathrm{~g}$

$=3.22 \mathrm{~g}$

Hence, the mass of aqueous solution required is 3.22 g.

Note: There is a slight variation in this answer and the one given in the NCERT textbook.