Question

Nalorphene $(C_{19}H_{21}NO_3 )$, 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 $1.5 \times 10^{–3} m$ aqueous solution required for the above dose.

Answer 1

The correct answer is: 3.22 g
The molar mass of nalorphene $(C_{19}H_{21}NO_3)$ is given as:
$19 × 12 + 21 × 1+1 \times 14+ 3 \times 16=311\, g\, mol^{-1}$
In $1.5 \times 10^{-3} m$ aqueous solution of nalorphene,
1 kg (1000 g) of water contains $1.5 \times 10^{-3} mol= 1.5 \times 10^{-3} \times 311 g$
$= 0.4665 g$
Therefore, total mass of the solution =(1000+0.4665)g
= 1000.4665 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:
$\frac{(1000.4665 \times 1.5 \times 10^{-3})}{0.4665} g$
= 3.22 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.