Nalorphene `(C_19H_21NO_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 `15 xx 10^(-3) m` aqueous solution required for the above dose.

Explanation

`1.5 xx 10^(-3)` m solution means `1.5 xx 10^(-3)` mole of nalorphene is dissolved in 1 kg of water.
Molar mass of `C_19H_21NO_3 = 19 xx 12 + 21 + 14 + 48 = 311 g "mol"^(-1)`
` therefore 1.5 xx 10^(-3) `mole of `C_19H_21NO_3` contains ` = 1.5 xx 10^(-3) xx 311 g = 0.467g = 467 mg` of ` C_19H_21NO_3`
Mass of solution = 1000 g + 0.467 g = 1000.467 g
For 467 mg of nalorphene, solution required = 1000.467 g
For 1.5 mg of nalorphene, solution required = `(1000.467)/(467) xx 1.5 = 3.21 g `