Nalophene `(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 `1.5xx10^(-3)` m aqueous solution required for the above dose.

Explanation

The molar mass of nalorphene `C_(19)H_(21)NO_(3)` is given as :
`19xx12+21xx1+1xx14+3xx16`
= 311 g `mol^(-1)`
In `1.5xx10^(-3)`m aqueous solution of nalorphene, 1 kg (1000 g) of water contains
`= 1.5xx10^(-3)` mol of nalorphene i.e.,
`= 1.5xx10^(-3)`
= 311 g
= 0.4665 g of nalorphene
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 :
`= (1000.4665xx1.5xx10^(-3))/(0.4665)`
= 3.22 g
Hence, the mass of aqueous solution required is 3.22 g.