Hydrogen cyanice `(HCN)` is a volatile, colorless liquid with the odor of certain fruit pits (such as peach and cherry pits). The compound is highly posisonous. How many molecules are there in `56 mg HCN` the average foxic dose ?
Strategy : The molecule mass of `HCN` is 27.03 amu. Thus, its molar mass is 27.03 g. First convert the mass of sample in moles, then convert moles to number of molecules.
grams of `HCN rarr` mole of `HCN rarr` molecules of HCN

Explanation

step 1: Number f moles of `HCN = ("mass of HCN")/("Molar mass of HCN")`
`= (0.056 g)/(27.03 g mol^(-1))`
`( :' 1 mg = 10^(-3) g)`
`= 0.002 mol HCN`
step 2 : Number of `HCN` molecules
= (Number of HCN) `xx` (Avogadro's constant)
`= (0.02 mol HCN) ((6.022xx10^(32) "molecules")/(1 mol HCN))`
`= 1.20xx10^(21) HCN` molecules
We can combine the two steps using conversion factors as follows : ? HCN molecules
`= 0.056g HCN xx ("1 mol HCN")/(27.03g HCN)`
`xx (6.022xx10^(23) "HCN molecules")/("1 mol HCN")`
`= 1.20xx10^(21) HCN` molecules