Question

Difficult molecular formula question? (See below)

The following appeared on my practise test:
You discover the formula of a new compound to be `C_(4y)H_(7y)O_y` , where y is a unit positive integer between 1 and 9; for example, if y = 2, then the molecular formula would be `C_42H_72O_2`. Determine the molecular formula if the molar mass ofhe compound is 725.22 g/mol. Show all work – maximum marks will be rewarded for solving using a single equation.

Answer 1

The molecular formula of the given compound is `C_(4y)H_(7y)O_y`.Here y represents the unit place of a number as evident from the given example. 4 and 7 represent the tens place of the number of Carbon atoms and the number of H atoms in the molecule.

Hence molecular formula of the compound should actually be represnted as follows `C_((4*10+y))H_((7*10+y))O_y`

Using atomic masses of constituent elements the caculated molar mass becomes
`12(40+y)+1(70+y)+16y`
`=550+29yg"/mol"`

Equating this with the given molar mass we get

`550+29y=725.22`
`=>y=175.22/29~~6`

So the molecular formula of the compound is

`C_((4*10+y))H_((7*10+y))O_y`

`=C_((4*10+6))H_((7*10+6))O_6`

`=C_46H_76O_6`