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.

1 Answer
P dilip_k
Feb 1, 2017

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#

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