Difficult molecular formula question? (See below)

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Difficult molecular formula question? (See below)

The following appeared on my practise test:
You discover the formula of a new compound to be $C_{4 y} H_{7 y} O_{y}$ $C_(4y)H_(7y)O_y$ , where y is a unit positive integer between 1 and 9; for example, if y = 2, then the molecular formula would be $C_{42} H_{72} O_{2}$ $C_42H_72O_2$ . 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.

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Answer 1 · 2017-02-01T02:01:05

The molecular formula of the given compound is $C_{4 y} H_{7 y} O_{y}$ $C_(4y)H_(7y)O_y$ .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 $C_{(4 \cdot 10 + y)} H_{(7 \cdot 10 + y)} O_{y}$ $C_((4*10+y))H_((7*10+y))O_y$

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

Equating this with the given molar mass we get

$550 + 29 y = 725.22$ $550+29y=725.22$
$\Rightarrow y = \frac{175.22}{29} \approx 6$ $=>y=175.22/29~~6$

So the molecular formula of the compound is

$C_{(4 \cdot 10 + y)} H_{(7 \cdot 10 + y)} O_{y}$ $C_((4*10+y))H_((7*10+y))O_y$

$= C_{(4 \cdot 10 + 6)} H_{(7 \cdot 10 + 6)} O_{6}$ $=C_((4*10+6))H_((7*10+6))O_6$

$= C_{46} H_{76} O_{6}$ $=C_46H_76O_6$

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Difficult molecular formula question? (See below)

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