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Question

The empirical formula of an organic gaseous compound containing carbon and hydrogen is $$CH_{2}$$. The volume occupied by certain mass of this gas is exactly half of the volume occupied by the same mass of nitrogen gas under identical conditions. The molecular formula of the organic gas is _______________.

A
$$C_2 H_4$$
B
$$CH_2$$
C
$$C_6 H_{12}$$
D
$$C_4 H_8$$
Solution
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Correct option is D. $$C_4 H_8$$
Molar mass of $$N_2 =28\ g/mol$$

The volume occupied by the gas is half of the gas of $$N_2$$

$$\dfrac {1}{2}V_{ N_2}=V_{gas}$$

We know $$V\ \propto $$ No. of moles

Moles of gas $$=\dfrac {1}{2}$$ moles of $$N_2\quad [28\ g \ N_2=1\ mole]$$
$$=\dfrac {1}{2}\times 1$$
$$=0.5$$ mole of gas

As both gases have the same mass so we can say:

$$0.5$$ mole gas $$\longrightarrow 28.\ gm $$ mass

1 mole gas $$\longrightarrow x\ gm$$ mass

$$x=\dfrac {28}{0.5}$$

$$\boxed {x=56}$$

$$\therefore $$ Molecular mass of organic gas $$=56$$

Gas has empirical mass $$=14$$

$$\therefore \ n=\dfrac {molecular\ mass}{empirical\ mass}=\dfrac {56}{14}=4$$

$$\therefore \ $$ Molecular formula $$=(CH_2)_4$$

$$\Rightarrow \ C_4H_8$$

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