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A gaseous compound X contains 44.4% Carbon, 51.9% Nitrogen and 3.7% Hydrogen. Under like conditions, same volume of X as that of Hydrogen took 50 seconds to diffuse whereas Hydrogen took 9.62 seconds. What is the molecular formula of X?

(A) $C_2H_2N_4$ (B) $C_2H_4N$ (C) $C_2HN_2$ (D) $C_2H_2N_2$
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1 Answer

Since the gas took $\large\frac{50}{9.62}$ times longer than Hydrogen its rate of diffusion would be $\large\frac{9.62}{50}$ times that of Hydrogen.
$\Rightarrow \large\frac{9.62}{50} = \large\sqrt \frac{m_{H_2}}{m_{gas}}$
Given $m_{H_2} = 2 \rightarrow m_{gas} = \large(\frac{50}{9.62})$$^2 \times 2 = 54$
Among all the options presented to us above, the one option with a molar mass of $54$ is (D) $C_2H_2N_2$.
Note: We need not use the data of composition of gas.
answered Mar 11, 2014 by balaji.thirumalai

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