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JEE Advanced
Exam
JEE Advanced
Subject
Chemistry
Chapter
States of Matter

JEE Advanced · Chemistry · States of Matter

A certain saturated hydrocarbon effuses about half as fast as H_2 O...

A certain saturated hydrocarbon effuses about half as fast as H2O\mathrm{H}_2 \mathrm{O} vapour. Number of carbons in the formula of this hydrocarbon are?

Correct answer

5

Step-by-step solution

rCH2n+2rH2O=12=MH2OMCnH2n+2∴MCnH2n+2=4×18=72∴12×n+1×(2n+2)=72∴14n+2=72∴n=5\begin{aligned} & \frac{\mathrm{r}_{\mathrm{C}_{\mathrm{H}_{2 n+2}}}}{\mathrm{r}_{\mathrm{H}_2 \mathrm{O}}}=\frac{1}{2}=\sqrt{\frac{\mathrm{M}_{\mathrm{H}_2 \mathrm{O}}}{\mathrm{M}_{\mathrm{C}_n \mathrm{H}_{2 n+2}}}} \\ & \therefore \mathrm{M}_{\mathrm{C}_n \mathrm{H}_{2 n+2}}=4 \times 18=72 \\ & \therefore 12 \times \mathrm{n}+1 \times(2 \mathrm{n}+2)=72 \\ & \therefore 14 \mathrm{n}+2=72 \\ & \therefore \mathrm{n}=5\end{aligned}
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