Geraniol a volatile organic compound is a component of rose

Question

Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is 0.46 gL^{$-$ 1} at 257 $^\circ$ C and 100 mm Hg. The molar mass of geraniol is ____________ g mol^{$-$ 1}. (Nearest Integer)

[Given : R = 0.082 L atm K^{$-$ 1} mol^{$-$ 1}]

DivineJEE · Accepted Answer

From ideal gas equation we know

PV = nRT

\Rightarrow PV = {W \over M}RT

\Rightarrow P = {W \over V}\,.\,{{RT} \over M}

\Rightarrow P = d\,.\,{{RT} \over M}

[

\because

d = {W \over V}

]

We know, 760 mm of Hg = 1 atm

\therefore

100 mm of Hg =

{{100} \over {760}}

atm

\therefore

Pressure (P) =

{{100} \over {760}}

atm

Density (d) = 0.46

R = 0.082 L atm K

-

1 mol^{$-$
1}

T = (257 + 273) K = 530 K

Putting the values in above equation, we get

{{100} \over {760}} = {{0.46 \times 0.082 \times 530} \over M}

\Rightarrow

M = 152

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