Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is 0.46 gL$$^{-1}$$ at 257°C and 100 mmHg. The molar mass of geraniol is ______ (Nearest Integer)
[Given R = 0.082 L atm K$$^{-1}$$ mol$$^{-1}$$]

To determine the molar mass of geraniol, we begin with the given density $$d = 0.46\ \mathrm{g\ L^{-1}}$$, temperature $$T = 257^\circ\mathrm{C} = 257 + 273 = 530\ \mathrm{K}$$, pressure $$P = \frac{100}{760}\ \mathrm{atm}$$, and the ideal gas constant $$R = 0.082\ \mathrm{L\ atm\ K^{-1}\ mol^{-1}}$$.

Applying the ideal gas equation and expressing the number of moles as $$n = \frac{m}{M}$$ leads to the relation $$PV = nRT = \frac{m}{M}RT$$. Rewriting in terms of density $$d = \frac{m}{V}$$ gives $$PM = dRT \quad\Longrightarrow\quad M = \frac{dRT}{P}$$.

Substituting the numerical values yields $$M = \frac{0.46 \times 0.082 \times 530}{\frac{100}{760}}$$. The numerator is calculated as $$0.46 \times 0.082 \times 530 = 0.46 \times 43.46 = 19.9916$$, while the denominator is $$\frac{100}{760} = 0.13158$$. Hence, $$M = \frac{19.9916}{0.13158} = 151.9 \approx 152\ \mathrm{g\ mol^{-1}}$$.

Thus, the molar mass of geraniol is $$152\ \mathrm{g\ mol^{-1}}$$.