Question

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 mm Hg. The molar mass of geraniol is ____ g mol ^–1. (Nearest Integer) [Given: R = 0.082 L atm K^–1 mol^–1]

Answer 1

Correct Answer: 152

To find the molar mass of geraniol, we use the ideal gas law equation:

PV = nRT

Given:

• Density (d) = 0.46 gL^–1
• Temperature (T) = 257°C = 257 + 273 = 530 K
• Pressure (P) = 100 mm Hg = 100/760 atm ≈ 0.1316 atm
• R = 0.082 L atm K^–1 mol^–1

We know:

d = mass/volume

For ideal gases, the molar mass (M) is determined from the equation:

M = dRT/P

Substitute the known values:

M = (0.46 gL^–1)(0.082 L atm K^–1 mol^–1)(530 K) / 0.1316 atm

Calculating this gives:

M ≈ (0.46)(0.082)(530)/0.1316 ≈ 152.09 g mol^–1

The nearest integer for the molar mass is 152 g mol^–1.

This value falls within the expected range of 152,152.