Identify the compounds

The two structural isomers are:

• $C_2H_5OH$ = ethanol
• $CH_3OCH_3$ = dimethyl ether

They have the same molecular formula $C_2H_6O$, hence the same molar mass.

Check each parameter

Option A: Heat of vaporization

Heat of vaporization depends on the strength of intermolecular forces.

• Ethanol has hydrogen bonding.
• Dimethyl ether does not have hydrogen bonding of the same extent.

Therefore, their heats of vaporization are different.

Option B: Gaseous densities at the same temperature and pressure

For an ideal gas, $\rho = \frac{PM}{RT}$ where:

• $\rho$ = density
• $P$ = pressure
• $M$ = molar mass
• $R$ = gas constant
• $T$ = temperature

Since both isomers have the same molar mass $M$, and are at the same $P$ and $T$, $\rho_{\text{ethanol}} = \rho_{\text{dimethyl ether}}$

So gaseous densities are same.

Option C: Boiling points

Boiling point depends on intermolecular forces.

• Ethanol has stronger intermolecular attraction due to hydrogen bonding.
• Dimethyl ether has weaker intermolecular forces.

Hence boiling points are different.

Option D: Vapour pressure at the same temperature

Vapour pressure also depends on intermolecular forces.

Since the intermolecular forces differ, their vapour pressures at the same temperature are different.

Conclusion

The only parameter that has the same value for both structural isomers is: $\boxed{\text{B: Gaseous densities at the same temperature and pressure}}$

Comparison with stored correct answer

Stored correct answer: B

This matches the derived answer.