For which of the following parameters the structural isomers $$C_2H_5OH$$ and $$CH_3OCH_3$$ would be expected to have the same values? (Assume ideal behaviour)

Isomeric Differences vs. Ideal Gas Behavior

Ethanol and dimethyl ether share the same molecular formula ($$\text{C}_2\text{H}_4\text{O}$$) and therefore have identical molar masses ($$M = 46.07 \text{ g mol}^{-1}$$). However, their differing functional groups lead to radically different intermolecular forces in the condensed phases:

• Ethanol ($$\text{C}_2\text{H}_5\text{OH}$$): Contains a polar $$-\text{OH}$$ group capable of forming strong intermolecular hydrogen bonds.
• Dimethyl ether ($$\text{CH}_3\text{OCH}_3$$): A polar molecule that experiences only weaker dipole-dipole interactions, with no capacity for self-hydrogen bonding.

Option-by-Option Analysis:

• Option A: Heat of vaporization

  Because ethanol molecules are held together by strong hydrogen bonds, it requires significantly more energy to convert liquid ethanol into gas than it does for dimethyl ether. Thus, their heats of vaporization are quite different.

  Result: Different values




• Option B: Gaseous densities at the same temperature and pressure

  Assuming ideal gas behavior, the density ($$\rho$$) of a gas is derived from the ideal gas law ($$PV = nRT$$):

  $$\rho = \frac{P \cdot M}{R \cdot T}$$

  Where:

  • $$P$$ is the pressure, $$T$$ is the temperature, and $$R$$ is the universal gas constant.
  • $$M$$ is the molar mass of the substance.

  Since both compounds are structural isomers, their molar masses ($$M$$) are exactly identical. Under identical temperature ($$T$$) and pressure ($$P$$) conditions, their gaseous densities must be exactly equal.

  Result: Same value [Our Answer]




• Option C: Boiling points

  Due to the presence of extensive intermolecular hydrogen bonding, ethanol has a much higher boiling point ($$\sim 351 \text{ K}$$) compared to dimethyl ether ($$\sim 249 \text{ K}$$), which exists as a gas at room temperature.

  Result: Different values




• Option D: Vapour pressure at the same temperature

  Weaker intermolecular attractions allow molecules to escape into the vapor phase more easily. Consequently, dimethyl ether exhibits a drastically higher vapor pressure than ethanol at any given temperature.

  Result: Different values

Conclusion:

While condensed-phase properties differ due to hydrogen bonding, their identical molar masses ensure that their gaseous densities remain perfectly identical under ideal conditions.

Answer: Option B — Gaseous densities at the same temperature and pressure