Propanol (C3H8O) has a boiling point of 97.0 ºC and ΔHvap =42.27 kJ mol-1. Calculate ΔS for the process given below. CH3CH2CH2OH (l) → CH3CH2CH2OH (g)

Question

Propanol (C3H8O) has a boiling point of 97.0 ºC and ΔHvap =42.27 kJ mol-1. Calculate ΔS for the process given below. CH3CH2CH2OH (l) → CH3CH2CH2OH (g)

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To solve this, we recognize that the process given is liquid propanol turning into gas at its boiling point, so we should use the thermodynamic relation ΔS = ΔH_vap / T_actual, where ΔH_vap is the enthalpy of vaporization and T is the temperature (in kelvin) at which the phase transition occurs.

Option a: -0.436 kJ mol-1 K-1. This value is negative, which would imply a decrease in entropy for vaporization. In a liquid-to-gas transition, entropy increases because the gas phase has more disorder; thus a negative sign is incorrect.

Option b: 0.114 kJ mol-1 K-1. This matches the expected sign and magnitude. Calculate T: 97.0 °C = 97.0 + 273.15 = 370.15 K. Then ΔS = ΔH_vap / T = 42.27 kJ/mol / 370.15 K ≈ 0.114 kJ mol-1 K-1. The units are kJ mol-1 K-1, which are customary for molar entropy change in such calculations, and the magnitude aligns with the given data.

Option c: 0.436 kJ mol-1. While the positive sign is appropriate, the magnitude is about four times larger than the correct value. This would suggest using a temperature around 100 K, which is not consistent with the actual boiling point in kelvin, so this is not correct.

Option d: -0.114 kJ mol-1. This option has the wrong sign and the wrong interpretation for a liquid-to-gas transition, where entropy should increase (positive), not decrease. The magnitude half-incorrectly mirrors the correct value but remains negative, so it mischaracterizes the process.

In summary, only option b provides the correct positive entropy change and the correct magnitude derived from ΔS = ΔH_vap / T at the boiling point temperature.

Propanol (C3H8O) has a boiling point of 97.0 ºC and ΔHvap =42.27 kJ mol-1. Calculate ΔS for the process given below. CH3CH2CH2OH (l) → CH3CH2CH2OH (g)

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