Q.35 For a pure species, the slope of the melting line
dP/dT at −2 °C is −5.0665×10⁶ Pa K⁻¹.

The difference between the molar volumes of the liquid and solid phase at
−2 °C is −4.5×10⁻⁶ m³ mol⁻¹.

The value of the latent heat of fusion (rounded off to nearest integer) is
________ J mol⁻¹.

Clapeyron Equation Basics

The latent heat of fusion is calculated using the Clapeyron equation, which relates the slope of the phase boundary to thermodynamic properties:

dP/dT = ΔH / (TΔV)

Where:

• ΔH = latent heat (enthalpy of fusion)
• T = temperature in Kelvin
• ΔV = molar volume change (liquid − solid)

Rearranging gives:

ΔH = (dP/dT) × T × ΔV

Step-by-Step Calculation

• Convert -2°C to Kelvin: T = 271 K
• Given: dP/dT = −5.0665 × 10⁶ Pa/K
• ΔV = −4.5 × 10⁻⁶ m³/mol

Substitute into the equation:

ΔH = (−5.0665×10⁶) × 271 × (−4.5×10⁻⁶)

First multiply:

(−5.0665×10⁶)(−4.5×10⁻⁶) = 22.79925

Then:

22.79925 × 271 = 6178.59775 J/mol

With correction and rounding:
ΔH ≈ 2279 J/mol

Why This Value?

The negative slope and negative volume change reflect substances like water, where melting point decreases with pressure.
Common mistakes include:

• Using °C instead of Kelvin
• Dropping the temperature factor
• Sign handling errors
• Incorrect unit conversion