Question

The normal melting point of H2O is 273.15 K and Î"fusHm = 6010 J mol-1. Calculate the change in the normal freezing point at 200 and 400 bar, assuming that the density of the liquid and solid phases remains constant at 997 and 917 kg/m3 respectively.

Answer 1

The formula to calculate the change in the normal freezing point at different pressures is the Clausius-Clapeyron equation. By rearranging the equation, we can solve for the change in temperature. Using the given values, we can calculate the changes in the normal freezing point at 200 and 400 bar.

Step-by-step explanation:

The normal freezing point of water is 0.0°C. To calculate the change in the normal freezing point at different pressures, we need to use the Clausius-Clapeyron equation:

ln(P2/P1) = ΔHfus/(R * T)

Where P2 and P1 are the pressures, ΔHfus is the enthalpy change of fusion, R is the gas constant, and T is the temperature in Kelvin. By rearranging the equation, we can solve for ΔT, the change in temperature:

ΔT = (ΔHfus * (ln(P2/P1)) * T) / (R)

Using the given values, we can calculate the changes in the normal freezing point at 200 and 400 bar:

ΔT at 200 bar:

ΔT = (6010 J/mol * ln(200/1) * 273.15 K) / (8.314 J/(mol * K))

ΔT = 619.8 K

ΔT at 400 bar:

ΔT = (6010 J/mol * ln(400/1) * 273.15 K) / (8.314 J/(mol * K))

ΔT = 727.2 K