How can I calculate enthalpy of fusion?

1 Answer
Mar 28, 2018

Answer:

The explanation below offers an approach to the enthalpy of fusion given the specific heat of the substance in question in both its solid state and in the liquid state among other information.

Explanation:

This approach to the enthalpy change of fusion requires the following information:

  • Mass of the sample;
  • Specific heat of the substance under solid and liquid state #c_{"solid"}# and #c_{"liquid"}#;
  • The melting point of this substance, #t_{"m.p."}#;
  • The temperature before and after the heating process, #t_{"initial"}# and #t_{"final"}#. Note that here it is assumed that #t_{"initial"} <t_{"m.p."}<t_{"final"}# to ensure that the solid melts completely;
  • Heat added during the whole process, #Q#; This value might be measured indirectly, for instance from the temperature change of another substance with known heat;
  • Number of moles of particles in the sample;

Refer to the heating curve below: pay attention to the first plateau of the curve since the question is concerned only about the enthalpy change of fusion, which corresponds to the melting process.
Heating Curve, Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0

Heat added, which corresponds to the horizontal axis of the heating curve, is divided into three major parts.

The first slant section from the left represents the sample in its solid state, with the part of the horizontal axis underneath resembling the heat absorbed to raise the substance in question in the solid state to the melting point from the initial temperature.

Similarly, the second slope resembles the sample in its liquid state, and the section of the axis below it resembles the heat absorb to attain the final temperature- which is assumed to be higher than that the melting point- after it melts completely.

The horizontal line resembles the sample at the melting equilibrium where it exists in both solid and liquid states, so the section of the axis underneath represents the latent heat of fusion. That is:
#Q=Q_{"solid"}+L_F+Q_{"liquid"}#

#L_F=Q-Q_{"solid"}-Q_{"liquid"}#

It is possible to calculate both #Q_{"solid"}# and #Q_{"liquid"}# from the equation #Delta Q= c*m*Delta t#:
#Q_{"solid"}=c_{"solid"} * m*(t_{"m.p."}-t_{"initial"})#
#Q_{"liquid"}=c_{"liquid"} * m* (t_{"final"}-t_{"m.p."})#

Therefore
#L_F#
#=Q-c_{"solid"} * m*(t_{"m.p."}-t_{"initial"})-c_{"liquid"} * m* (t_{"final"}-t_{"m.p."})#

Plug in values and evaluate to find the latent heat of fusion, #L_F#, of the entire sample. The enthalpy of fusion #Delta H_{fusion}# is related to #L_F# by the equation
#Delta H_{fusion}=(L_F)/(n)#
Where #n# is the number, in moles, of particles in the sample.