Calculate the Enthalpy of Fusion

How to Calculate the Enthalpy of Fusion

Materials and Data Required

To calculate the enthalpy of fusion, accurate measurements and specific data points about the substance are required. First, determine the specific heats of the substance in its solid (Csp(s) = 2.10 J/gK) and liquid (Csp(l) = 4.18 J/gK) states. Second, calculate the mass of your sample. Additionally, know the melting point of the substance and record the temperatures before and after heating.

Equipment Needed

For the experimental setup, a calorimeter is essential for measuring the heat changes. A coffee cup calorimeter is suitable for simple experiments like measuring the heat of fusion of ice, while more complex chemical reactions might require a bomb calorimeter.

Calculation Steps

Begin by heating your sample to its melting point and assume complete melting. Calculate the heat added (Q) during this process. Using the formula L_F = Q - Q_{solid} - Q_{liquid}, compute the latent heat of fusion. Determine the number of moles in your sample and use the formula ΔH_{fusion} = L_F / n to find the enthalpy of fusion.

Formula and Example

The general formula for heat of fusion is q = mH_f, where q is the heat energy, m the mass, and H_f the heat of fusion. For instance, the heat of fusion for water is notably 334 J/g.

By following these guidelines and ensuring accurate measurement, calculating the enthalpy of fusion becomes a straightforward task, essential for understanding phase transitions in materials.

How to Calculate the Enthalpy of Fusion

The enthalpy of fusion is a crucial thermodynamic property, representing the energy required for a substance to transition from solid to liquid at constant pressure. This guide explains the step-by-step calculation of the enthalpy of fusion, essential for understanding phase transitions in materials.

Gather Required Information

Begin by collecting all necessary data: the mass m of the sample, specific heats of the substance in both solid and liquid states, melting point, temperatures before and after heating, and total heat added during the process.

Calculate Total Heat Added

Use the formula Q = Q_{solid} + LF + Q_{liquid} to calculate the total heat added, where LF is the latent heat of fusion.

Compute Heat for Solid and Liquid Phases

Calculate the heat absorbed by the solid Q_{solid} and the liquid Q_{liquid} using ΔQ = cmΔt, where c is the specific heat and Δt is the temperature change.

Determine Latent Heat of Fusion

From the total heat added, subtract the heat absorbed by the solid and liquid to find the latent heat of fusion: LF = Q - Q_{solid} - Q_{liquid}.

Calculate Enthalpy of Fusion

Finally, to find the enthalpy of fusion, use the formula ΔH_{fusion} = LF/n, where n is the number of moles of the substance. This calculation provides the energy per mole needed to melt the substance, expressing the enthalpy of fusion in terms of energy per mole.

Understanding these calculations and the significance of the enthalpy of fusion enhances the study of material properties and phase transitions, pivotal in many scientific and industrial applications.

Examples of Calculating Enthalpy of Fusion

Example 1: Water/Ice Transition

Determine the enthalpy of fusion for water. Water typically has a melting point of 0^\circ C. The known enthalpy of fusion for ice is approximately 6.01 \text{ kJ/mol}. For instance, if converting 10 moles of ice to water at this temperature, the energy required is calculated as: 10 \text{ mol} \times 6.01 \text{ kJ/mol} = 60.1 \text{ kJ}.

Example 2: Melting Aluminum

Calculate the enthalpy required to melt aluminum, which has an enthalpy of fusion of 10.7 \text{ kJ/mol} and melts at 660.3^\circ C. For a sample of 5 moles, the energy needed is: 5 \text{ mol} \times 10.7 \text{ kJ/mol} = 53.5 \text{ kJ}.

Example 3: Pure Iron Transition

Iron, with a melting point of 1538^\circ C, has an enthalpy of fusion of 13.8 \text{ kJ/mol}. To melt 8 moles of iron, the required heat can be calculated as follows: 8 \text{ mol} \times 13.8 \text{ kJ/mol} = 110.4 \text{ kJ}.

Example 4: Silver Melting

Silver melts at 961.8^\circ C and has an enthalpy of fusion of 11.3 \text{ kJ/mol}. When melting 7 moles of silver, calculate the energy as 7 \text{ mol} \times 11.3 \text{ kJ/mol} = 79.1 \text{ kJ}.

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