The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔH_fus = 5.59 kJ/mol. (b) Calculate the value of ΔS when 60.0 g of Ga(l) solidifies at 29.8 °C.

Verified step by step guidance

1. Determine the molar mass of gallium (Ga). You can find this information on the periodic table.
2. Calculate the number of moles of gallium using the formula: number of moles = mass (g) / molar mass (g/mol).
3. Use the given molar enthalpy of fusion (ΔH_fus) to calculate the total enthalpy change for the solidification process by multiplying the number of moles by ΔH_fus.
4. Apply the formula for entropy change (ΔS) at constant temperature: ΔS = ΔH / T, where ΔH is the enthalpy change and T is the temperature in Kelvin. Convert the temperature from °C to K by adding 273.15.
5. Substitute the values of ΔH and T into the formula to find ΔS, ensuring that the units are consistent (Joules and Kelvin).

Key Concepts

Molar Enthalpy of Fusion

Molar enthalpy of fusion (ΔH_fus) is the amount of energy required to change one mole of a substance from a solid to a liquid at its melting point. In this case, for gallium, ΔH_fus is given as 5.59 kJ/mol, indicating the energy needed for the phase transition from liquid to solid. This value is crucial for calculating the entropy change during the solidification process.

Entropy Change (ΔS)

Entropy (S) is a measure of the disorder or randomness in a system. The change in entropy (ΔS) during a phase transition can be calculated using the formula ΔS = ΔH/T, where ΔH is the enthalpy change and T is the temperature in Kelvin. For gallium solidifying, this relationship helps quantify how the disorder decreases as the liquid transitions to a solid state.

Temperature Conversion to Kelvin

In thermodynamic calculations, temperatures must be expressed in Kelvin (K) rather than Celsius (°C). The conversion is done by adding 273.15 to the Celsius temperature. For gallium, the freezing point of 29.8 °C converts to approximately 302.95 K, which is essential for accurately calculating the entropy change during the solidification process.