Suppose that heat was added to a 21.8-g sample of solid zinc...

Suppose that heat was added to a $21.8-g$ sample of solid zinc at the rate of $9.84 \mathrm{~J} / \mathrm{s}$. After the temperature reached the normal melting point of zinc, $420 .{ }^{\circ} \mathrm{C}$, it remained constant for $3.60$ minutes. Calculate $\Delta H_{\text {fusion }}^{\circ}$ at $420 .{ }^{\circ} \mathrm{C}$, in $\mathrm{J} / \mathrm{mol}$, for zinc.

Key Concepts

Latent Heat of Fusion

Latent heat of fusion refers to the amount of energy required to change a substance from a solid to a liquid state at its melting point without any temperature change. This concept is essential in understanding phase transitions where the energy added does not increase temperature but is used to overcome the intermolecular forces holding the solid together.

Phase Change at Constant Temperature

During a phase change, such as from solid to liquid, the temperature remains constant while the substance absorbs energy. This characteristic allows us to measure the energy specifically associated with the phase transition without the complications of simultaneous temperature changes.

Heat Transfer and Power Input

Heat transfer in this context is determined by the rate at which energy is added to the system, often expressed in joules per second (watts). The power input, when multiplied by the duration of energy application, gives the total energy supplied, which is crucial for calculating how much energy is used in transforming the phase of the substance.

Molar Energy Conversion

Molar energy conversion involves the process of converting the energy change per sample mass to an energy change per mole. This requires knowledge of the substance’s molar mass, and it is fundamental when expressing thermodynamic properties, like enthalpy of fusion, on a per-mole basis for standardization and comparison.

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