More than 150 years ago Pierre Dulong and A. T. Petit...

More than 150 years ago Pierre Dulong and A. T. Petit discovered a rule of thumb that the heat capacity of one mole of a pure solid element is about $6.0$ calories per ${ }^{\circ} \mathrm{C}$ (i.e., about $\left.25 \mathrm{~J} /{ }^{\circ} \mathrm{C}\right)$. A $100.2-\mathrm{g}$ sample of an unknown metal at $99.9^{\circ} \mathrm{C}$ is placed in $50.6 \mathrm{~g}$ of water at $24.8^{\circ} \mathrm{C}$. The temperature is $36.6^{\circ} \mathrm{C}$ when the system comes to equilibrium. Assume all heat lost by the metal is absorbed by the water. What is the likelv identity of this metal?

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Key Concepts

Conservation of Energy in Calorimetry

This principle states that energy cannot be created or destroyed, only transferred. In a calorimetry experiment, the heat lost by a hot object is equal to the heat gained by a cooler one, assuming no energy loss to the surroundings. This concept is fundamental in calculating the unknown heat capacities or properties of substances by tracking changes in temperature and mass.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius (or Kelvin). It plays a crucial role in calorimetry analyses, where it allows us to relate the heat exchanged during temperature changes to the mass and temperature difference, enabling the determination of thermal properties of materials.

Dulong-Petit Law

The Dulong-Petit law is an empirical rule stating that the molar heat capacity of many solid elements is roughly constant, near 3R (approximately 25 J/(mol·°C)), which translates to about 6 cal/(mol·°C). This law helps in identifying metals by comparing their measured heat capacities with the expected molar heat capacity, assisting in deducing the element's molar mass and, consequently, its identity.

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