For estimating the molar heat capacity of a crystalline solid compound from its constituent elements, which empirical rule is used?

Introduction / Context:
When tabulated heat capacities of complex solids are unavailable, engineers and chemists use empirical additivity rules to estimate values for preliminary design and calculations. Knowing which rule applies to solids can save significant effort in early-stage material and process evaluations.

Given Data / Assumptions:

• We need an estimate of a crystalline solid’s molar heat capacity at constant pressure over moderate temperatures.
• Constituent elements and their atomic heat capacities are known or can be looked up.
• We accept empirical additivity with typical uncertainties.

Concept / Approach:
Kopp’s rule states that the molar heat capacity of a solid compound is approximately the sum of the atomic heat capacities of its constituent elements multiplied by their stoichiometric coefficients. It is useful near ambient to moderate temperatures where lattice vibrations dominate. Other named relations serve different purposes: Trouton’s rule estimates molar entropy of vaporization; the Antoine equation correlates vapor pressure with temperature; the Kistyakowsky relation appears in reaction rate or thermodynamic correlations, not in solid heat capacity additivity.

Step-by-Step Solution:
Identify the property: molar heat capacity of a solid compound.Select the appropriate empirical rule using atomic contributions.Kopp’s rule fits this description directly.Choose option “Kopp’s rule.”

Verification / Alternative check:
Comparisons with measured values for many inorganic salts show Kopp’s estimates are often within a reasonable engineering tolerance at room temperature, though deviations grow at high T or for complex structures.

Why Other Options Are Wrong:
Trouton’s rule deals with ΔSvap, not solid Cp.Antoine equation is for vapor pressure curves.Kistyakowsky equation is unrelated to solid heat capacity additivity.

Common Pitfalls:
Overextending Kopp’s rule outside its validity range; ignoring temperature dependence; mixing molar and mass-based heat capacities.

Final Answer:
Kopp’s rule