approximately 6.0 calories per mole-degree C. Knowing that the specific heat capacity of three metals in Joules per gram-degree C. is 0.45 for Fe, 0.24 for Ag, and 0.13 for Au. Do these metals agree with the Law of DuLong and Petit? How do you know this? Using your understanding of bonding in metals, explain why this law appears to hold.
Answer:
Simply multiply the specific heat capacity with the molar mass to obtain the heat capacity per mole
C_Fe = 0.45 J/(gK) · 55.845 g/mol = 25.13J/(molK)
C_Ag = 0.24 J/(gK) · 107.87g/mol = 25.89J/(molK) C_Au = 0.13 J/(gK) · 196.97 g/mol = 25.61J/(molK)
According the DuLong-Petit law the hat capacity per mole is:
C = 3R = 3 · 8.3144 J/(molK) = 24.94 J/(molK) = 5.97cal/(molK)
You see the metals agree with the law. The real heat capacities per mole are slightly higher, but the error is with max 3.8 % quite small.
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