Which of the following is closest to the molar heat capacity at constant pressure (C_p) of solid gold, Au(s)?

• A. 8.31 J mol^{-1} K^{-1}
• B. 25.4 J mol^{-1} K^{-1}
• C. 50.2 J mol^{-1} K^{-1}
• D. 3.47 J mol^{-1} K^{-1}

Answer: (B)

Verified step by step guidance

1. Recall that the molar heat capacity at constant pressure, \(C_p\), for many solid metals can be approximated using the Dulong-Petit law, which states that the molar heat capacity is roughly \$3R\(, where \)R$ is the ideal gas constant.
2. Identify the value of the ideal gas constant \(R\), which is approximately \$8.314\ \text{J mol}^{-1} \text{K}^{-1}$.
3. Calculate the approximate molar heat capacity using the Dulong-Petit law: \(C_p \approx 3 \times R\).
4. Multiply \$3\( by \)8.314\ \text{J mol}^{-1} \text{K}^{-1}$ to get the estimated molar heat capacity for solid gold.
5. Compare this calculated value to the given options to determine which is closest to the expected molar heat capacity of solid gold.