Question

Use the empirical rule of Dulong and Petit stated in Problem 7 to estimate the specific heat capacities of vanadium, gallium, and silver.

Short answer

The specific heat capacities of vanadium, gallium, and silver is ${\text{0.491JK}}^{\text{- 1}}{\text{g}}^{\text{- 1}}$,${\text{0.399JK}}^{\text{- 1}}{\text{g}}^{\text{- 1}}$ and ${\text{0.232JK}}^{\text{- 1}}{\text{g}}^{\text{- 1}}$, respectively.

Step-by-step solution

The given Information.

The specific heat capacities of nickel, zinc, rhodium, tungsten, gold, and uranium are 0.444, 0.388, 0.243, 0.132, 0.129 and ${\text{0.116 JK}}^{\text{- 1}}{\text{g}}^{\text{- 1}}$.

Dulong and Petit Law.

The Dulong and Petit Law declares that the molar heat capacities of the metallic elements possess a value ${\mathbf{\text{25.0 JK}}}^{\mathbf{\text{- 1}}}{\mathbf{\text{mol}}}^{\mathbf{\text{- 1}}}$. The d-block elements (vanadium, gallium, and silver) are metallic and comprise molar heat capacities of ${\mathbf{\text{25.0 JK}}}^{\mathbf{\text{- 1}}}{\mathbf{\text{mol}}}^{\mathbf{\text{- 1}}}$.

The specific heat capacities of different elements.

Thespecific heat capacity of vanadiumis;

$$\begin{gathered} \text{Specific heat capacity of vanadium =}\frac{\text{Molar heat capacity}}{\text{Atomic mass}} \\ \text{=}\frac{{\text{25.0 JK}}^{\text{- 1}}{\text{mol}}^{\text{- 1}}}{{\text{50.94 g mol}}^{\text{- 1}}} \\ {\text{= 0.491JK}}^{\text{- 1}}{\text{g}}^{\text{- 1}} \end{gathered}$$

The specific heat capacity of gallium is;

$$\begin{gathered} \text{Specific heat capacity of gallium =}\frac{\text{Molar heat capacity}}{\text{Atomic mass}} \\ \text{=}\frac{{\text{25.0 JK}}^{\text{- 1}}{\text{mol}}^{\text{- 1}}}{{\text{62.72 g mol}}^{\text{- 1}}} \\ {\text{= 0.399JK}}^{\text{- 1}}{\text{g}}^{\text{- 1}} \end{gathered}$$

The specific heat capacity of silver is;

$$\begin{gathered} \text{Specific heat capacity of silver =}\frac{\text{Molar heat capacity}}{\text{Atomic mass}} \\ \text{=}\frac{{\text{25.0 JK}}^{\text{- 1}}{\text{mol}}^{\text{- 1}}}{{\text{107.87 g mol}}^{\text{- 1}}} \\ {\text{= 0.232JK}}^{\text{- 1}}{\text{g}}^{\text{- 1}} \end{gathered}$$