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Chapter 10: Problem 21

Calculate \(C\) for indium metal given that 1.0 mol In absorbs 53 J during the following process. $$\operatorname{In}(s, 297.5 \mathrm{K}) \longrightarrow \operatorname{In}(s, 299.5 \mathrm{K})$$

Short Answer

Expert verified
The molar heat capacity of indium is 26.5 J/K/mol.

Step by step solution

01

Identify given quantities

First, identify the given quantities in the exercise: \n\n1. \(q\) (heat absorbed) = 53 J \n2. \(\Delta T\) (temperature difference) = 299.5 K - 297.5 K = 2 K \n3. number of moles, \(n\) = 1.0 mol
02

Use the formula to calculate the molar heat capacity

Insert the given quantities into the formula \(q = C \Delta T\). After that, solve it for \(C\):\n\n\(C = \frac{q}{\Delta T}\), \nwhere \(q\) is 53 J and \(\Delta T\) is 2 K. Inserting these values gives:\n\n\(C = \frac{53 \, \text{J}}{2 \, \text{K}} = 26.5 \, \text{J/K/mol}\).
03

Interpret the result

The molar heat capacity \(C\) of indium is 26.5 J/K/mol. In other words, when 1 mole of indium is heated, it absorbs 26.5 J of heat to raise its temperature by 1 K.

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Most popular questions from this chapter

Given the entropy change for the first two reactions below, calculate the entropy change for the third reaction below. \begin{equation} \begin{array}{c}{\mathrm{S}_{8}(s)+8 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{SO}_{2}(g) \Delta S=89 \mathrm{J} / \mathrm{K}} \\ {2 \mathrm{SO}_{2}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g) \Delta S=-188 \mathrm{J} / \mathrm{K}} \\ {\mathrm{S}_{8}(s)+12 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{SO}_{3}(g) \Delta S=?}\end{array} \end{equation}

What is molar enthalpy change?

What is dependent on the average kinetic energy of the atoms in a substance?

What information is needed to be certain that a chemical reaction is nonspontaneous?

What is molar heat capacity, and how can it be measured?
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