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Chapter 1: Problem 47

What is the molar heat capacity of the iron wire? 1\. \(1.4 \mathrm{kcal} / \mathrm{mol}\) 2\. \(9.5 \mathrm{cal} / \mathrm{mol}\) 3\. \(25 \mathrm{cal} / \mathrm{mol}\) 4\. \(78 \mathrm{kcal} / \mathrm{mol}\)

Short Answer

Expert verified
The molar heat capacity of the iron wire is approximately \(25 \mathrm{cal} / \mathrm{mol}\). The correct answer is option 3.

Step by step solution

01

Identify the definition of molar heat capacity

Molar heat capacity (C) is the amount of heat energy required to increase the temperature of 1 mole of a substance by 1 degree Celsius. Its unit is usually cal/mol or Kcal/mol.
02

Look up the molar heat capacity of iron

To find the molar heat capacity of iron, we can check a reference such as a chemistry textbook, or look for a credible source online. From a credible source, we find that the molar heat capacity of iron at constant pressure (Cp) is \(25.10 \mathrm{cal} / \mathrm{mol} \cdot \mathrm{K}\).
03

Compare the given options with the molar heat capacity value found

Now we will compare the value we found to the options given: 1. \(1.4 \mathrm{kcal} / \mathrm{mol} = 1400 \mathrm{cal} / \mathrm{mol}\) 2. \(9.5 \mathrm{cal} / \mathrm{mol}\) 3. \(25 \mathrm{cal} / \mathrm{mol}\) 4. \(78 \mathrm{kcal} / \mathrm{mol}= 78000 \mathrm{cal} / \mathrm{mol}\) Comparing the options to the molar heat capacity for iron we found \(25.10 \mathrm{cal} / \mathrm{mol} \cdot \mathrm{K}\), option 3 is the closest to the correct value.
04

Choose the correct option

Based on our comparison, the molar heat capacity of the iron wire is approximately \(25 \mathrm{cal} / \mathrm{mol}\). So, the correct answer is option 3.

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