Question

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

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

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.

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 \(25.10 \mathrm{cal} / \mathrm{mol} \cdot \mathrm{K}\).

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.

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.

Key concepts

Chemistry Education

Chemistry education involves understanding concepts that extend beyond mere memorization of terms or formulas. It’s about grasping the underlying principles that govern the behavior of matter. In our study of molar heat capacity, it’s important not just to know the definition but to comprehend its significance in chemistry and real-world applications.

• Molar heat capacity is a fundamental property that tells us how much energy is needed to change the temperature of a given amount of substance, reflecting its ability to store heat.
• This concept relates directly to thermodynamics, as it occurs when substances absorb or release energy.
• The ability to retrieve and apply specific values from reference materials is a vital skill, showing the importance of chemistry resources, such as textbooks or credible online databases, in education.

Application in exercises like the one provided helps solidify knowledge by providing practical contexts where theoretical concepts are tested. This aids students in transitioning from rote learning to developing a deeper understanding of chemistry.

Thermodynamics

Thermodynamics, the branch of physical science that studies heat and temperature and their relation to energy and work, plays a vital role in understanding molar heat capacity. Molar heat capacity is directly linked to thermodynamic principles because it describes how a substance responds to energy changes.

• In thermodynamics, molar heat capacity can indicate how different materials will behave when subjected to heat.
• This property helps in predicting the energy needed to alter temperature, which is crucial in many chemical processes and industrial applications.
• Understanding concepts like the First Law of Thermodynamics can provide context: the increase in internal energy of a system equals the heat added to the system minus the work done by the system.

Grasping these principles allows us to compute energy exchanges and comprehend the broader implications of energy conservation and transfer.

Iron Properties

Iron, as an element, possesses specific physical and chemical properties that determine how it interacts with energy. Its molar heat capacity is just one aspect that reveals much about its nature and its behavior in different environments.

• Iron's molar heat capacity at constant pressure is approximately 25 cal/mol·K, indicating how much heat it can absorb without drastically changing temperature.
• The structure of iron atoms enables them to vibrate and rotate upon heating, affecting its heat capacity.
• This property is crucial for industries that rely on iron's thermal properties, as it impacts processes such as metal working and construction.

Iron's thermal properties underscore its usefulness and popularity in various applications, making it an important subject of study in both chemistry and material science.