A Sample Of Iron (Fe) With A Mass Of 2.00 G Releases 9,840 Cal When It Freezes At Its Freezing Point. What Is The Heat Of Fusion For Iron? Use $q = N \Delta H$.A. $2,771.8 \, \text{cal/mol}$ B. $2,747.7 \, \text{cal/mol}$

Introduction

The heat of fusion, also known as the enthalpy of fusion, is the amount of energy required to change the state of a substance from solid to liquid at its melting point. In this article, we will explore the concept of heat of fusion and calculate the heat of fusion of iron using a given sample.

What is Heat of Fusion?

Heat of fusion is a measure of the energy required to change the state of a substance from solid to liquid. It is an important thermodynamic property that helps us understand the behavior of substances under different conditions. The heat of fusion is typically denoted by the symbol ΔH and is usually expressed in units of energy per mole, such as calories per mole (cal/mol) or joules per mole (J/mol).

Calculating Heat of Fusion

To calculate the heat of fusion of iron, we need to use the formula:

q = nΔH

where q is the amount of heat released, n is the number of moles of iron, and ΔH is the heat of fusion.

Given Data

We are given a sample of iron with a mass of 2.00 g that releases 9,840 cal when it freezes at its freezing point. We need to use this data to calculate the heat of fusion of iron.

Calculating the Number of Moles

To calculate the number of moles of iron, we need to know the molar mass of iron. The molar mass of iron is 55.85 g/mol.

We can calculate the number of moles of iron using the formula:

n = mass of iron / molar mass of iron

n = 2.00 g / 55.85 g/mol

n = 0.0358 mol

Calculating the Heat of Fusion

Now that we have the number of moles of iron, we can calculate the heat of fusion using the formula:

q = nΔH

We are given that q = 9,840 cal. We can rearrange the formula to solve for ΔH:

ΔH = q / n

ΔH = 9,840 cal / 0.0358 mol

ΔH = 2,747.7 cal/mol

Conclusion

In this article, we calculated the heat of fusion of iron using a given sample. We used the formula q = nΔH and the given data to calculate the number of moles of iron and the heat of fusion. The calculated heat of fusion of iron is 2,747.7 cal/mol.

Discussion

The heat of fusion of iron is an important thermodynamic property that helps us understand the behavior of iron under different conditions. The calculated heat of fusion of iron can be used to predict the behavior of iron in various applications, such as in the production of steel and in the design of heat exchangers.

Comparison with Other Options

We compared our calculated heat of fusion of iron with the given options and found that our calculated value is closest to option B, which is 2,747.7 cal/mol.

Limitations of the Calculation

The calculation of the heat of fusion of iron is based on the given data and the formula q = nΔH. However, there are some limitations to this calculation. For example, the calculation assumes that the heat of fusion is constant over the entire range of temperatures, which may not be the case in reality. Additionally, the calculation assumes that the sample of iron is pure and free of impurities, which may not be the case in reality.

Future Work

In future work, we can improve the calculation of the heat of fusion of iron by using more accurate data and more sophisticated formulas. For example, we can use the formula ΔH = q / n, where q is the amount of heat released and n is the number of moles of iron, but we can also use more advanced formulas that take into account the temperature dependence of the heat of fusion.

Conclusion

In conclusion, we calculated the heat of fusion of iron using a given sample and the formula q = nΔH. The calculated heat of fusion of iron is 2,747.7 cal/mol. This value can be used to predict the behavior of iron in various applications and can be compared with other options to determine the most accurate value.

Q: What is the heat of fusion of iron?

A: The heat of fusion of iron is the amount of energy required to change the state of iron from solid to liquid at its melting point. It is an important thermodynamic property that helps us understand the behavior of iron under different conditions.

Q: How is the heat of fusion of iron calculated?

A: The heat of fusion of iron is calculated using the formula q = nΔH, where q is the amount of heat released, n is the number of moles of iron, and ΔH is the heat of fusion.

Q: What is the molar mass of iron?

A: The molar mass of iron is 55.85 g/mol.

Q: How do I calculate the number of moles of iron?

A: To calculate the number of moles of iron, you need to divide the mass of iron by its molar mass. For example, if you have 2.00 g of iron, you can calculate the number of moles as follows:

n = mass of iron / molar mass of iron n = 2.00 g / 55.85 g/mol n = 0.0358 mol

Q: What is the heat of fusion of iron in joules per mole?

A: The heat of fusion of iron is 2,747.7 cal/mol. To convert this value to joules per mole, you can use the conversion factor 1 cal = 4.184 J. Therefore, the heat of fusion of iron in joules per mole is:

ΔH = 2,747.7 cal/mol x 4.184 J/cal ΔH = 11,485 J/mol

Q: Can I use the heat of fusion of iron to predict the behavior of iron in different applications?

A: Yes, the heat of fusion of iron can be used to predict the behavior of iron in different applications. For example, in the production of steel, the heat of fusion of iron can be used to determine the amount of energy required to melt the iron.

Q: What are some limitations of the calculation of the heat of fusion of iron?

A: Some limitations of the calculation of the heat of fusion of iron include:

• The calculation assumes that the heat of fusion is constant over the entire range of temperatures, which may not be the case in reality.
• The calculation assumes that the sample of iron is pure and free of impurities, which may not be the case in reality.

Q: How can I improve the calculation of the heat of fusion of iron?

A: To improve the calculation of the heat of fusion of iron, you can use more accurate data and more sophisticated formulas. For example, you can use the formula ΔH = q / n, where q is the amount of heat released and n is the number of moles of iron, but you can also use more advanced formulas that take into account the temperature dependence of the heat of fusion.

Q: What are some real-world applications of the heat of fusion of iron?

A: Some real-world applications of the heat of fusion of iron include:

• The production of steel
• The design of heat exchangers
• The development of new materials and technologies

Q: Can I use the heat of fusion of iron to determine the melting point of iron?

A: Yes, the heat of fusion of iron can be used to determine the melting point of iron. The melting point of iron is the temperature at which the heat of fusion of iron is zero. Therefore, if you know the heat of fusion of iron, you can use it to determine the melting point of iron.