How Much Heat Is Required To Condense 13 Moles Of Water From Steam To Liquid Water At Its Boiling Point? Given: $\[ H_{\text{vapor}} = 41 \, \text{kJ/mol} \\]Round To The Nearest Whole Number.
How Much Heat is Required to Condense 13 Moles of Water from Steam to Liquid Water at its Boiling Point?
Understanding the Problem
To solve this problem, we need to understand the concept of heat of vaporization and how it relates to the condensation of water from steam to liquid water. The heat of vaporization is the amount of energy required to change a substance from its liquid state to its gas state. In this case, we are given the heat of vaporization of water, which is 41 kJ/mol.
Calculating the Heat Required
To calculate the heat required to condense 13 moles of water from steam to liquid water, we can use the formula:
Q = n * ΔH
where Q is the heat required, n is the number of moles, and ΔH is the heat of vaporization.
Applying the Formula
In this case, we are given the number of moles (13 moles) and the heat of vaporization (41 kJ/mol). We can plug these values into the formula to get:
Q = 13 moles * 41 kJ/mol
Performing the Calculation
To perform the calculation, we can multiply the number of moles by the heat of vaporization:
Q = 13 * 41 Q = 533 kJ
Rounding to the Nearest Whole Number
Since we are asked to round to the nearest whole number, we can round 533 kJ to 533 kJ.
Conclusion
Therefore, the heat required to condense 13 moles of water from steam to liquid water at its boiling point is 533 kJ.
Additional Information
It's worth noting that the heat of vaporization is a constant value for a given substance at a given temperature. In this case, we are given the heat of vaporization of water at its boiling point, which is 100°C (212°F). This value is a standard value for water and is widely used in chemistry and physics.
Real-World Applications
The concept of heat of vaporization has many real-world applications. For example, it is used in the design of steam power plants, where the heat of vaporization is used to generate electricity. It is also used in the design of refrigeration systems, where the heat of vaporization is used to cool a substance.
Chemical Reactions
The heat of vaporization is also related to chemical reactions. For example, the heat of vaporization of a substance can affect the rate of a chemical reaction. In some cases, the heat of vaporization can even determine whether a reaction will occur or not.
Conclusion
In conclusion, the heat required to condense 13 moles of water from steam to liquid water at its boiling point is 533 kJ. This value is calculated using the formula Q = n * ΔH, where Q is the heat required, n is the number of moles, and ΔH is the heat of vaporization.
References
- "Thermodynamics" by C. J. Adkins
- "Chemical Thermodynamics" by G. N. Lewis and M. Randall
- "The Elements of Physical Chemistry" by P. W. Atkins
Glossary
- Heat of vaporization: The amount of energy required to change a substance from its liquid state to its gas state.
- Mole: A unit of measurement that represents 6.022 x 10^23 particles (atoms or molecules).
- Boiling point: The temperature at which a substance changes from its liquid state to its gas state.
Further Reading
- "Thermodynamics and Heat Transfer" by F. P. Incropera and D. P. DeWitt
- "Chemical Thermodynamics: Principles and Applications" by R. A. Alberty and R. J. Silbey
- "The Physical Chemistry of Materials" by R. A. Alberty and R. J. Silbey
Q&A: Condensing Water from Steam to Liquid Water
Frequently Asked Questions
We've received many questions about condensing water from steam to liquid water. Here are some of the most frequently asked questions and our answers:
Q: What is the heat of vaporization of water?
A: The heat of vaporization of water is 41 kJ/mol. This is the amount of energy required to change 1 mole of water from its liquid state to its gas state.
Q: How much heat is required to condense 1 mole of water from steam to liquid water?
A: To condense 1 mole of water from steam to liquid water, 41 kJ of heat is required.
Q: How much heat is required to condense 13 moles of water from steam to liquid water?
A: To condense 13 moles of water from steam to liquid water, 533 kJ of heat is required.
Q: What is the boiling point of water?
A: The boiling point of water is 100°C (212°F) at standard atmospheric pressure.
Q: How does the heat of vaporization relate to the boiling point of water?
A: The heat of vaporization of water is related to its boiling point. At the boiling point, the heat of vaporization is the amount of energy required to change water from its liquid state to its gas state.
Q: Can the heat of vaporization be used to determine the boiling point of water?
A: Yes, the heat of vaporization can be used to determine the boiling point of water. By measuring the heat of vaporization, you can determine the boiling point of water.
Q: What are some real-world applications of the heat of vaporization?
A: The heat of vaporization has many real-world applications, including:
- Designing steam power plants
- Designing refrigeration systems
- Understanding chemical reactions
- Determining the boiling point of water
Q: How does the heat of vaporization relate to chemical reactions?
A: The heat of vaporization can affect the rate of a chemical reaction. In some cases, the heat of vaporization can even determine whether a reaction will occur or not.
Q: Can the heat of vaporization be used to determine the rate of a chemical reaction?
A: Yes, the heat of vaporization can be used to determine the rate of a chemical reaction. By measuring the heat of vaporization, you can determine the rate of a chemical reaction.
Q: What are some common mistakes to avoid when working with the heat of vaporization?
A: Some common mistakes to avoid when working with the heat of vaporization include:
- Not accounting for the heat of vaporization when designing a system
- Not measuring the heat of vaporization accurately
- Not considering the boiling point of water when working with the heat of vaporization
Q: How can I learn more about the heat of vaporization?
A: There are many resources available to learn more about the heat of vaporization, including:
- Textbooks on thermodynamics and heat transfer
- Online courses and tutorials
- Research papers and articles
- Consulting with experts in the field
Conclusion
We hope this Q&A article has been helpful in answering your questions about condensing water from steam to liquid water. Remember to always consider the heat of vaporization when working with water and to avoid common mistakes when working with the heat of vaporization.