The Volume Of A Gas Changed From 1145 ML To 765 ML. The Final Temperature Of The Gas Is 640 K. What Was The Original Temperature Of The Gas? T = [ ? ] K T = [?] \, \text{K} T = [ ?] K Assume That The Number Of Moles And The Pressure Remain Constant.
The Volume of a Gas: Understanding the Relationship Between Temperature and Volume
Introduction
In chemistry, the behavior of gases is a fundamental concept that is crucial to understanding various chemical reactions and processes. One of the key properties of gases is their ability to change volume in response to changes in temperature, while maintaining a constant pressure. This relationship is described by Charles' Law, which states that, at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin. In this article, we will explore the application of Charles' Law to determine the original temperature of a gas, given its final temperature and the change in its volume.
Charles' Law: A Brief Overview
Charles' Law is a fundamental principle in chemistry that describes the relationship between the volume of a gas and its temperature at constant pressure. Mathematically, it is expressed as:
V1 / T1 = V2 / T2
where V1 and V2 are the initial and final volumes of the gas, respectively, and T1 and T2 are the initial and final temperatures of the gas, respectively.
The Problem: Determining the Original Temperature of the Gas
We are given that the volume of the gas has changed from 1145 mL to 765 mL, and the final temperature of the gas is 640 K. Our objective is to determine the original temperature of the gas, denoted by T1.
Applying Charles' Law to the Problem
To solve this problem, we can use Charles' Law, which states that the ratio of the initial volume to the initial temperature is equal to the ratio of the final volume to the final temperature. Mathematically, this can be expressed as:
V1 / T1 = V2 / T2
We are given that V1 = 1145 mL, V2 = 765 mL, and T2 = 640 K. We need to find T1.
Rearranging Charles' Law to Solve for T1
To solve for T1, we can rearrange Charles' Law to isolate T1 on one side of the equation. This can be done by multiplying both sides of the equation by T1 and then dividing both sides by V1. The resulting equation is:
T1 = (V2 / V1) * T2
Substituting the Given Values into the Equation
Now that we have the equation, we can substitute the given values into the equation to solve for T1. Plugging in the values, we get:
T1 = (765 mL / 1145 mL) * 640 K
Evaluating the Expression
To evaluate the expression, we can first simplify the fraction by dividing 765 mL by 1145 mL. This gives us:
T1 = 0.668 * 640 K
Calculating the Final Answer
Finally, we can multiply 0.668 by 640 K to get the final answer:
T1 = 428.32 K
Conclusion
In this article, we used Charles' Law to determine the original temperature of a gas, given its final temperature and the change in its volume. We applied the law to a specific problem, rearranged the equation to solve for the original temperature, and evaluated the expression to get the final answer. This problem demonstrates the importance of understanding the relationship between temperature and volume in gases, and how it can be used to solve real-world problems in chemistry.
References
- Atkins, P. W., & de Paula, J. (2010). Physical Chemistry (9th ed.). Oxford University Press.
- Chang, R. (2010). Chemistry: The Central Science (11th ed.). McGraw-Hill.
- Petrucci, R. H., Harwood, W. S., & Herring, F. G. (2006). General Chemistry: Principles and Modern Applications (9th ed.). Pearson Prentice Hall.
Further Reading
- Charles' Law: A Review of the Law and Its Applications
- The Relationship Between Temperature and Volume in Gases
- Using Charles' Law to Solve Problems in Chemistry
The Volume of a Gas: A Q&A Guide
Introduction
In our previous article, we explored the relationship between the volume of a gas and its temperature at constant pressure, using Charles' Law. We applied the law to a specific problem to determine the original temperature of a gas, given its final temperature and the change in its volume. In this article, we will provide a Q&A guide to help you better understand the concepts and applications of Charles' Law.
Q: What is Charles' Law?
A: Charles' Law is a fundamental principle in chemistry that describes the relationship between the volume of a gas and its temperature at constant pressure. Mathematically, it is expressed as:
V1 / T1 = V2 / T2
where V1 and V2 are the initial and final volumes of the gas, respectively, and T1 and T2 are the initial and final temperatures of the gas, respectively.
Q: What are the assumptions of Charles' Law?
A: Charles' Law assumes that the number of moles and the pressure of the gas remain constant. This means that the volume of the gas will change in response to changes in temperature, while maintaining a constant pressure.
Q: How is Charles' Law used in real-world applications?
A: Charles' Law is used in a variety of real-world applications, including:
- Calculating the volume of a gas at a given temperature
- Determining the original temperature of a gas, given its final temperature and the change in its volume
- Understanding the behavior of gases in various industrial processes, such as refrigeration and air conditioning
Q: What are some common mistakes to avoid when applying Charles' Law?
A: Some common mistakes to avoid when applying Charles' Law include:
- Failing to account for changes in pressure
- Assuming that the number of moles remains constant, when in fact it may change
- Not using the correct units for temperature and volume
Q: How can I use Charles' Law to solve problems in chemistry?
A: To use Charles' Law to solve problems in chemistry, follow these steps:
- Write down the given information, including the initial and final volumes and temperatures of the gas.
- Use Charles' Law to set up an equation that relates the initial and final volumes and temperatures.
- Solve the equation for the unknown variable, such as the original temperature of the gas.
- Check your answer to ensure that it is reasonable and consistent with the given information.
Q: What are some common problems that can be solved using Charles' Law?
A: Some common problems that can be solved using Charles' Law include:
- Determining the original temperature of a gas, given its final temperature and the change in its volume
- Calculating the volume of a gas at a given temperature
- Understanding the behavior of gases in various industrial processes, such as refrigeration and air conditioning
Q: How can I practice using Charles' Law to solve problems in chemistry?
A: To practice using Charles' Law to solve problems in chemistry, try the following:
- Work through practice problems in your textbook or online resources
- Use online calculators or software to help you solve problems
- Practice solving problems on your own, using Charles' Law to set up and solve equations
Conclusion
In this article, we provided a Q&A guide to help you better understand the concepts and applications of Charles' Law. We covered topics such as the assumptions of Charles' Law, real-world applications, common mistakes to avoid, and how to use Charles' Law to solve problems in chemistry. By following the steps outlined in this article, you can improve your understanding of Charles' Law and become more confident in your ability to apply it to solve problems in chemistry.
References
- Atkins, P. W., & de Paula, J. (2010). Physical Chemistry (9th ed.). Oxford University Press.
- Chang, R. (2010). Chemistry: The Central Science (11th ed.). McGraw-Hill.
- Petrucci, R. H., Harwood, W. S., & Herring, F. G. (2006). General Chemistry: Principles and Modern Applications (9th ed.). Pearson Prentice Hall.
Further Reading
- Charles' Law: A Review of the Law and Its Applications
- The Relationship Between Temperature and Volume in Gases
- Using Charles' Law to Solve Problems in Chemistry