Combined Gas Law

Brightstorm

3 Sept 201004:02

Summary

TLDRThis educational video script introduces the Combined Gas Law, which unifies Boyle's Law, Charles's Law, and Gay-Lussac's Law to describe the relationship between pressure, volume, and temperature of a gas. The script walks through an example problem where a gas's initial conditions and changes in pressure and temperature are given, and the new volume is calculated using the Combined Gas Law. The process involves converting temperatures to Kelvin, setting up the equation, and solving for the unknown volume, resulting in a new volume of 580.58 liters.

Takeaways

📚 The lesson introduces three fundamental gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law, which describe the relationships between pressure, volume, and temperature of a gas.
🔍 Boyle's Law relates pressure and volume, stating that at a constant temperature, the pressure of a gas is inversely proportional to its volume.
🌡️ Charles's Law connects volume and temperature, indicating that at a constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin.
🔄 Gay-Lussac's Law shows the relationship between pressure and temperature, asserting that at a constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin.
🔗 The Combined Gas Law is formed by combining Boyle's, Charles's, and Gay-Lussac's Laws, accounting for changes in pressure, volume, and temperature simultaneously.
🧩 The formula for the Combined Gas Law is \( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \), where \( P \) stands for pressure, \( V \) for volume, and \( T \) for temperature in Kelvin.
📘 An example problem is presented involving a gas at 110 kilopascals and 30°C with an initial volume of 2 liters, which is then heated to 80°C and the pressure increased to 440 kilopascals.
⚖️ The problem requires converting Celsius temperatures to Kelvin by adding 273, which is done for both the initial and final temperatures.
🔢 The solution process involves substituting the given values into the Combined Gas Law equation and solving for the unknown variable, which in this case is the new volume (\( V_2 \)) of the gas.
📝 The calculation involves cross-multiplying and isolating \( V_2 \) to find the new volume, which is determined to be 0.58 liters.
📚 The lesson concludes with a demonstration of how to apply the Combined Gas Law to practical problems involving changes in the state of a gas.

Q & A

What are the three gas laws mentioned in the script?
-The three gas laws mentioned are Boyle's Law, Charles's Law, and Gay-Lussac's Law.
What does Boyle's Law relate to?
-Boyle's Law relates the pressure and volume of a particular gas, stating that at a constant temperature, the pressure of a gas is inversely proportional to its volume.
What is the relationship described by Charles's Law?
-Charles's Law relates the volume and temperature of a particular gas, stating that at a constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin.
How does Gay-Lussac's Law connect pressure and temperature?
-Gay-Lussac's Law states that at a constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin.
What is the Combined Gas Law and why is it used?
-The Combined Gas Law is a single law that combines Boyle's Law, Charles's Law, and Gay-Lussac's Law to describe the relationship between pressure, volume, and temperature of a gas when all three variables are changing.
What formula represents the Combined Gas Law?
-The formula for the Combined Gas Law is P1V1/T1 = P2V2/T2, where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.
What is the initial condition of the gas in the example problem?
-The initial condition of the gas in the example is 110 kilopascals pressure, 30°C temperature, and 2 liters volume.
How is the temperature converted from Celsius to Kelvin?
-The temperature is converted from Celsius to Kelvin by adding 273 to the Celsius temperature.
What are the final conditions of the gas in the example problem after the changes?
-The final conditions are 440 kilopascals pressure and 80°C temperature, with the volume to be determined.
How is the new volume calculated in the example problem?
-The new volume is calculated by using the Combined Gas Law formula and cross-multiplying to isolate V2, the unknown variable.
What is the final answer for the new volume of the gas in the example problem?
-The final answer for the new volume of the gas is 0.58 liters.

Outlines

00:00

📚 Introduction to Gas Laws

The script begins with an introduction to the three fundamental gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. Boyle's Law explains the relationship between pressure and volume of a gas, Charles's Law discusses the relationship between volume and temperature, and Gay-Lussac's Law addresses the relationship between pressure and temperature. The video then introduces the concept of the combined gas law, which integrates these laws to account for changes in pressure, volume, and temperature simultaneously.

🔍 Applying the Combined Gas Law

The script proceeds with an example to demonstrate the application of the combined gas law. It involves a scenario where a gas initially at 110 kilopascals and 30°C fills a container with a volume of 2 liters. The challenge is to find the new volume when the temperature is increased to 80°C and the pressure is raised to 440 kilopascals. The script guides through the process of converting Celsius to Kelvin, identifying the initial and final states of the gas, and setting up the combined gas law equation to solve for the unknown volume.

🧐 Solving for the New Volume

The script concludes with a step-by-step calculation to determine the new volume of the gas using the combined gas law. It involves cross-multiplying the known values of pressure, volume, and temperature to isolate the variable V2, which represents the new volume. The calculation is detailed, showing the process of converting units, setting up the equation, and solving for V2, which is found to be 0.58 liters. This final step illustrates the practical application of the combined gas law in solving for changes in gas volume under varying conditions.

Mindmap

Keywords

💡Boyle's Law

Boyle's Law is a fundamental principle in physics that describes the inverse relationship between the pressure and volume of a gas when the temperature is held constant. In the video, Boyle's Law is introduced as the first of the three gas laws discussed, setting the stage for understanding the combined gas law. The script mentions it in the context of explaining how the relationship between pressure and volume is a foundational concept for the combined gas law.

💡Charles's Law

Charles's Law is another key gas law that relates the volume of a gas to its temperature, assuming the pressure is constant. The video script explains Charles's Law as the second law, emphasizing its importance in understanding how the volume of a gas changes with temperature. It is used to illustrate the second variable relationship that will be combined in the overall gas law.

💡Gay-Lussac's Law

Gay-Lussac's Law, often mispronounced as 'gayc' in the script, relates the pressure of a gas to its temperature when the volume is held constant. The video script briefly introduces this law as the third of the gas laws, which is essential for understanding the combined relationship between pressure and temperature in the context of the combined gas law.

💡Combined Gas Law

The Combined Gas Law is the culmination of Boyle's, Charles's, and Gay-Lussac's Laws, which allows for the calculation of the behavior of a gas when pressure, volume, and temperature are all variables. The video script focuses on this law as the main topic, explaining how it combines the individual relationships into a single equation to solve for unknowns in gas behavior scenarios.

💡Numerator

In the context of the combined gas law formula presented in the video, the numerator refers to the top part of a fraction where variables like pressure (P1) and volume (V1) are placed. The script mentions that in the gas laws, pressure and volume are always on the numerator, which is crucial for setting up the combined gas law equation correctly.

💡Denominator

The denominator in the script refers to the bottom part of a fraction in the combined gas law formula, where the temperature (T1) is placed. The video explains that the temperature is in the denominator, which is an important aspect of the formula's structure and helps in the calculation of gas behavior under varying conditions.

💡Kilopascals

Kilopascals (kPa) is a unit of pressure used in the script to measure the pressure of the gas. The video uses this unit for both the initial and final pressure values in the example problem, emphasizing the importance of using consistent units when applying the combined gas law.

💡Temperature Conversion

The script demonstrates the process of converting temperatures from Celsius to Kelvin, which is necessary for scientific calculations involving gases. The video shows this conversion by adding 273 to the Celsius temperature to obtain the Kelvin temperature, which is used in the combined gas law calculations.

💡Cross Multiplication

Cross multiplication is a technique used in algebra to solve equations involving fractions. In the script, this method is applied to the combined gas law equation to isolate and solve for the unknown variable, which in the example is the new volume (V2) of the gas.

💡Variable

In the context of the video, a variable represents an unknown quantity that needs to be determined through calculations. The script uses the term 'variable' specifically when referring to the unknown volume (V2) that the combined gas law equation is being used to solve.

💡Isolate

To isolate a variable in mathematics means to get it alone on one side of the equation, which allows for solving the equation. The script describes the process of isolating the variable V2 by dividing both sides of the combined gas law equation by the product of the known quantities to find the new volume of the gas.

Highlights

Introduction to the three gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law, which describe the relationships between pressure, volume, and temperature of a gas.

Combining the three gas laws to form the Combined Gas Law, which accounts for changes in pressure, volume, and temperature simultaneously.

The Combined Gas Law formula: P1V1/T1 = P2V2/T2, where P, V, and T represent pressure, volume, and temperature respectively, with subscripts 1 and 2 denoting initial and final states.

Example problem: A gas at 110 kPa and 30°C fills a flexible container with an initial volume of 2 L. The temperature is raised to 80°C and the pressure increased to 440 kPa. The task is to find the new volume.

Conversion of Celsius temperatures to Kelvin by adding 273, to maintain consistency in units for temperature.

Identifying the initial conditions: P1 = 110 kPa, T1 = 303 K, V1 = 2 L.

Identifying the final conditions after changes: P2 = 440 kPa, T2 = 353 K, and the unknown V2 to be calculated.

Ensuring units are consistent, especially for pressure which can be measured in different units.

Using the Combined Gas Law formula to set up the equation for calculating the new volume V2.

Cross-multiplying to isolate the variable V2 in the equation.

Performing the calculation: 353 * 110 * 2 equals 77760.

Setting up the second part of the equation: 303 * 440 * V2 equals 133320V2.

Isolating V2 by dividing 77760 by 133320.

Calculating the new volume V2 to be approximately 0.58 L.

Demonstration of the step-by-step process of using the Combined Gas Law to solve for an unknown variable in a gas law problem.

Emphasis on the importance of unit consistency and the correct application of the Combined Gas Law in practical problems.

Conclusion summarizing the method and result of using the Combined Gas Law to find the new volume of a gas under changed conditions.