A 4.8-liter Sample Of Gas Is At 10 Degrees Celsius. At That Temperature, It Has A Pressure Of 1.2 Atmospheres. Assume We Change The Temperature To 198 K And Hold The Volume Constant. What Pressure Would We Expect The Gas To Have?
Introduction
The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. In this article, we will explore the ideal gas law and use it to solve a problem involving a change in temperature and pressure.
The Ideal Gas Law
The ideal gas law is given by the equation:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the gas constant
- T is the temperature of the gas in Kelvin
Given Information
We are given a 4.8-liter sample of gas at a temperature of 10 degrees Celsius. At this temperature, the gas has a pressure of 1.2 atmospheres. We are asked to find the pressure of the gas when the temperature is changed to 198 K, while holding the volume constant.
Converting Temperature to Kelvin
First, we need to convert the initial temperature from Celsius to Kelvin. The formula for converting Celsius to Kelvin is:
T(K) = T(°C) + 273.15
Substituting the given value, we get:
T(K) = 10 + 273.15 = 283.15 K
Applying the Ideal Gas Law
Since the volume is held constant, we can rearrange the ideal gas law equation to solve for pressure:
P = nRT / V
We know the initial pressure (P1), initial temperature (T1), and the final temperature (T2). We can use the ideal gas law to find the final pressure (P2).
Using the Gas Constant
The gas constant (R) is a fundamental constant that relates the pressure, volume, and temperature of a gas. The value of R is approximately 8.3145 J/mol·K.
Solving for Final Pressure
We can now substitute the given values into the equation:
P2 = P1 × (T2 / T1)
Substituting the values, we get:
P2 = 1.2 atm × (198 K / 283.15 K)
Calculating the Final Pressure
Now, we can calculate the final pressure:
P2 = 1.2 atm × 0.698
P2 = 0.8384 atm
Conclusion
In this article, we used the ideal gas law to solve a problem involving a change in temperature and pressure. We found that the final pressure of the gas would be approximately 0.8384 atm when the temperature is changed to 198 K, while holding the volume constant.
Importance of the Ideal Gas Law
The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. Understanding the ideal gas law is essential for predicting the behavior of gases in various applications, such as chemical reactions, gas mixtures, and industrial processes.
Limitations of the Ideal Gas Law
While the ideal gas law is a powerful tool for predicting the behavior of gases, it has some limitations. The ideal gas law assumes that the gas molecules are point particles with no volume, which is not true for real gases. Additionally, the ideal gas law does not take into account the intermolecular forces between gas molecules, which can affect the behavior of the gas.
Real-World Applications of the Ideal Gas Law
The ideal gas law has numerous real-world applications in various fields, including:
- Chemical Engineering: The ideal gas law is used to design and optimize chemical reactors, distillation columns, and other process equipment.
- Materials Science: The ideal gas law is used to study the behavior of gases in materials, such as porous materials and nanomaterials.
- Atmospheric Science: The ideal gas law is used to study the behavior of gases in the atmosphere, including the greenhouse effect and climate change.
Future Research Directions
Future research directions in the field of ideal gas law include:
- Developing more accurate models: Researchers are working to develop more accurate models that take into account the intermolecular forces between gas molecules and the finite size of gas molecules.
- Applying the ideal gas law to complex systems: Researchers are working to apply the ideal gas law to complex systems, such as gas mixtures and porous materials.
- Using the ideal gas law to study biological systems: Researchers are working to use the ideal gas law to study biological systems, such as the behavior of gases in living cells and tissues.
Introduction
The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. In this article, we will answer some frequently asked questions about the ideal gas law, including its limitations, real-world applications, and future research directions.
Q1: What is the ideal gas law?
A1: The ideal gas law is a mathematical equation that relates the pressure, volume, and temperature of a gas. It is given by the equation:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the gas constant
- T is the temperature of the gas in Kelvin
Q2: What are the assumptions of the ideal gas law?
A2: The ideal gas law assumes that the gas molecules are point particles with no volume, that there are no intermolecular forces between gas molecules, and that the gas is in a state of thermal equilibrium.
Q3: What are the limitations of the ideal gas law?
A3: The ideal gas law has several limitations, including:
- Assumes point particles: The ideal gas law assumes that gas molecules are point particles with no volume, which is not true for real gases.
- Does not account for intermolecular forces: The ideal gas law does not take into account the intermolecular forces between gas molecules, which can affect the behavior of the gas.
- Does not account for finite size of gas molecules: The ideal gas law assumes that gas molecules have no volume, which is not true for real gases.
Q4: What are the real-world applications of the ideal gas law?
A4: The ideal gas law has numerous real-world applications in various fields, including:
- Chemical Engineering: The ideal gas law is used to design and optimize chemical reactors, distillation columns, and other process equipment.
- Materials Science: The ideal gas law is used to study the behavior of gases in materials, such as porous materials and nanomaterials.
- Atmospheric Science: The ideal gas law is used to study the behavior of gases in the atmosphere, including the greenhouse effect and climate change.
Q5: How is the ideal gas law used in everyday life?
A5: The ideal gas law is used in everyday life in various ways, including:
- Air conditioning and refrigeration: The ideal gas law is used to design and optimize air conditioning and refrigeration systems.
- Gas cylinders and tanks: The ideal gas law is used to design and optimize gas cylinders and tanks.
- Medical equipment: The ideal gas law is used to design and optimize medical equipment, such as ventilators and oxygen tanks.
Q6: What are some common mistakes to avoid when using the ideal gas law?
A6: Some common mistakes to avoid when using the ideal gas law include:
- Not converting units: Failing to convert units from one system to another can lead to incorrect results.
- Not accounting for intermolecular forces: Failing to account for intermolecular forces can lead to incorrect results.
- Not accounting for finite size of gas molecules: Failing to account for the finite size of gas molecules can lead to incorrect results.
Q7: What are some future research directions in the field of ideal gas law?
A7: Some future research directions in the field of ideal gas law include:
- Developing more accurate models: Researchers are working to develop more accurate models that take into account the intermolecular forces between gas molecules and the finite size of gas molecules.
- Applying the ideal gas law to complex systems: Researchers are working to apply the ideal gas law to complex systems, such as gas mixtures and porous materials.
- Using the ideal gas law to study biological systems: Researchers are working to use the ideal gas law to study biological systems, such as the behavior of gases in living cells and tissues.
Conclusion
The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. In this article, we have answered some frequently asked questions about the ideal gas law, including its limitations, real-world applications, and future research directions. By understanding the ideal gas law, we can better design and optimize various systems and equipment, and make more accurate predictions about the behavior of gases in various applications.