What Volume In Liters Would 20.0 Moles Of Sulfur Dioxide Occupy At $75.3^{\circ} C$ With A Pressure Of 3.00 Atm?
Understanding the Problem
To solve this problem, we need to apply the ideal gas law, which relates the pressure, volume, temperature, and amount of a gas. The ideal gas law is given by the equation:
PV = nRT
where:
- P is the pressure of the gas in atmospheres (atm)
- V is the volume of the gas in liters (L)
- n is the number of moles of the gas
- R is the gas constant, which is equal to 0.08206 L atm/mol K
- T is the temperature of the gas in Kelvin (K)
Converting Temperature to Kelvin
The given temperature is in degrees Celsius, so we need to convert it to Kelvin. The formula to convert Celsius to Kelvin is:
T (K) = T (°C) + 273.15
Plugging in the given temperature, we get:
T (K) = 75.3 + 273.15 = 348.45 K
Applying the Ideal Gas Law
Now that we have the temperature in Kelvin, we can plug in the values into the ideal gas law equation:
P = 3.00 atm n = 20.0 mol R = 0.08206 L atm/mol K T = 348.45 K
Rearranging the equation to solve for volume, we get:
V = nRT / P
Plugging in the values, we get:
V = (20.0 mol)(0.08206 L atm/mol K)(348.45 K) / (3.00 atm)
Calculating the Volume
Now, let's calculate the volume:
V = (20.0 mol)(0.08206 L atm/mol K)(348.45 K) / (3.00 atm) V = 235.19 L
Conclusion
Therefore, 20.0 moles of sulfur dioxide would occupy a volume of approximately 235.19 L at a pressure of 3.00 atm and a temperature of 75.3°C.
Understanding the Significance of the Ideal Gas Law
The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, temperature, and amount of a gas. It is a powerful tool for predicting the behavior of gases under different conditions. In this problem, we applied the ideal gas law to calculate the volume of sulfur dioxide at a given pressure and temperature.
Real-World Applications of the Ideal Gas Law
The ideal gas law has numerous real-world applications, including:
- Calculating the volume of gases in industrial processes
- Predicting the behavior of gases in chemical reactions
- Designing gas storage tanks and pipelines
- Understanding the properties of gases in atmospheric science
Limitations of the Ideal Gas Law
While the ideal gas law is a powerful tool, it has some limitations. For example:
- It assumes that the gas is ideal, meaning that it has no intermolecular forces and no volume
- It assumes that the gas is in a state of equilibrium
- It does not take into account the behavior of real gases, which can deviate from the ideal gas law under certain conditions
Conclusion
In conclusion, the ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, temperature, and amount of a gas. By applying the ideal gas law, we can calculate the volume of gases under different conditions. However, it is essential to understand the limitations of the ideal gas law and to use it in conjunction with other laws and principles to accurately predict the behavior of gases.
Frequently Asked Questions
- What is the ideal gas law? The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, temperature, and amount of a gas.
- What is the formula for the ideal gas law? The formula for the ideal gas law is: PV = nRT
- What are the units of the gas constant (R)? The units of the gas constant (R) are: L atm/mol K
- What is the temperature in Kelvin? The temperature in Kelvin is: 348.45 K
- What is the volume of sulfur dioxide?
The volume of sulfur dioxide is: 235.19 L
Q&A: Ideal Gas Law
Q: What is the ideal gas law?
A: The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, temperature, and amount of a gas. It is a powerful tool for predicting the behavior of gases under different conditions.
Q: What is the formula for the ideal gas law?
A: The formula for the ideal gas law is: PV = nRT
Where:
- P is the pressure of the gas in atmospheres (atm)
- V is the volume of the gas in liters (L)
- n is the number of moles of the gas
- R is the gas constant, which is equal to 0.08206 L atm/mol K
- T is the temperature of the gas in Kelvin (K)
Q: What are the units of the gas constant (R)?
A: The units of the gas constant (R) are: L atm/mol K
Q: What is the temperature in Kelvin?
A: The temperature in Kelvin is: 348.45 K
Q: What is the volume of sulfur dioxide?
A: The volume of sulfur dioxide is: 235.19 L
Q: What is the pressure of the gas?
A: The pressure of the gas is: 3.00 atm
Q: What is the number of moles of the gas?
A: The number of moles of the gas is: 20.0 mol
Q: What is the ideal gas law used for?
A: The ideal gas law is used to:
- Calculate the volume of gases in industrial processes
- Predict the behavior of gases in chemical reactions
- Design gas storage tanks and pipelines
- Understand the properties of gases in atmospheric science
Q: What are the limitations of the ideal gas law?
A: The ideal gas law has some limitations, including:
- It assumes that the gas is ideal, meaning that it has no intermolecular forces and no volume
- It assumes that the gas is in a state of equilibrium
- It does not take into account the behavior of real gases, which can deviate from the ideal gas law under certain conditions
Q: What is the significance of the ideal gas law?
A: The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, temperature, and amount of a gas. It is a powerful tool for predicting the behavior of gases under different conditions.
Q: How is the ideal gas law used in real-world applications?
A: The ideal gas law is used in a variety of real-world applications, including:
- Calculating the volume of gases in industrial processes
- Predicting the behavior of gases in chemical reactions
- Designing gas storage tanks and pipelines
- Understanding the properties of gases in atmospheric science
Q: What are some common mistakes to avoid when using the ideal gas law?
A: Some common mistakes to avoid when using the ideal gas law include:
- Not converting the temperature to Kelvin
- Not using the correct units for the gas constant (R)
- Not taking into account the limitations of the ideal gas law
Q: How can I apply the ideal gas law to a real-world problem?
A: To apply the ideal gas law to a real-world problem, you can follow these steps:
- Identify the given values (pressure, volume, temperature, and number of moles)
- Convert the temperature to Kelvin
- Plug in the values into the ideal gas law equation
- Solve for the unknown value (volume, pressure, temperature, or number of moles)
Q: What are some common misconceptions about the ideal gas law?
A: Some common misconceptions about the ideal gas law include:
- The ideal gas law is only used for ideal gases
- The ideal gas law is only used for gases at high temperatures and pressures
- The ideal gas law is only used for gases in a state of equilibrium
Q: How can I improve my understanding of the ideal gas law?
A: To improve your understanding of the ideal gas law, you can:
- Practice applying the ideal gas law to different problems
- Review the limitations of the ideal gas law
- Use online resources and tutorials to supplement your learning
- Ask your instructor or a tutor for help if you are struggling with the concept.