What Volume Is Occupied By 500 G Of Fluorine Gas At 5.00°C And A Pressure Of 735 Torr?
Introduction
To determine the volume occupied by 500 g of fluorine gas at a given temperature and pressure, we need to use the ideal gas law. The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas. It is expressed mathematically as:
PV = nRT
Where:
- P is the pressure of the gas in pascals (Pa)
- V is the volume of the gas in cubic meters (m³)
- n is the number of moles of the gas
- R is the gas constant in pascals per cubic meters per kelvin (Pa·m³/K)
- T is the temperature of the gas in kelvin (K)
Understanding the Given Information
We are given the following information:
- Mass of fluorine gas: 500 g
- Temperature: 5.00°C
- Pressure: 735 Torr
First, we need to convert the given information into the appropriate units for the ideal gas law. We will convert the mass of fluorine gas from grams to moles, the temperature from Celsius to Kelvin, and the pressure from Torr to pascals.
Converting Mass to Moles
To convert the mass of fluorine gas from grams to moles, we need to know the molar mass of fluorine gas. The molar mass of fluorine gas (F2) is 38.00 g/mol.
We can calculate the number of moles of fluorine gas using the following formula:
n = mass / molar mass
n = 500 g / 38.00 g/mol n = 13.16 mol
Converting Temperature to Kelvin
To convert the temperature from Celsius to Kelvin, we can use the following formula:
T (K) = T (°C) + 273.15
T (K) = 5.00°C + 273.15 T (K) = 278.15 K
Converting Pressure to Pascals
To convert the pressure from Torr to pascals, we can use the following conversion factor:
1 Torr = 133.322 pascals
P (Pa) = 735 Torr x 133.322 Pa/Torr P (Pa) = 97851.19 Pa
Applying the Ideal Gas Law
Now that we have converted the given information into the appropriate units, we can apply the ideal gas law to determine the volume occupied by 500 g of fluorine gas.
Rearranging the ideal gas law to solve for volume, we get:
V = nRT / P
Substituting the values we have calculated, we get:
V = (13.16 mol) (8.3145 J/mol·K) (278.15 K) / (97851.19 Pa) V = 0.0333 m³
Conclusion
Therefore, the volume occupied by 500 g of fluorine gas at 5.00°C and a pressure of 735 Torr is approximately 0.0333 m³.
Additional Information
It's worth noting that the ideal gas law assumes that the gas is an ideal gas, which means that it obeys the ideal gas equation. However, real gases may deviate from this equation due to intermolecular forces and other factors. In this case, we have assumed that fluorine gas behaves as an ideal gas.
References
- Ideal Gas Law: PV = nRT
- Molar Mass of Fluorine Gas: 38.00 g/mol
- Conversion Factors:
- 1 Torr = 133.322 pascals
- 1°C = 1 K
Introduction
The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas. In our previous article, we used the ideal gas law to determine the volume occupied by 500 g of fluorine gas at a given temperature and pressure. In this article, we will answer some frequently asked questions (FAQs) about the ideal gas law.
Q: What is the ideal gas law?
A: The ideal gas law is a mathematical equation that relates the pressure, volume, and temperature of a gas. It is expressed mathematically as:
PV = nRT
Where:
- P is the pressure of the gas in pascals (Pa)
- V is the volume of the gas in cubic meters (m³)
- n is the number of moles of the gas
- R is the gas constant in pascals per cubic meters per kelvin (Pa·m³/K)
- T is the temperature of the gas in kelvin (K)
Q: What are the assumptions of the ideal gas law?
A: The ideal gas law assumes that the gas is an ideal gas, which means that it obeys the ideal gas equation. This means that the gas:
- Has no intermolecular forces
- Has no volume
- Is composed of point particles
- Has a constant gas constant
Q: What is the gas constant (R)?
A: The gas constant (R) is a constant that relates the pressure, volume, and temperature of a gas. It is expressed mathematically as:
R = 8.3145 J/mol·K
Q: How do I convert the ideal gas law from one unit system to another?
A: To convert the ideal gas law from one unit system to another, you need to convert the pressure, volume, and temperature from one unit system to another. For example, to convert the ideal gas law from Torr to pascals, you can use the following conversion factor:
1 Torr = 133.322 pascals
Q: Can I use the ideal gas law to calculate the volume of a gas at a given temperature and pressure?
A: Yes, you can use the ideal gas law to calculate the volume of a gas at a given temperature and pressure. To do this, you need to rearrange the ideal gas law to solve for volume:
V = nRT / P
Q: What are some common applications of the ideal gas law?
A: The ideal gas law has many common applications in chemistry and physics, including:
- Calculating the volume of a gas at a given temperature and pressure
- Calculating the pressure of a gas at a given volume and temperature
- Calculating the temperature of a gas at a given pressure and volume
- Calculating the number of moles of a gas at a given pressure and volume
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 pressure, volume, and temperature to the correct units
- Not using the correct gas constant (R)
- Not rearranging the ideal gas law to solve for the correct variable
- Not considering the assumptions of the ideal gas law
Conclusion
The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas. In this article, we have answered some frequently asked questions (FAQs) about the ideal gas law, including its assumptions, the gas constant (R), and common applications and mistakes to avoid. By understanding the ideal gas law, you can calculate the volume, pressure, and temperature of a gas with ease.
Additional Information
- Ideal Gas Law: PV = nRT
- Gas Constant (R): 8.3145 J/mol·K
- Conversion Factors:
- 1 Torr = 133.322 pascals
- 1°C = 1 K