What Mass Of Water Vapor Would Have A Pressure Of 0.750 Atm, A Volume Of 25 L, And A Temperature Of 303 K?
The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed 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, and T is the temperature of the gas in Kelvin. In this article, we will use the ideal gas law to determine the mass of water vapor that would have a pressure of 0.750 atm, a volume of 25 L, and a temperature of 303 K.
The Ideal Gas Law Equation
The ideal gas law equation is given by:
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)
Rearranging the Ideal Gas Law Equation
To solve for the number of moles of the gas, we can rearrange the ideal gas law equation as follows:
n = PV / RT
Substituting the Given Values
We are given the following values:
- P = 0.750 atm
- V = 25 L
- T = 303 K
We can substitute these values into the rearranged ideal gas law equation as follows:
n = (0.750 atm)(25 L) / (0.08206 L atm/mol K)(303 K)
Calculating the Number of Moles
Now, we can calculate the number of moles of the gas:
n = (0.750 atm)(25 L) / (0.08206 L atm/mol K)(303 K) = 0.0193 mol
Converting Moles to Mass
To convert the number of moles to mass, we need to know the molar mass of water vapor. The molar mass of water (H2O) is 18.02 g/mol.
We can convert the number of moles to mass as follows:
mass = n x molar mass = 0.0193 mol x 18.02 g/mol = 0.347 g
Conclusion
In this article, we used the ideal gas law to determine the mass of water vapor that would have a pressure of 0.750 atm, a volume of 25 L, and a temperature of 303 K. We first rearranged the ideal gas law equation to solve for the number of moles of the gas, and then substituted the given values into the equation. Finally, we converted the number of moles to mass using the molar mass of water vapor.
Understanding the Significance 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 used to calculate the pressure, volume, and temperature of a gas, as well as the number of moles of the gas. The ideal gas law is also used to determine the mass of a gas, as we did in this article.
Real-World Applications of the Ideal Gas Law
The ideal gas law has many real-world applications, including:
- Calculating the pressure of a gas in a container
- Determining the volume of a gas in a container
- Calculating the temperature of a gas in a container
- Determining the number of moles of a gas in a container
- Calculating the mass of a gas in a container
Limitations of the Ideal Gas Law
The ideal gas law is a simplified model that assumes that gases behave ideally. However, real gases do not behave ideally, and the ideal gas law has several limitations. These limitations include:
- The ideal gas law assumes that gases are ideal, which is not true for real gases
- The ideal gas law assumes that the volume of a gas is constant, which is not true for real gases
- The ideal gas law assumes that the temperature of a gas is constant, which is not true for real gases
Conclusion
Q: What is the ideal gas law?
A: The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed 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, and T is the temperature of the gas in Kelvin.
Q: What is the gas constant (R)?
A: The gas constant (R) is a constant that is used in the ideal gas law equation. It is equal to 0.08206 L atm/mol K.
Q: What is the ideal gas law equation?
A: The ideal gas law equation is:
PV = nRT
Q: How do I use the ideal gas law equation to solve for the number of moles of a gas?
A: To solve for the number of moles of a gas, you can rearrange the ideal gas law equation as follows:
n = PV / RT
Q: What is the molar mass of water vapor?
A: The molar mass of water vapor (H2O) is 18.02 g/mol.
Q: How do I convert the number of moles to mass?
A: To convert the number of moles to mass, you can multiply the number of moles by the molar mass of the gas.
mass = n x molar mass
Q: What are some real-world applications of the ideal gas law?
A: Some real-world applications of the ideal gas law include:
- Calculating the pressure of a gas in a container
- Determining the volume of a gas in a container
- Calculating the temperature of a gas in a container
- Determining the number of moles of a gas in a container
- Calculating the mass of a gas in a container
Q: What are some limitations of the ideal gas law?
A: Some limitations of the ideal gas law include:
- The ideal gas law assumes that gases are ideal, which is not true for real gases
- The ideal gas law assumes that the volume of a gas is constant, which is not true for real gases
- The ideal gas law assumes that the temperature of a gas is constant, which is not true for real gases
Q: Can I use the ideal gas law to calculate the pressure of a gas in a container?
A: Yes, you can use the ideal gas law to calculate the pressure of a gas in a container. To do this, you can rearrange the ideal gas law equation as follows:
P = nRT / V
Q: Can I use the ideal gas law to determine the volume of a gas in a container?
A: Yes, you can use the ideal gas law to determine the volume of a gas in a container. To do this, you can rearrange the ideal gas law equation as follows:
V = nRT / P
Q: Can I use the ideal gas law to calculate the temperature of a gas in a container?
A: Yes, you can use the ideal gas law to calculate the temperature of a gas in a container. To do this, you can rearrange the ideal gas law equation as follows:
T = PV / nR
Q: Can I use the ideal gas law to determine the number of moles of a gas in a container?
A: Yes, you can use the ideal gas law to determine the number of moles of a gas in a container. To do this, you can rearrange the ideal gas law equation as follows:
n = PV / RT
Q: Can I use the ideal gas law to calculate the mass of a gas in a container?
A: Yes, you can use the ideal gas law to calculate the mass of a gas in a container. To do this, you can multiply the number of moles by the molar mass of the gas.
mass = n x molar mass
Conclusion
In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is used to calculate the pressure, volume, and temperature of a gas, as well as the number of moles of the gas. The ideal gas law is also used to determine the mass of a gas, as well as to calculate the pressure, volume, and temperature of a gas in a container. However, the ideal gas law has several limitations, including the assumption that gases are ideal, the assumption that the volume of a gas is constant, and the assumption that the temperature of a gas is constant.