What Is The Pressure Of 0.540 Mol Of An Ideal Gas At 35.5 L And 223 K?Use P V = N R T PV = NRT P V = N RT And R = 8.314 L ⋅ K P A M O L ⋅ K R = 8.314 \frac{L \cdot KPa}{mol \cdot K} R = 8.314 M O L ⋅ K L ⋅ K P A .A. 0.715 KPa B. 2.45 KPa C. 28.2 KPa D. 62.7 KPa

Mar 12, 2025 by ADMIN 267 views

**What is the Pressure of an Ideal Gas?**

Understanding the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. The ideal gas law is expressed by the equation:

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 meter per mole per kelvin (Pa·m³/mol·K)
T is the temperature of the gas in kelvin (K)

Given Values

In this problem, we are given the following values:

n = 0.540 mol
V = 35.5 L
T = 223 K
R = 8.314 L·kPa/mol·K

Converting Units

Before we can plug in the values into the ideal gas law equation, we need to convert the units of the given values to match the units of the gas constant.

V = 35.5 L (no conversion needed)
T = 223 K (no conversion needed)
R = 8.314 L·kPa/mol·K (no conversion needed)

Plugging in Values

Now that we have the given values in the correct units, we can plug them into the ideal gas law equation:

PV = nRT

P = (nRT) / V

P = (0.540 mol × 8.314 L·kPa/mol·K × 223 K) / 35.5 L

P = (0.540 × 8.314 × 223) / 35.5

P = 62.7 kPa

Conclusion

Therefore, the pressure of 0.540 mol of an ideal gas at 35.5 L and 223 K is 62.7 kPa.

Answer

The correct answer is D. 62.7 kPa.

Discussion

The ideal gas law is a powerful tool for predicting the behavior of gases under different conditions. By using the ideal gas law equation, we can calculate the pressure, volume, and temperature of a gas given the number of moles, volume, and temperature.

In this problem, we used the ideal gas law equation to calculate the pressure of 0.540 mol of an ideal gas at 35.5 L and 223 K. We plugged in the given values into the equation and solved for the pressure.

The ideal gas law equation is a fundamental concept in chemistry and is used to describe the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas.

References

Ideal Gas Law. (n.d.). Retrieved from https://en.wikipedia.org/wiki/Ideal_gas_law
Gas Constant. (n.d.). Retrieved from https://en.wikipedia.org/wiki/Gas_constant

Practice Problems

Calculate the pressure of 0.250 mol of an ideal gas at 20.0 L and 298 K.
Calculate the volume of 0.500 mol of an ideal gas at 101.3 kPa and 298 K.
Calculate the temperature of 0.750 mol of an ideal gas at 25.0 L and 101.3 kPa.

Solutions

P = (nRT) / V P = (0.250 mol × 8.314 L·kPa/mol·K × 298 K) / 20.0 L P = 3.01 kPa
V = nRT / P V = (0.500 mol × 8.314 L·kPa/mol·K × 298 K) / 101.3 kPa V = 20.0 L
T = PV / nR T = (101.3 kPa × 25.0 L) / (0.750 mol × 8.314 L·kPa/mol·K) T = 298 K
Ideal Gas Law Q&A =====================

Frequently Asked Questions

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 by the equation: PV = nRT

Q: What are the variables in the ideal gas law equation? A: The variables in the ideal gas law equation are:

P: the pressure of the gas in pascals (Pa)
V: the volume of the gas in cubic meters (m³)
n: the number of moles of the gas
R: the gas constant in pascals per cubic meter per mole per kelvin (Pa·m³/mol·K)
T: the temperature of the gas in kelvin (K)

Q: What is the gas constant (R)? A: The gas constant (R) is a physical constant that relates the pressure, volume, and temperature of a gas. It is approximately equal to 8.314 L·kPa/mol·K.

Q: How do I use the ideal gas law equation to solve problems? A: To use the ideal gas law equation to solve problems, you need to plug in the given values into the equation and solve for the unknown variable. For example, if you are given the pressure, volume, and temperature of a gas, you can use the equation to solve for the number of moles of the gas.

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 pressure of a gas in a container
Calculating the volume of a gas in a container
Calculating the temperature of a gas in a container
Calculating the number of moles of a gas in a container

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 units correctly
Not plugging in the correct values into the equation
Not solving for the correct variable
Not checking the units of the answer

Q: Can the ideal gas law be used to describe real gases? A: The ideal gas law is a simplified equation that assumes that gases behave ideally. However, real gases do not behave ideally and the ideal gas law is not accurate for all situations. In general, the ideal gas law is a good approximation for gases at low pressures and high temperatures.

Q: What are some limitations of the ideal gas law? A: Some limitations of the ideal gas law include:

It assumes that gases behave ideally
It does not take into account the intermolecular forces between gas molecules
It does not take into account the size and shape of gas molecules
It is not accurate for high-pressure and low-temperature situations

Q: Can the ideal gas law be used to solve problems involving mixtures of gases? A: The ideal gas law can be used to solve problems involving mixtures of gases, but it requires some modifications to the equation. The ideal gas law can be used to calculate the partial pressure of each gas in the mixture, and then the total pressure of the mixture can be calculated by summing the partial pressures.

Q: What are some common problems that can be solved using the ideal gas law? A: Some common problems that can be solved using the ideal gas law include:

Calculating the pressure of a gas in a container
Calculating the volume of a gas in a container
Calculating the temperature of a gas in a container
Calculating the number of moles of a gas in a container
Calculating the partial pressure of each gas in a mixture

Q: How do I know if the ideal gas law is a good approximation for a particular situation? A: The ideal gas law is a good approximation for situations where the gas is at low pressure and high temperature. If the gas is at high pressure and low temperature, the ideal gas law may not be a good approximation and a more complex equation may be needed.

Q: Can the ideal gas law be used to solve problems involving gases in different states of matter? A: The ideal gas law can be used to solve problems involving gases in different states of matter, but it requires some modifications to the equation. The ideal gas law can be used to calculate the pressure, volume, and temperature of a gas in a container, regardless of whether the gas is in a liquid or solid state.

Q: What are some common applications of the ideal gas law in real-world situations? A: The ideal gas law has many common applications in real-world situations, including:

Calculating the pressure of a gas in a container in a chemical plant
Calculating the volume of a gas in a container in a laboratory
Calculating the temperature of a gas in a container in a refrigerator
Calculating the number of moles of a gas in a container in a chemical reaction
Calculating the partial pressure of each gas in a mixture in a gas mixture.