5. Use The Combined Gas Law To Solve This Problem:A Chemist Collects 56.7 ML Of Nitrogen Gas At 25°C And 740 Torr. What Would The Volume Of The Nitrogen Be At STP? Show Your Calculations.6. What Is The Mole Fraction Formula?7. What Is The Ideal Gas Law

Feb 27, 2025 by ADMIN 253 views

Understanding the Ideal Gas Law and Its Applications in Chemistry

The Ideal Gas Law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is a combination of several gas laws, including the Combined Gas Law, which is used to solve problems involving changes in temperature, pressure, and volume of gases. In this article, we will explore the Combined Gas Law, the mole fraction formula, and the Ideal Gas Law, and provide step-by-step calculations to solve a problem involving the collection of nitrogen gas at STP.

5. Using the Combined Gas Law to Solve a Problem

The Combined Gas Law is a mathematical equation that combines the three gas laws: Boyle's Law (P1V1 = P2V2), Charles' Law (V1/T1 = V2/T2), and Gay-Lussac's Law (P1/T1 = P2/T2). The equation is as follows:

P1V1/T1 = P2V2/T2

Where:

P1 and P2 are the initial and final pressures
V1 and V2 are the initial and final volumes
T1 and T2 are the initial and final temperatures

To solve the problem, we need to convert the given values to the same units. The initial volume is given as 56.7 mL, and the initial pressure is 740 torr. We need to convert the pressure to atmospheres (atm) and the volume to liters (L).

Converting Units

1 atm = 760 torr 1 L = 1000 mL

Initial pressure (P1) = 740 torr / 760 torr/atm = 0.973 atm Initial volume (V1) = 56.7 mL / 1000 mL/L = 0.0567 L Initial temperature (T1) = 25°C + 273 = 298 K

Solving the Problem

We are asked to find the volume of the nitrogen gas at STP (Standard Temperature and Pressure), which is defined as 0°C and 1 atm.

Final pressure (P2) = 1 atm Final temperature (T2) = 0°C + 273 = 273 K

Now, we can plug in the values into the Combined Gas Law equation:

P1V1/T1 = P2V2/T2 0.973 atm x 0.0567 L / 298 K = 1 atm x V2 / 273 K

Simplifying the equation, we get:

V2 = (0.973 atm x 0.0567 L / 298 K) x (273 K / 1 atm) V2 = 0.0235 L

Therefore, the volume of the nitrogen gas at STP is 0.0235 L.

6. The Mole Fraction Formula

The mole fraction formula is used to calculate the number of moles of a component in a mixture. It is defined as the number of moles of a component divided by the total number of moles in the mixture.

Mole fraction (x) = number of moles of component / total number of moles

For example, if we have a mixture of 2 moles of nitrogen and 3 moles of oxygen, the mole fraction of nitrogen would be:

x = 2 moles / (2 moles + 3 moles) = 2/5 = 0.4

7. The Ideal Gas Law

The Ideal Gas Law is a mathematical equation that describes the behavior of ideal gases under various conditions. It is a combination of the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law. The equation is as follows:

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

The Ideal Gas Law can be used to calculate the pressure, volume, or temperature of a gas, given the other three variables.

Applications of the Ideal Gas Law

The Ideal Gas Law has numerous applications in chemistry, including:

Calculating the pressure of a gas at a given temperature and volume
Determining the volume of a gas at a given temperature and pressure
Finding the number of moles of a gas at a given temperature and pressure
Calculating the temperature of a gas at a given pressure and volume

In conclusion, the Combined Gas Law, the mole fraction formula, and the Ideal Gas Law are fundamental concepts in chemistry that describe the behavior of gases under various conditions. By understanding these concepts, chemists can solve problems involving changes in temperature, pressure, and volume of gases, and make predictions about the behavior of gases in different situations.
Ideal Gas Law and Gas Laws Q&A

In this article, we will answer some frequently asked questions about the Ideal Gas Law and gas laws.

Q: What is the Ideal Gas Law?

A: The Ideal Gas Law is a mathematical equation that describes the behavior of ideal gases under various conditions. It is a combination of the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law. The equation is as follows:

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

Q: What is the difference between the Ideal Gas Law and the Real Gas Law?

A: The Ideal Gas Law is an idealized equation that assumes that gases behave perfectly, meaning that they have no intermolecular forces and occupy no volume. The Real Gas Law, on the other hand, takes into account the imperfections of real gases and is a more accurate representation of their behavior.

Q: What is the significance of the gas constant (R) in the Ideal Gas Law?

A: The gas constant (R) is a fundamental constant that relates the pressure, volume, and temperature of a gas. It is a measure of the energy of a gas and is used to calculate the number of moles of a gas.

Q: How is the Ideal Gas Law used in real-world applications?

A: The Ideal Gas Law has numerous applications in chemistry, including:

Calculating the pressure of a gas at a given temperature and volume
Determining the volume of a gas at a given temperature and pressure
Finding the number of moles of a gas at a given temperature and pressure
Calculating the temperature of a gas at a given pressure and volume

Q: What is the difference between the mole fraction and the mole percentage?

A: The mole fraction is the number of moles of a component divided by the total number of moles in the mixture, while the mole percentage is the mole fraction multiplied by 100.

Q: How is the mole fraction used in real-world applications?

A: The mole fraction is used to calculate the number of moles of a component in a mixture, which is essential in many chemical reactions and processes.

Q: What is the significance of the standard temperature and pressure (STP) in the Ideal Gas Law?

A: The standard temperature and pressure (STP) is a set of conditions that is used as a reference point for many chemical reactions and processes. It is defined as 0°C and 1 atm.

Q: How is the Ideal Gas Law used to calculate the volume of a gas at STP?

A: The Ideal Gas Law can be used to calculate the volume of a gas at STP by rearranging the equation to solve for V:

V = nRT / P

Where:

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
P is the pressure of the gas

Q: What is the difference between the ideal gas and the real gas?

A: The ideal gas is a hypothetical gas that behaves perfectly, meaning that it has no intermolecular forces and occupies no volume. The real gas, on the other hand, is a gas that has imperfections and does not behave perfectly.

Q: How is the Ideal Gas Law used to calculate the number of moles of a gas?

A: The Ideal Gas Law can be used to calculate the number of moles of a gas by rearranging the equation to solve for n:

n = PV / RT

Where:

n is the number of moles of the gas
P is the pressure of the gas
V is the volume of the gas
R is the gas constant
T is the temperature of the gas

Q: What is the significance of the gas constant (R) in the Ideal Gas Law?

Q: How is the Ideal Gas Law used in real-world applications?

A: The Ideal Gas Law has numerous applications in chemistry, including:

Calculating the pressure of a gas at a given temperature and volume
Determining the volume of a gas at a given temperature and pressure
Finding the number of moles of a gas at a given temperature and pressure
Calculating the temperature of a gas at a given pressure and volume

Conclusion

The Ideal Gas Law and gas laws are fundamental concepts in chemistry that describe the behavior of gases under various conditions. By understanding these concepts, chemists can solve problems involving changes in temperature, pressure, and volume of gases, and make predictions about the behavior of gases in different situations.