Ideal Gas Law

Ideal Gas Law

High School

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Learning Objectives

Key Vocabulary

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Ideal Gas

A hypothetical gas with molecules that have no volume or attractions, perfectly obeying all gas laws.

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Avogadro's Law

Equal volumes of gases at the same temperature and pressure contain an equal number of molecules.

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Molar Volume

The volume that one mole of a substance occupies at a specific temperature and pressure.

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STP

Standard Temperature and Pressure is a temperature of 0°C and a pressure of 1 atm.

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Properties of Gases

Pressure and Volume

• Gas behavior is defined by four properties: Pressure (P), Volume (V), Temperature (T), and Amount (n).

• Pressure and volume are inversely proportional; as one increases, the other must decrease.

• Decreasing the volume of a gas increases the frequency of molecular collisions, which increases pressure.

Pressure, Temp & Amount

• Pressure and temperature are directly proportional, meaning they increase or decrease together.

• Raising the temperature increases the molecules' kinetic energy, causing more frequent and forceful collisions.

• Pressure is also directly proportional to the amount of gas in the container.

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Solved Example 1
A 5.0 L container holds 0.75 moles of oxygen gas at a temperature of 298 K. What is the pressure inside the container in atmospheres (atm)?

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Step 1: Analyze and Sketch the Problem

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Solved Example 1
A 5.0 L container holds 0.75 moles of oxygen gas at a temperature of 298 K. What is the pressure inside the container in atmospheres (atm)?

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Step 2: Solve for the Unknown

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Solved Example 1
A 5.0 L container holds 0.75 moles of oxygen gas at a temperature of 298 K. What is the pressure inside the container in atmospheres (atm)?

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Step 3: Evaluate the Answer

• The units have cancelled correctly to give the answer in atmospheres (atm), which was the required unit for pressure.

• The answer is reasonable. A pressure of about 3.67 atm is expected for this amount of gas at room temperature in a 5.0 L container.

Multiple Choice

If the temperature of a gas in a rigid container is increased, what happens to the pressure?

• It remains the same because the volume is constant.

• It increases because the molecules collide with the walls more often and with more force.

• It decreases because the molecules move faster and find more space.

• It increases because the number of moles has increased.

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Avogadro's Law and Molar Volume

Standard Conditions (STP)

Room Conditions (RTP)

• ​At RTP (298 K and 1 atm), the volume of one mole of any ideal gas is 24 L.

• ​​Avogadro's number is 6.022 x 10²³, the number of molecules in one mole of any substance.

• ​This means the volume of a gas is directly proportional to its number of moles at constant conditions.

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Solved Example 2
A container with 2.0 moles of nitrogen gas has a volume of 40.0 L. If 1.0 mole of nitrogen is added, what is the new volume, assuming temperature and pressure are constant?

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Step 1: Analyze and Sketch the Problem

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Solved Example 2
A container with 2.0 moles of nitrogen gas has a volume of 40.0 L. If 1.0 mole of nitrogen is added, what is the new volume, assuming temperature and pressure are constant?

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Step 2: Solve for the Unknown

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Solved Example 2
A container with 2.0 moles of nitrogen gas has a volume of 40.0 L. If 1.0 mole of nitrogen is added, what is the new volume, assuming temperature and pressure are constant?

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Step 3: Evaluate the Answer

Multiple Choice

According to Avogadro's Law, what is the volume occupied by one mole of any ideal gas at STP?

• 6.022 x 10²³ L

• 24.0 L

• It depends on the type of gas.

• 22.4 L

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The Ideal Gas Model

• The volume of gas molecules is negligible compared to the container's volume.

• ​There are no attractive or repulsive forces between the gas molecules.

• Molecules are in constant, random, straight-line motion with perfectly elastic collisions.

• Average kinetic energy is proportional to the absolute temperature in Kelvin.

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Multiple Choice

Which of the following is NOT an assumption of the Kinetic Molecular Theory for an ideal gas?

• There are strong attractive forces between gas molecules.

• The volume of the gas molecules is negligible.

• Collisions between molecules are perfectly elastic.

• Gas molecules are in constant, random motion.

The Ideal Gas Law Equation

Multiple Choice

In the ideal gas law equation $$PV=nRT$$ , what does the variable "n" represent?

• The ideal gas constant.

• The temperature in Celsius.

• The number of moles of the gas.

• The pressure of the gas.

Calculations: Unit Conversion

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Temperature

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Pressure

• A common conversion is from kilopascals (kPa) to the SI unit, Pascals (Pa).

• To convert from kilopascals to Pascals, you will need to multiply by 1000.

• For example, a pressure of 1 kPa is the same as 1000 Pa.

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Volume

• The standard SI unit for volume is the cubic meter (m³).

• To convert cubic decimeters (dm³) to m³, you must divide by 1000.

• To convert cubic centimeters (cm³) to m³, divide by 1,000,000.

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Solved Example 6
Calculate the number of moles of ammonia gas (NH₃) contained in a 3.0 L vessel at 300 K with a pressure of 1.50 atm.

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Step 1: Analyze and Sketch the Problem

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Solved Example 6
Example: Using PV=nRT

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Step 2: Solve for the Unknown

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Solved Example 6
Example: Using PV=nRT

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Step 3: Evaluate the Answer

• The final answer is in atmospheres (atm), which is a correct unit for pressure.

• The calculated pressure of 1.50 atm is a reasonable value for a gas in this scenario.

Multiple Choice

A temperature of 25°C is recorded for a gas. What temperature value must be used in the ideal gas law equation?

• 273 K

• 298 K

• -248 K

• 25 K

Multiple Choice

If you need to solve for temperature (T) using the ideal gas law, how would you rearrange the equation $$PV = nRT$$ ?

• $$T = \frac{P}{VnR}$$

• $$T = \frac{nR}{PV}$$

• $$T = \frac{PV}{nR}$$

• $$T = \frac{nRT}{PV}$$

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Common Misconceptions About Gases

Misconception	Correction
All gases behave ideally under all conditions.	Real gases deviate at high pressures and low temperatures.
Temperature in Celsius can be used in the ideal gas law.	Temperature must always be converted to Kelvin for gas law calculations.
The molar volume of a gas (22.4 L/mol) is always constant.	The 22.4 L/mol value is only valid at Standard Temperature and Pressure (STP).

Multiple Choice

How does the Kinetic Molecular Theory explain the direct relationship between the temperature and pressure of a gas in a fixed volume?

• Higher temperature causes molecules to move in straight lines, which increases pressure.

• Higher temperature increases the kinetic energy of molecules, causing more frequent and forceful collisions.

• Higher temperature increases the size of the gas molecules, increasing the force of collisions.

• Higher temperature makes the molecules stick together, increasing density and pressure.

Multiple Choice

If you have two identical containers at the same temperature and pressure, one with 1 mole of Oxygen (O₂) and one with 1 mole of Methane (CH₄), which statement is correct?

• The Methane container has a greater volume.

• The volumes cannot be compared without knowing the molar masses.

• The Oxygen container has a greater volume.

• Both containers have the same volume.

Multiple Choice

A sample of gas occupies 1.20 L at 265 K and 0.900 atm. How would you calculate the number of moles (n) in this sample? (R = 0.0821 L·atm/mol·K)

• n = (1.20 L * 265 K) / (0.0821 * 0.900 atm)

• n = (0.0821 * 265 K) / (0.900 atm * 1.20 L)

• n = (0.900 atm * 265 K) / (0.0821 * 1.20 L)

• n = (0.900 atm * 1.20 L) / (0.0821 * 265 K)

Multiple Choice

Under what conditions would a real gas like methane (CH₄) most significantly deviate from the behavior predicted by the ideal gas law?

• High temperature and low pressure, where intermolecular forces and particle volume are negligible.

• When the number of moles is exactly 1, as the law is most accurate then.

• At Standard Temperature and Pressure (STP), where it behaves most ideally.

• Low temperature and high pressure, where intermolecular forces and particle volume are significant.

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Summary

Poll

On a scale of 1-4, how confident are you with using the Ideal Gas Law to solve problems?

• 1

• 2

• 3

• 4