The Ideal Gas Law and Gas Constant: Study Notes

Gases

The Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that describes the relationship between pressure, volume, temperature, and the amount of gas. It is widely used to predict the behavior of gases under various conditions.

• Formula: $PV = nRT$

• P: Pressure of the gas (usually in atm, mmHg, or Pa)

• V: Volume of the gas (usually in liters)

• n: Amount of gas (in moles)

• R: Universal gas constant

• T: Temperature (in Kelvin)

Example: A 500 mL container at a pressure of 800 mmHg contains 20.3 g nitrogen gas at 50 °C. Determine the correct units needed for the Ideal Gas Law.

Additional info: Always convert pressure to atm, volume to liters, and temperature to Kelvin for consistency with the gas constant R.

Gas Constant (R)

The gas constant (R) is a proportionality constant in the Ideal Gas Law. Its value depends on the units used for pressure and volume.

• Common values of R:

R Value	Pressure Units	Volume Units
0.0821	atm	L
62.4	mmHg	L
8.314	Pa	m3

• Choose the value of R that matches the units of pressure and volume in your calculation.

Example: How many moles of H2 are contained in a 25.0 L tank at 190 °C and 1.30 atm?

Additional info: Convert temperature to Kelvin: $T(K) = T(°C) + 273.15$

Practice Problems

Practice problems help reinforce the application of the Ideal Gas Law in real-world scenarios.

• Practice 1: How many grams of carbon dioxide, CO2, are present in a 0.150 L flask recorded at 525 mmHg and 32 °C?

• Practice 2: How many liters of HNO3 gas, measured at 28 °C and 780 torr, are required to prepare 2.01 L of 4.15 M solution of nitric acid?

• Practice 3: When 0.073 g argon is added to a 500 cm3 container with a sample of oxygen gas, the total pressure of the gases is found to be 1.52 atm at a temperature of 342 K. What is the mass of the oxygen gas in the bulb?

Example Solution: Use the Ideal Gas Law to solve for the unknown quantity, converting all units as necessary.

Additional info: For mass calculations, first solve for moles using $n = \frac{PV}{RT}$, then convert moles to grams using the molar mass.