Overview
This lecture covers the ideal gas law equation, its components and units, and demonstrates step-by-step how to solve a typical problem using the formula.
The Ideal Gas Law Equation
- The ideal gas law is PV = nRT.
- P represents pressure, measured in atmospheres (atm).
- V represents volume, measured in liters (L).
- n is the number of moles (mol) of gas.
- R is the gas constant, 0.082 atm·L/(mol·K).
- T is temperature in Kelvin (K).
- To convert Celsius to Kelvin, add 273 to the Celsius temperature.
Problem-Solving Steps
- Identify all given data: mass (in kg or g), pressure (atm), temperature (Celsius), molar mass (g/mol).
- Convert mass to grams if needed (e.g. 12 kg = 12,000 g).
- Calculate the number of moles using n = mass (g) / molar mass (g/mol).
- Convert temperature to Kelvin: K = °C + 273.
- Rearrange the ideal gas law to solve for volume: V = nRT/P.
- Substitute all known values with correct units into the formula.
- Check unit consistency and cancel as appropriate to ensure the answer is in liters.
- Perform calculation to find the volume.
Final Answer Example
- For the example problem, using 12,000 g gas with molar mass 58 g/mol at 1 atm and 25°C:
- n = 12,000 / 58 = 206.9 mol
- T = 25 + 273 = 298 K
- V = (206.9 mol) × 0.082 × 298 / 1 atm = 5,055.8 L
Key Terms & Definitions
- Ideal Gas Law — a relationship between pressure, volume, moles, temperature, and a constant (PV = nRT).
- Molar Mass — mass of one mole of a substance (g/mol).
- Kelvin (K) — temperature unit used in gas law calculations, °C + 273.
Action Items / Next Steps
- Practice similar problems using PV = nRT.
- Remember to convert all units as needed (mass to grams, °C to K).
- Review the method for identifying and rearranging required formula components.