Ideal Gas Law

Overview

The lecture focuses on the Ideal Gas Law, which is a cornerstone of many gas-related calculations in chemistry. The law is expressed as:

• Equation: ( PV = nRT )
• Mnemonic: Often referred to as "pevnert."

Key Components:

• P: Pressure
• V: Volume
• n: Number of moles
• R: Ideal Gas Constant
• T: Temperature

Ideal Conditions

• The Ideal Gas Law applies when gases behave ideally.
• Limitations: Breaks down under extremely high pressures or low temperatures.
• Despite this, most gases behave close to ideally under normal conditions.

Ideal Gas Constant

• R is calculated using conditions at Standard Temperature and Pressure (STP):
  • 1 mole of gas = 22.4 liters
  • STP: 1 atm pressure, 273 K temperature (0°C)
• Value of R: 0.08206 L atm / (mol K)

Units and Conversions

• Always convert units to: atm (pressure), liters (volume), moles (n), Kelvin (temperature).
• Common conversions:
  • Pressure from kPa to atm
  • Volume from milliliters to liters
  • Temperature from Celsius to Kelvin (add 273)

Example Calculation

1. Problem: How many grams of methanol from 3.50 liters of hydrogen gas at 575 psi and 55°C?
2. Steps:
   • Convert psi to atm: 1 atm = 14.7 psi
   • Convert Celsius to Kelvin
   • Use Ideal Gas Law to solve for moles (n):
     • Rearrange to ( n = \frac{PV}{RT} )
   • Convert moles to grams using molar mass

Derived Gas Laws

The Ideal Gas Law can be used to derive other gas laws:

Boyle's Law

• Formula: ( P_1V_1 = P_2V_2 )
• Constants: Temperature and moles

Charles's Law

• Formula: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} )
• Constants: Pressure and moles

Gay-Lussac's Law

• Formula: ( \frac{P_1}{T_1} = \frac{P_2}{T_2} )
• Constants: Volume and moles

Avogadro's Law

• Focus: Volume and moles

Combined Gas Law

• Focus: Pressure, volume, and temperature

Understanding the Laws

• Concept: Variables not involved in the changes remain constant.
• Visualization: Helpful diagrams show which variables are constant in each law.

Key Takeaways

• Understand each derived gas law: name, formula, and constants.
• Applicability: Ideal Gas Law is used primarily but knowledge of all laws is essential.