IDEAL-GAS-LAW

Ideal Gas Law Overview

• Definition of an ideal gas and its characteristics.

Definition of Ideal Gas

• An ideal gas is defined by two main properties:

  • All collisions between atoms or molecules are perfectly elastic.

  • There are no intermolecular attractive forces.

Ideal Gas Law Equation

• The relationship between pressure (P), volume (V), moles of gas (n), and temperature (T) is given by the ideal gas law:

  • Equation: PV = nRT

    • P = pressure (in atmospheres)

    • V = volume (in liters)

    • n = moles of gas present

    • R = universal gas constant (0.0821 atm·L/mol·K)

    • T = temperature (in Kelvin)

Variables Explained

• Pressure (P):

  • Measured in atmospheres (atm).

• Volume (V):

  • Measured in liters (L).

• Moles of gas (n):

  • Represents the quantity of gas present.

• Universal Gas Constant (R):

  • Value: 0.0821 atm·L/mol·K, used to convert the units.

• Temperature (T):

  • Measured in Kelvin (K).

Variations of the Ideal Gas Law

• The ideal gas law can be rearranged to solve for any variable:

  • To find Pressure: P = nRT/V

  • To find Volume: V = nRT/P

  • To find Temperature: T = PV/nR

Example Problem 1

• Problem: Given 4 moles of gas at a pressure of 5.6 atm and a volume of 12 liters, find the temperature.

  • Formula Used: T = PV/nR

  • Calculation:

    • T = (5.6 atm)(12 L)/ (4 mol)(0.0821 L·atm/K·mol)

    • T = 204.63 K

Example Problems for Practice

• Problem 1: If I have 21 moles of gas held at a pressure of 78 atm and a temperature of 900K, what is the volume of the gas?

• Problem 2: If I have 72 liters of gas held at a pressure of 3.4 atm and a temperature of 225 K, how many moles of gas do I have?