Gas (Gas laws)

1. Gas laws
    (a) Boyle's law (The pressure – volume relationship)
        For a fixed amount of gas at a constant temperature, the volume of gas is inversely proportional to the pressure of gas.
    

         At constant mass and temperature,       
                    
                 PV = k     where k = proportionality constant

        At different pressure and volume,
              P1V1 = P2V2      where P1 = initial pressure
                                               V1 = initial volume
                                               P2 = final pressure
                                               V2 = final volume

    (b) Charles’s law (The temperature – volume relationship)
         For a fixed amount of gas at constant pressure, the volume of gas is directly proportional to its absolute temperature (in Kelvin).
    
         At constant mass and pressure,
               
               V/T = k          where k = proportionality constant

         At different temperature,
                     where V1 = initial volume
                                                       T1 = initial temperature
                                                       V2 = final volume
                                                       T2 = final temperature

     (c) Avogadro’s law (The volume – amount relationship)
         At constant pressure and temperature, the volume of gas is directly proportional to the number of moles of the gas present.
         At constant pressure and temperature,
                 
                V/n = k           where k = proportionality constant

             
  
         At standard temperature and pressure (STP),
                1 mol of any gas occupies a volume of 22.4 L

2. Graphs of Gas laws
    (a) Boyle's law
  
   

    (b)  Charles's law
   
  
 
3. Combined gas law (Combination of Boyle's and Charles's law)
    At constant mass,
          where P1 = initial pressure
                                                             V1 = initial volume                   
                                                             T1 = initial temperature
                                                             P2 = final pressure
                                                             V2 = final volume
                                                             T2 = final temperature

4. Ideal gas equation (Combination of Boyle's, Charles's and Avogadro's law)
 
      
     
    
     where R = 0.08206 L atm mol^-1 K^-1 @ 8.314 J mol^-1 K^-1

 5. Determination of molar mass and density using ideal gas equation