Dalton's law

DALTON’S LAW

Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting ideal gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.

KINETIC THEORY OF GASES

• Assumptions or postulates of the kinetic molecular theory of gases are given below.
  • Gases consist of large number of identical particles (atoms or molecules) that are so small and so far apart on the average that the actual volume of the molecules is negligible in comparison to the empty space between them
  • There is no force of attraction or repulsion  between the particles of a gas
  • Particles of a gas are always in constant and random motion.
  • Collisions of gas molecules are perfectly elastic.
  • At any particular time, different particles in the gas have different speeds and hence different kinetic energies

We can derive from kinetic theory they of gases

A gas molecule has velocity v and can be broken into thro components v_x, v_y and v_z.

Travelling in x-axis momentum = mv_x change in momentum after collision = - 2mv_x. If gone back of comes back after time ‘t’ 

                  

No. of collies is one second     

Change in momentum per second     

Change in momentum on all three axis   

   

     

               

For one mole of gas n = N and  m x N = M (Mol. Wt.)

  

     

Kinetic Energy    for one mole gas n = N and PV = RT

   

  

  

So kinetic energy, depends only on temperature

For one molecules    

k = Boltzman constant

  

 

m = mass of gas particle

 n = no. of gas particle

V_rms = root mean square velocity

PV =        m. n. V²_rms 

K.E. =    RT     for one mole of gas

K.E. =    kT      for one molecule where

    k = Boltzman constant =

MAXWELL’S DISTRIBUTION OF SPEED AT DIFFERENT TEMPERATURE

MAXWELL’S DISTRIBUTION OF SPEED FOR DIFFERENT GASES

DIFFERENT VELOCITIES FOR GASES

1. The first typical velocity is the easiest to calculate and termed as the most probable velocity V_MP. The velocity at the top of the curve is the most probable velocity as the largest number of molecules have this velocity.
2. Average velocity of gas is simply the mean of all gas speeds possessed by all gas particles.    
3. Root mean square velocity is the square root of the mean of velocity squares V_RMS =

   DIFFERENT VELOCITIES FOR GASES

    

    

    

   IMPORTANT SHORTCUT

   V_rms: V_avg: V_MP = 1.224 :1.128:1 and = 1: 0.92 :0.816

DIFFUSION OF GASES

DIFFUSION VS. EFFUSION

Diffusion- The tendency of the molecules of a given substance to move from regions of higher concentration to regions of lower concentration.

Examples: A sent spreading throughout a room or people entering a theme park.

Effusion: The process by which gas particles under pressure pass through a tiny hole.

Example: Air slowly leaking out of a tire or helium leaking out of a balloon.

Graham’s law of diffusion  when pressure is same.

Graham’s law of diffusionr   when pressure is also different