Dissociation (chemistry) - Gases

Gases

The degree of dissociation in gases is denoted by the symbol α where α refers to the percentage of gas molecules which dissociate. Various relationships between K_p and α exist depending on the stoichiometry of the equation. The example of dinitrogen tetroxide (N₂O₄) dissociating to nitrogen dioxide (NO₂) will be taken.

N₂O₄ 2NO₂

If the initial concentration of dinitrogen tetroxide is 1 mole per litre, this will decrease by α at equilibrium giving, by stoichiometry, 2α moles of NO₂. The equilibrium constant (in terms of pressure) is given by the equation;

Where p represents the partial pressure. Hence, through the definition of partial pressure and using p_T to represent the total pressure and x to represent the mole fraction;

The total number of moles at equilibrium is (1-α)+(2α) which is equivalent to 1+α. Thus, substituting the mole fractions with actual values in term of alpha and simplifying;

This equation is in accordance with Le Chatelier's Principle. K_p will remain constant with temperature. The addition of pressure to the system will increase the value of p_T so α must decrease to keep K_p constant. In fact, increasing the pressure of the equilibrium favours a shift to the left favouring the formation of dinitrogen tetroxide (as on this side of the equilibrium there is less pressure since pressure is proportional to number of moles) hence decreasing the extent of dissociation α.