ESSENCE OF CHEMICAL PROCESS ENGINEERING I - EXERCISE 2

 EXERCISE 2

A mixture of 2 mol of CO and 3 mol of O₂ is heated to 2600K at a pressure of 2 atm. Determine the equilibrium composition, assuming the mixture consists of CO₂, CO and O₂.

 

CO + 0.5O₂ = CO₂             : ln K = 2.801 (at 2600K)

 

Solutions

A reactive gas mixture is heated to a high temperature. The equilibrium composition at that temperature is to be determined.

Assumptions

1.     The equilibrium composition consists of CO₂, CO, and O₂

2.     The constituents of the mixture are ideal gases

Analysis

The stoichiometric and actual reactions in this case are as follows:

Stoichiometric:      CO      +     1/2O₂     ->      CO₂   (thus vco2 =1, vco = 1, vo2 = 1/2)

Actual:          2CO    +         3O₂     ->        xCO₂              +            yCO             +         zO₂

                                                                    product              reactants (leftover)

C balance:                2 = x   +    y                                     or        y = 2    -    x

O balance:                8 = 2x   +    y     +     2z               or        z = 3    -    x/2

Total number of moles:             N_{total    =}             x   +    y     +     z     =    5    -    x/2

Pressure:                 P  = 2 atm

ln K_p  =         2.801

K_p       =         16.461

 

x   =     1.886

                        y          =   2 - x            =     0.114

                z      =     3 - x/2      =     2.057

The equilibrium composition 

1.886CO₂    +    0.114CO     +    2.057O₂