7.23 At 1127 K and 1 atm pressure, a gaseous mixture of CO and CO2 in equilibrium with soild carbon has 90.55% CO by mass

C (s) + CO2 (g) 2CO (g)

Calculate Kc for this reaction at the above temperature.

Let the total mass of the gaseous mixture be 100 g.
Mass of CO = 90.55 g
And, mass of CO2= (100 – 90.55) = 9.45 g

Now, the number of moles of COnco=90.5528=3.234 mol

 Number of moles of CO2, nco2=9.4544=0.215 mol

The partial pressure of CO, 

 

   pco=nconco+nco2×ptotal          =3.2343.234+0.215×1          =0.938 atm  

The partial pressure of CO2,

 

     pco2=nco2nco+nco2×ptotal                         =0.2153.234+0.215×1                        =0.062 atm                          

Therefore Kp=

=CO2CO2 =0.93820.062      =14.19                        

For the given reaction,

n=2-1=1We know that,Kp=KcRTn14.19=Kc0.082×11271Kc=14.190.082×1127=0.154approx.