Question

Consider the synthesis of CH2O:   CO(g)+H2(g)->CH2O(g).          

At 25^o C, this reaction is accompanied by the change of  G^0=6.5 kcal/mol and H^0=-1.3 kcal/mol.

You also know that:  CP of CH2O(g) =4.498+13.953x10^-3T - 3.730x10^-6 T^2 cal/deg mol.           

CP of H2(g) = 6.9469-0.1999x10^-3 T +4.808x10^-7 T^2 cal/deg mol           

CP of CO(g) =6.3424+1.8393x10^-3 T -2.801x10^-7 T^2 cal/deg mol       

(a) Calculate the value of Kp at 1000K assuming delta H is independent of temperature.       

(b) Calculate the value of Kp at 1000K taking into account the variation of delta H with temperature, and compare the result with that in (a).

Answer 1

Consider the synthesis of CH₂O, we have

CO (g) + H₂ (g) CH₂O (g)

At 25 ⁰C, we have

G⁰ = 6.5 kcal/mol   and   H⁰ = -1.3 kcal/mol

Given that :

CP of CH₂O (g) = [(4.498) + (13.953 x 10^-3) T - (3.730 x 10^-6) T²] cal/deg mol

CP of H₂ (g) = [(6.9469) - (0.1999 x 10^-3) T + (4.808 x 10^-7) T²] cal/deg mol           

CP of CO (g) = [(6.3424) + (1.8393 x 10^-3) T - (2.801 x 10^-7) T²] cal/deg mol   

(a) Calculate the value of K_p at 1000 K assuming H is independent of temperature.   

using a formula, we have

K_p = [x_CH2O] / [x_CO] [x_H2]

K_p = [(4.498) + (13.953 x 10^-3) T - (3.730 x 10^-6) T²] / [(6.3424) + (1.8393 x 10^-3) T - (2.801 x 10^-7) T²] [(6.9469) - (0.1999 x 10^-3) T + (4.808 x 10^-7) T²]

K_p = [(4.498) + (13.953 x 10^-3) (1000) - (3.730 x 10^-6) (1000)²] / [(6.3424) + (1.8393 x 10^-3) (1000) - (2.801 x 10^-7) (1000)²] [(6.9469) - (0.1999 x 10^-3) (1000) + (4.808 x 10^-7) (1000)²]

K_p = (14.721) / (7.9016) (7.2278)

K_p = 0.257