Question

Determine the value of the equilibrium constant, Kgoal, for the reaction

CO2(g)?C(s)+O2(g), Kgoal=?

by making use of the following information:

1. 2CO2(g)+2H2O(l)?CH3COOH(l)+2O2(g), K1=5.40

Answer 1

Look at the K goal reaction: we want one mole of CO2 on the left. The only place that CO2 appears is in reaction 1, but there are 2 moles CO2 on the left. Multiply eqn. 1 by 1/2. The new K1' = square root (K1) = square root (5.40 x 10^-16) = 2.32 x 10^-8.

eqn. 1' : CO2 + H2O ==> 1/2 CH3COOH + O2 . . . . .K1' = 2.32 x 10^-8

Note that in the K goal equation there is one C on the right. The only place C appears is in eqn. 3, but there are 2 moles of C there. Like eqn. 1, multiply eqn. 3 by 1/2 and K3' = square root (K3) = square root (2.68 x 10^-9) = 5.18 x 10^-5

eqn. 3': 1/2 CH3COOH ==> C + H2 + 1/2 O2 . . . . .K3' = 5.18 x 10^-5

Add K1' and K3' together to get eqn. 4. K4 = K1' x K3' = (2.32 x 10^-8)(5.18 x 10^-5) = 1.20 x 10^-12

eqn 4: eqn 1' === CO2 + H2O ==> 1/2 CH3COOH + O2
. . . +eqn 3' === 1/2 CH3COOH ==> C + H2 + 1/2 O2
======================================...
= eqn 4 === CO2 + H2O ==> C + H2 + 3/2 O2 . . .K4 = 1.20 x 10^-12

The only difference between eqn. 4 and the K goal eqn. is that we need to subtract H2O from the left and H2 and 1/2 O2 on the right. Take 1/2 of eqn. 2. K2' = square root K2 = square root (1.06 x 10^10) = 1.03 x 10^5.

eqn. 2' = H2 + 1/2 O2 ==> H2O

add eqn. 2' to eqn 4.

. . .eqn. 2' === H2 + 1/2 O2 ==> H2O
. .+eqn 4 === CO2 + H2O ==> C + H2 + 3/2 O2
====================================
. = eqn K goal === CO2 ==> C + O2

K goal = K4 x K2' = (1.20 x 10^-12)(1.03 x 10^5) = 1,24 x 10^-7

Answer 2

2CO2(g) + 2H2O-------------> CH3COOH(l) + 2O2(g) ; K1 = 5.4*10^-16................(1)

2H2(g) + O2(g) -------------> 2H2O(l) ; K2 = 1.06*10^-10.............(2)

CH3COOH(l) ---------------> C(s) + 2H2(g) + O2(g) ; K3 = 2.68*10^-9..............(3)

now the required reaction can be obtained by {(1) +(3) -(2)}/2

thus, Kgoal = {(5.4*10^-16)*(2.68*10^-9)}/2*(1.06*10^-10)

thus, Kgoal = 6.83*10^-15

Answer 3

sqrt(k1*k2*k3)=12.38 *10^(-8)