Will equilibrium constant for the reaction change IF I write the equation 2SO2+O2 = 2SO3 in the form SO2+1/2O2 = SO3 ?

Question

Does the value of Kp change IF I change stoichiometric coefficients, e.g. halve them? For example, if I write SO2+ 1/2 O2 = SO3 instead of 2SO2 + O2 = 2SO3? (sorry I couldn't find the reversibilitu sign).

Answer 1

Not sure Lauren and I are reading the question the same.  The way I understand the question, my answer would be "yes", the value of the Kp would change.  Look at the following:

 

2SO₂ + O₂ <==> 2SO₃;  K_p = (SO₃)²/((SO₂)²(O²)

 

SO₂ + 1/2O₂ <==> SO₃;  K_p = (SO₃)/(SO₂)(O2)^1/2

 

In the second equation where you divided by 2, the right side of the K_p equation is essentially the square root of the right side of the equation of the first equation.  Thus, the Kp would have to be the square root also,  You can prove this yourself by using an example.

 

At equilibrium, say the pressures are as follows:

SO₂ = 0.48

O₂ = 0.40

SO₃ = 1.12

Plug the values in and see what you get for K_p. 

Bottom line:  If you manipulate or change the coefficients of the balanced reaction, the K_p or K_c must be changed in the same manner. If you divide by 2, you need to take the square root of the K, and if you multiply by 2, you need to square the K

Answer 2

Nope.  Equilibrium is the ratio of the product/s concentration/s(to the appropriate power) to the reactant/s concentration/s (to the appropriate power).  So, it's not dependent on how you write the balanced chemical equation.