Calculate the value of k p for the equation c ( s ) + co 2 ( g ) − ⇀ ↽ − 2 co ( g ) k p = ? given that at a certain temperature c ( s ) + 2 h 2 o ( g ) − ⇀ ↽ − co 2 ( g ) + 2 h 2 ( g ) k p 1 = 3.79 a t m h 2 ( g ) + co 2 ( g ) − ⇀ ↽ − h 2 o ( g ) + co ( g ) k p 2 = 0.601

Kp = 1.37

Explanation:

In order to do this, we need to apply the Hess's law which it states:

"The heat of any reaction  ΔHf°  for a specific reaction is equal to the sum of the heats of reaction for any set of reactions which in sum are equivalent to the overall reaction"

Now, here we don't have data for enthalpy but we do have Kp, so the principle is applied similarly, even is we have Kp.

First thing we should do is to get the overall reaction needed which is the following:

C(s) + CO2(g) <> 2CO(g)   (3)

To get to this reaction, we just need to sum the other two reactions, and multiply coefficients if it's needed so:

C(s) + 2H2O(g) <> CO2(g) + 2H2(g)   Kp1 = 3.79    (1)

H2(g) + CO2(g) <> H2O(g) + CO(g)    Kp2 = 0.601   (2)

Now, in order to get equation (3), let's look at equations 1 and 2. As we can see, in both equations we have molecules of H2 and water, which aren't present in the overall reaction 3, so we need to get rid of them. In order to do so, if look carefully, you'll see that if you substract molecule of H2 from 1 and from 2, you still have traces of H2 (Because 2H2 - H2 = H2), so, how can we equal both of the molecules?.

That's right, we need to multiply the coefficient of that molecule to equal the coefficient of reaction 1. However keep in mind, that doing so, it will multiply the coefficients of the other molecules too. So doing that we have:

2H2(g) + 2CO2(g) <> 2H2O(g) + 2CO(g)    Kp = (0.601)²

Now, by multiplying the coefficients of the reaction, it also affects the value of Kp; remember that Kp is a value that you can obtain by doing this:

Kp = P(products) / P(reactants)

If we modify the coefficients by two, Kp is altered:

Kp = P(prod)² / P(react)²

That is why we elevated the value of Kp. Now, summing both equation 2 and 4 we have:

C(s) + 2H2O(g) <> CO2(g) + 2H2(g)   Kp1 = 3.79

2H2(g) + 2CO2(g) <> 2H2O(g) + 2CO(g)    Kp = (0.601)²

C(s) + CO2(g) <> 2CO(g)   (3)

Now the value of Kp will be:

Kp = 3.79 x (0.601)² = 1.37