For the reaction 2CO(g)+O2 《=》2CO2 with equilibrium constant Kc. Suppose the equation is rewritten as CO + 1/2O2 《=》CO2 with an equilibrium constant Kc'.what is the relationship between Kc and Kc'

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To determine the relationship between Kc and Kc' for the given reaction, we need to evaluate the effect of the equation rewrite on the equilibrium constant.

Let's start with the original equilibrium expression for the reaction:

Kc = [CO2]^2 / ([CO]^2 * [O2])

Now, consider the rewritten equation by halving the coefficients:

CO + 1/2O2 《=》 CO2

The equilibrium expression for the rewritten equation will be:

Kc' = [CO2] / ([CO] * [O2]^(1/2))

To find the relationship between Kc and Kc', we can divide the two equations:

Kc' / Kc = ([CO2] / ([CO] * [O2]^(1/2))) / ([CO2]^2 / ([CO]^2 * [O2]))

Simplifying the expression:

Kc' / Kc = ([CO2] * [CO]^2 * [O2]) / ([CO2]^2 * [CO] * [O2]^(1/2))

Now, let's examine the components of this expression. Notice that [CO2] and [O2] are present in both the numerator and denominator, so they cancel out:

Kc' / Kc = ([CO] * [O2]^(1/2)) / [CO2]

Finally, recalling the original reaction equation, we know that [O2]^1/2 is equal to [O2], since [O2] raised to the power of 1/2 is the same as [O2].

Therefore, we can simplify the expression further:

Kc' / Kc = [CO] / [CO2]

In conclusion, the relationship between Kc and Kc' for the rewritten equation CO + 1/2O2 《=》 CO2 is Kc' / Kc = [CO] / [CO2].

Please note that this relationship is specific to the rewritten equation; it may differ for other reactions.

The relationship between Kc and Kc' can be determined by the stoichiometric coefficients in the balanced equation.

In the given reaction, 2CO(g) + O2 ⇌ 2CO2, the equilibrium constant Kc is defined as [CO2]^2 / [CO]^2 x [O2].

When the equation is rewritten as CO + 1/2O2 ⇌ CO2, the new equilibrium constant Kc' is defined as [CO2] / [CO] x [O2]^(1/2).

By comparing the two equilibrium expressions, we can see that Kc' can be obtained from Kc by taking the square root of Kc.

Therefore, the relationship between Kc' and Kc is Kc' = √Kc.