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'
Kc' will be the square root of Kc
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The equilibrium constants Kc and Kc' are related by the stoichiometric coefficients of the balanced chemical equation. In the given equation:
2CO(g) + O2 ⇌ 2CO2
The equilibrium constant Kc is defined as:
Kc = [CO2]^2 / ([CO]^2 * [O2])
Now, if we rewrite the equation as:
CO + 1/2O2 ⇌ CO2
The equilibrium constant Kc' is defined as:
Kc' = [CO2] / ([CO] * [O2]^1/2)
To find the relationship between Kc and Kc', we can manipulate the equations:
Kc' = [CO2] / ([CO] * [O2]^1/2)
= [CO2]^2 / ([CO] * [O2])
By comparing the two equations, we can see that Kc' is equal to Kc squared:
Kc' = Kc^2
Therefore, the relationship between Kc and Kc' is that Kc' is equal to Kc squared.
To determine the relationship between Kc and Kc' for the given reaction, we need to understand how equilibrium constants change when the equation is multiplied or divided by a coefficient.
Given the reaction: 2CO(g) + O2 ⇌ 2CO2
The equilibrium constant Kc is defined as the ratio of the products' concentrations raised to their coefficients divided by the reactants' concentrations raised to their coefficients:
Kc = ([CO2]² / [CO]² [O2])
Now, let's rewrite the equation as: CO + 1/2O2 ⇌ CO2
The equilibrium constant for this new equation is denoted as Kc', and it is determined in the same way:
Kc' = ([CO2] / [CO] [O2]^(1/2))
To find the relationship between Kc and Kc', we can examine the coefficients and determine how they affect the equilibrium constant:
In the first equation: 2CO(g) + O2 ⇌ 2CO2
The coefficients are 2, 1, and 2.
In the second equation: CO + 1/2O2 ⇌ CO2
The coefficients are 1, 1/2, and 1.
If we compare the two coefficient sets, we can see that the second equation's coefficients are half the values of the first equation's coefficients. As a result, dividing every coefficient in the first equation by 2 gives us the coefficients in the second equation.
By multiplying the coefficients in the first equation by 2, we can essentially transform it into the second equation:
2CO(g) + O2 ⇌ 2CO2 can be transformed to CO + 1/2O2 ⇌ CO2
The equilibrium constant is not altered when the reaction equation is multiplied or divided by a coefficient. Hence, Kc and Kc' are equal:
Kc = Kc'
In summary, the relationship between Kc and Kc' is that they are equal.