equilibrium constants for the following reactions
4Cu(s) + O2(g) 2Cu2O(s), K1
2CuO(s) Cu2O(s) + 1/2O2(g), K2
what is K for the system
2Cu(s) + O2(g) 2CuO(s)
?
(K1 ^(1/2)) / (K2)
K1,to the power of 1/2, over K2
To find the equilibrium constant for the given reaction:
2Cu(s) + O2(g) ↔ 2CuO(s)
We can use the equilibrium constants (K1 and K2) for the two reactions given.
Let's start by writing the equation in terms of the reactions with known equilibrium constants:
2Cu(s) + 1/2O2(g) ↔ Cu2O(s) (using reaction 1 multiplied by 2 and reversed)
2CuO(s) ↔ Cu2O(s) + 1/2O2(g) (using reaction 2)
Now, we can combine these two equations to get the desired reaction:
2Cu(s) + O2(g) ↔ 2CuO(s)
By multiplying the first equation by 2, we get:
4Cu(s) + O2(g) ↔ 2Cu2O(s)
However, this equation is not exactly the same as the given reaction. We need to reverse it, so it becomes:
2Cu2O(s) ↔ 4Cu(s) + O2(g)
Now, we can compare this new equation with the second one given to us:
2Cu2O(s) ↔ 4Cu(s) + O2(g) (using reaction 2)
We see that these two equations are the same, but with opposite directions. Therefore, the equilibrium constant for the reaction we need to find (K) is the reciprocal of K2:
K = 1/K2
So, to find K, you need to calculate the reciprocal of K2.
To calculate the equilibrium constant (K) for the given reaction:
2Cu(s) + O2(g) ⇌ 2CuO(s)
We can use the equilibria for the intermediate reactions, K1 and K2, to determine K for the overall reaction.
Since K is the product of the equilibrium constants for individual reactions, we can write:
K = K2 / K1
Substituting the given values of K1 and K2:
K = (K2) / (K1)
K = ((Cu2O)(1/2O2)) / ((Cu)^2)
K = (Cu2O * O2^(1/2)) / (Cu^2)
Therefore, K for the overall reaction 2Cu(s) + O2(g) ⇌ 2CuO(s) can be calculated using the equation above.