Calculate K at 298 K for the following reactions.
NO(g) + 1/2 O2(g)......> NO2(g)
Nog 86.60
No2 g 51
o2.... O
I got 6.81 x 10^-7........thank you.
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To calculate the equilibrium constant (K) at 298 K for the given reaction:
NO(g) + 1/2 O2(g) → NO2(g)
First, you need the equilibrium concentrations of the reactants and products. From the information provided, we have:
[NO] = 86.60
[NO2] = 51
[O2] = ?
However, the concentration of O2 is not given. So we cannot directly calculate K without knowing the concentration of O2.
Please provide the concentration of O2 to proceed with the calculation.
To calculate the equilibrium constant (K) at a given temperature, we need to use the concentrations of the reactants and products.
Given that the initial concentration of NO is 86.60 M, NO2 is 51 M, and O2 is not given, we can assume that it is zero since it is not mentioned.
The balanced equation for the reaction is:
NO(g) + 1/2 O2(g) → NO2(g)
To calculate K, we need to determine the concentrations of the reactants and products at equilibrium. The equation shows that the coefficient of NO is 1, NO2 is 1, and O2 is 1/2.
Let's denote the change in concentration for each species as:
Δ[NO] = [NO]equilibrium - [NO]initial
Δ[NO2] = [NO2]equilibrium - [NO2]initial
Δ[O2] = [O2]equilibrium - [O2]initial
Since O2 concentration is assumed to be zero initially and the reaction consumes NO and produces NO2, we have:
Δ[NO] = -[NO]initial
Δ[NO2] = [NO2]equilibrium - [NO2]initial
Δ[O2] = [O2]equilibrium - 0
Let's assume that at equilibrium, the concentration of NO is x M and the concentration of NO2 is y M.
Using the relationship between initial concentration, change, and equilibrium concentration, we can write:
[NO]equilibrium = [NO]initial - Δ[NO] = [NO]initial - (-[NO]initial) = 2[NO]initial
[NO2]equilibrium = [NO2]initial + Δ[NO2] = [NO2]initial + y
[O2]equilibrium = Δ[O2] = y/2
Now, we can write the expression for K in terms of the equilibrium concentrations:
K = ([NO2]equilibrium) / ([NO]equilibrium * [O2]equilibrium)
= ([NO2]initial + y) / ((2[NO]initial) * (y/2))
= (51 + y) / (2 * 86.60 * (y/2))
= (51 + y) / (86.60 * y)
Now, we need to solve for y. We can substitute the given value of [NO2]initial = 51 M into the equation:
6.81 x 10^-7 = (51 + y) / (86.60 * y)
Cross-multiplying:
6.81 x 10^-7 * (86.60 * y) = 51 + y
Dividing both sides by (86.60 * y):
6.81 x 10^-7 = (51 + y) / (86.60 * y)
[6.81 x 10^-7 / (86.60 * y)] = (51 + y) / (86.60 * y)
Now, we solve for y using a numerical method or a graphing calculator.
Finally, once we have the value of y, we can substitute it into the equation for K to calculate the equilibrium constant at 298 K.