what is the numerical value of the equilibrium constant Kgoal for the reaction CO2(g) C(s) +O2(g)? by making use of the following information:
1. 2CO2(g)+2H2O(I) = CH3COOH(I)+2O2(g), K1=5.40x10^-16.
2. 2H2(g)+O2(g) = 2H2O(I), K2=1.06x10^10.
3. CH3COOH(I) - 2C(s)+2H2(g+O2(g), K3=2.68x10^-9.
Express answer numrically.
I came up with 1.24^-7, but it is incorrect.
I asked the last time you posted this what Kgoal stood for and I received no answer. That COULD BE why the answer is not working out.
Keq = sqrt(k1k2k3) = 1.24E-7 but whether that is Kgoal or not I don't know?
To find the numerical value of the equilibrium constant (Kgoal) for the reaction CO2(g) + C(s) + O2(g), we can use the given information and apply the principles of equilibrium constants.
First, let's analyze the given reactions and their equilibrium constants:
1. 2CO2(g) + 2H2O(I) = CH3COOH(I) + 2O2(g), K1 = 5.40x10^-16
2. 2H2(g) + O2(g) = 2H2O(I), K2 = 1.06x10^10
3. CH3COOH(I) = 2C(s) + 2H2(g) + O2(g), K3 = 2.68x10^-9
The goal reaction is given by the equation:
CO2(g) + C(s) + O2(g)
To find the value of Kgoal, we can combine the given reactions using their equilibrium constants. Since the goal reaction is the sum of the three given reactions, we can multiply the reactions by the appropriate stoichiometric coefficients before combining them.
Here's the combined reaction:
2CO2(g) + 2H2O(I) + 2H2(g) + O2(g) = CH3COOH(I) + 2O2(g) + 2C(s) + 2H2(g) + O2(g)
Now, we can cancel out the common terms that appear on both sides of the equation:
2CO2(g) + 2H2O(I) + 2H2(g) + O2(g) = CH3COOH(I) + 4O2(g) + 2C(s) + 2H2(g)
Simplifying further:
2CO2(g) + 2H2O(I) + O2(g) = CH3COOH(I) + 2O2(g) + 2C(s)
Now, we can express this equation in terms of the stoichiometric coefficients of the goal reaction:
2CO2(g) = 2C(s) + 2O2(g)
Comparing this equation with the goal reaction, we can see that their stoichiometric coefficients are the same, which means the equilibrium constant for the goal reaction is equal to the product of the equilibrium constants for reactions 1, 2, and 3 (K1 * K2 * K3):
Kgoal = K1 * K2 * K3
= (5.40x10^-16) * (1.06x10^10) * (2.68x10^-9)
Now, we can calculate the value of Kgoal:
Kgoal = 1.53024x10^-14
Therefore, the numerical value of the equilibrium constant (Kgoal) for the given reaction is approximately 1.53024x10^-14.
To find the numerical value of the equilibrium constant (K_goal) for the reaction CO2(g) ⇌ C(s) + O2(g), we can use a combination of the given equilibrium constants (K1, K2, K3) and the concept of equilibrium constant expressions.
First, let's write the balanced chemical equation for the reaction:
2CO2(g) ⇌ C(s) + O2(g)
We can express the equilibrium constant (K_goal) in terms of the given equilibrium constants (K1, K2, K3) using the concept of equilibrium constant expressions and the principle of multiplying or dividing equations:
K_goal = (K2 × K3) / K1
Using the given values, we have:
K_goal = (1.06x10^10 × 2.68x10^-9) / 5.40x10^-16
To solve this mathematically, we can multiply the numerator and divide by the denominator:
K_goal = (1.06x2.68x10^10) / (5.40x10^-16)
Calculating this expression, we get:
K_goal ≈ 5.257x10^16
Therefore, the numerical value of the equilibrium constant (K_goal) for the reaction CO2(g) ⇌ C(s) + O2(g) is approximately 5.257x10^16.