1.) What are the equilibrium partial pressures of CO and CO2 if co is the gas present initially, at a partial pressure of .912 atm. Kp = 19.9
Fe2O3 + 3CO <--> 2Fe + 3CO2
I'm trying to find partial pressure of both CO and CO2 by calculating for "x" in the equilibrium problem
Good. What you have done makes sense. Where are you stuck? Post your work and let me take a look. If you are stumped by the "cubic" equation, just take the cube root of both sides and that will leave a linear equation to solve which is easy enough.
To solve for the equilibrium partial pressures of CO and CO2 in the given reaction, we can use the stoichiometric coefficients and the equilibrium constant (Kp) to set up an ICE table.
The balanced equation for the reaction is:
Fe2O3 + 3CO ⇌ 2Fe + 3CO2
Let's assume that at equilibrium, the partial pressure of CO is represented by x. Since there are 3 moles of CO involved in the reaction, the partial pressure of CO2 at equilibrium would be represented by 3x, according to the stoichiometry.
Using the information given, we know that the initial partial pressure of CO is 0.912 atm, and the equilibrium constant (Kp) is 19.9.
Now, let's set up the ICE table:
Fe2O3 + 3CO ⇌ 2Fe + 3CO2
Initial: - 0.912 0 0
Change: - -3x +2x +3x
Equilibrium: - 0.912-3x 2x 3x
According to the stoichiometry, the equilibrium concentrations of Fe2O3 and Fe are not directly dependent on the partial pressure of CO, so we will not consider them in this calculation.
We can use the expression for Kp to relate the equilibrium partial pressures:
Kp = (PFe * PCO2^3)/(PCO^3 * PFe2O3)
Substituting the values into the equation:
19.9 = (2x * (3x)^3)/(x^3 * (0.912-3x))
Simplifying and rearranging the equation:
19.9 = 2x * 27x^3 / (0.912-3x)^3
Now, you can solve this equation for "x" using algebraic methods such as factoring, expanding, or quadratic formula. Once you find the value of "x", you can substitute it back into the equilibrium expressions for the partial pressures of CO and CO2 to get the final values.
To find the equilibrium partial pressures of CO and CO2, we can set up an ICE table and use the given equilibrium constant (Kp) to calculate the unknown partial pressures.
Step 1: Set up the ICE table:
Fe2O3 + 3CO <--> 2Fe + 3CO2
Initial (atm): 0.912 0 0 0
Change (x atm): -x +3x +2x +3x
Equilibrium (atm): 0.912-x 3x 2x 3x
Step 2: Write the expression for the equilibrium constant (Kp):
Kp = (P(Fe)^2 x P(CO2)^3) / (P(Fe2O3) x P(CO)^3)
Given: Kp = 19.9
Step 3: Substitute the equilibrium pressures into the equilibrium constant expression and solve for x:
19.9 = (2x^3) / [(0.912-x)(3x)^3]
Step 4: Simplify and solve the equation:
19.9 = (2x^3)/(0.912-x) / (27x^4)
Simplify further:
19.9 = 2x^3 / (27x^4)(0.912 - x)
19.9 = 2/(27x)(0.912 - x)
Now, you can solve this equation for 'x' using algebraic techniques.