At 472 deg C the reaction reaches equilibrium with the following composition: [H2]=7.38atm, [N2]=2.46atm, [NH3]=0.166atm. Into the equilibrium mixture 1.5 atm of N2 is introduced:
a. Calculating Kp and Q, determine in which direction the reaction will proceed after addition of N2 and explain why?
b. Using an ICE chart, show the relationship between the initial conditions (after addition of N2), changes in partial pressures of each constituent. Do not solve for actual values but leave the ICE chart in terms of variables. (Hint: let y=partial pressure of N2 that reacts in the ICE chart.
c. Using the expression for Kp and the values in the ICE chart develop the equation which would allow to solve for the equilibrium concentrations.
d. Using the iterative technique, solve the equation and determine the equilibrium partial pressures of all constituents. Use +/- 5.0% of Kp as your criteria for “equality”
a. To determine in which direction the reaction will proceed after the addition of N2, we need to compare the calculated Q (reaction quotient) with the Kp (equilibrium constant).
1. Calculating Kp:
The equilibrium constant expression for the reaction is:
Kp = ([NH3]^2) / ([H2] ^ 3 * [N2])
Using the given equilibrium composition:
[H2] = 7.38 atm
[N2] = 2.46 atm
[NH3] = 0.166 atm
Substituting these values into the equilibrium constant expression:
Kp = (0.166^2) / (7.38^3 * 2.46)
Kp = 0.001148 (approximately)
2. Calculating Q:
After the addition of 1.5 atm of N2, the new concentration of N2 becomes:
[N2] = 2.46 atm + 1.5 atm = 3.96 atm
Using the equilibrium composition and the new concentration of N2, we can calculate Q:
Q = ([NH3]^2) / ([H2] ^ 3 * [N2])
Q = (0.166^2) / (7.38^3 * 3.96)
Q = 0.00003442 (approximately)
Now, comparing Q and Kp:
Q < Kp
Since Q is smaller than Kp, it means that the reaction is not yet at equilibrium. The reaction will proceed in the forward direction to reach equilibrium.
b. Using an ICE (Initial, Change, Equilibrium) chart, we can show the relationship between the initial conditions and the changes in partial pressures of each constituent. Let's assume x is the amount of N2 that reacts (in atm):
Initial:
[H2] = 7.38 atm
[N2] = 3.96 atm (initial 2.46 atm + added 1.5 atm)
[NH3] = 0.166 atm
Change:
[H2] decreases by 3x
[N2] decreases by x
[NH3] increases by 2x
Equilibrium:
[H2] = 7.38 - 3x
[N2] = 3.96 - x
[NH3] = 0.166 + 2x
c. Using the expression for Kp and the values in the ICE chart, we can develop the equation that allows us to solve for the equilibrium concentrations:
Kp = ([NH3]^2) / ([H2] ^ 3 * [N2])
Kp = (0.166 + 2x)^2 / (7.38 - 3x)^3 * (3.96 - x)
d. To solve the equation for the equilibrium partial pressures, using the iterative technique is often necessary. Here's a general outline of how to approach it:
1. Start with an initial guess for x (e.g., x = 0).
2. Calculate the value of Kp using the equation developed in step c.
3. Compare the calculated Kp with the given Kp.
4. If the calculated Kp is within +/- 5.0% of the given Kp, stop and proceed to the next step. Otherwise, adjust the initial guess for x and repeat steps 2-4.
5. Once the calculated Kp is within the desired range, substitute the value of x into the ICE chart equations to calculate the equilibrium partial pressures of all constituents ([H2], [N2], and [NH3]).
Continue adjusting the initial guess for x and repeating steps 2-5 until the calculated Kp is within the desired range. At that point, the equilibrium partial pressures of all constituents can be determined.