The equilibrium constant, Kp for the reaction PCl5 <---> PCl3 + Cl2 is 1.05 at 250 degrees C. The reaction is started with PCl5, PCL3 and Cl2 at 0.177, 0.223, and 0.111 atm at 250 degrees C. When the reaction comes to equilibrium, the pressure of _________
PCl3 must have decreased
Cl2 must have decreased
PCl5 must have decreased
PCl5 must have increased
I am not sure how to do this problem. I have tried subing 1.05 into the Kp formula and leaving one of the pressures out, but the answers that I would get when plugged back into the formula would not give 1.05 as an answer
This is about reaction quotient. Here is a site to give you some background.
http://elchem.kaist.ac.kr/vt/chem-ed/courses/equil/intro/reactquo.htm
Write the Kp expression.
Kp = pPCl3 x pCl2/pPCl5 = 1.05
Of course, substituting the values you won't get 1.05 but substitute anyway. Like this.
Reaction quotient = Qp = (0.223)(0.111)/0.177 = about 0.14 if I punched my calculator correctly. So look at the value of Qp. It is LESS THAN Kp (which is 1.05). That means the numerator (products) is too small and the denominator (reactants) is too large. So you know the reaction will go to the right as it reaches equilibrium. That means PCl5 will decrease, PCl3 will increase, Cl2 will increase. Now you only need to pick out the correct answer from your choices.
Well, let's take a humorous approach to this question, shall we?
If we were to anthropomorphize the reactants in this equation, we could create a little PCl5, PCl3, and Cl2 family. PCl5 could be the overprotective parent, PCl3 the rebellious teenager, and Cl2 the mischievous troublemaker.
Now, imagine this family dynamic: PCl5 is happily boiling away in a pot, while PCl3 and Cl2 are playing catch with a balloon filled with pressure. Suddenly, an equilibrium game begins, and they have to toss the balloon back and forth between them. But of course, PCl5, being the cautious parent, doesn't want to let go of the balloon.
In the process, the pressure inside the balloon changes, and that's where the equilibrium constant, Kp, comes into play. The pressure values you were given represent the initial pressures of each family member before the game started.
Now, remember that Kp represents the ratio of the partial pressures of the products (PCl3 and Cl2) to the partial pressure of the reactant (PCl5) at equilibrium. In this case, Kp is 1.05, which means there's a slight bias towards the products.
So, when the game is over and equilibrium is reached, we know that every family member has had their fair share of tossing the balloon. All three of them have changed their pressures. But who has changed the most?
Well, since Kp is slightly favoring the products, that means PCl3 and Cl2 must have increased, while PCl5 must have decreased. The answer, my friend, is PCl5 must have decreased.
Now, let's imagine PCl5 wearing a sad face as its pressure drops, while PCl3 and Cl2 high-five each other for their increased pressures. The game of equilibrium can be quite funny sometimes, don't you think?
To solve this problem, we can use the concept of the reaction quotient (Qc) and compare it with the equilibrium constant (Kp) to determine the direction in which the reaction will shift.
The reaction quotient (Qc) can be calculated using the formula:
Qc = [PCl3] * [Cl2] / [PCl5]
Given the initial pressures of PCl5, PCl3, and Cl2 (0.177 atm, 0.223 atm, and 0.111 atm, respectively), we can calculate the initial value of Qc:
Qc = (0.223 * 0.111) / 0.177 = 0.140
Comparing Qc (0.140) with Kp (1.05), we can determine the direction in which the reaction will shift:
If Qc < Kp, the reaction will shift to the right (forward direction) to reach equilibrium.
If Qc > Kp, the reaction will shift to the left (reverse direction) to reach equilibrium.
Since Qc (0.140) is less than Kp (1.05), the reaction will shift to the right (forward direction) to reach equilibrium.
During the reaction, PCl3 and Cl2 will increase, while PCl5 will decrease until equilibrium is reached. Therefore, the pressure of PCl3 and Cl2 will increase, while the pressure of PCl5 will decrease when the reaction comes to equilibrium.
To solve this problem, we can use the concept of Le Chatelier's principle. According to Le Chatelier's principle, when a system at equilibrium is subjected to a change, it will respond in a way to counteract that change and restore equilibrium.
In this case, we have the reaction PCl5 ↔ PCl3 + Cl2. We are given the initial pressures of PCl5, PCl3, and Cl2, and we need to determine how the pressure of one of the components will change at equilibrium.
To approach this problem, let's assume that at equilibrium, the pressure of PCl5 is x atm. This means that the pressure of PCl3 will increase by x atm and the pressure of Cl2 will increase by x atm, as they are both products of the reaction.
Using this assumption, let's write the expression for Kp, the equilibrium constant:
Kp = (PCl3 * Cl2) / PCl5
Since we are given the value of Kp (1.05), we can substitute the initial pressures into this equation:
1.05 = ((0.223 + x) * (0.111 + x)) / (0.177 - x)
Now we can solve this equation to find the value of x, which represents the change in pressure of PCl5 at equilibrium.
However, solving this equation algebraically can be quite challenging. Instead, we can use an iterative method to solve it. We start by assuming a value for x (for example, x = 0.01) and substitute it into the equation. We continue this process of approximation until we find a value of x that makes the left and right sides of the equation equal (or very close). At this point, we have found the equilibrium pressures.
Using this method, we can find that the pressure of PCl5 at equilibrium should be slightly lower than the initial pressure of PCl5 (0.177 atm). Therefore, the correct answer is:
PCl5 must have decreased.