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The equilibrium constant $\left(K_{P}\right)$ for the reaction $\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)$ is 2.93 at $127^{\circ} \mathrm{C}$ Initially there were 2.00 moles of $\mathrm{PCl}_{3}$ and 1.00 mole of $\mathrm{Cl}_{2}$ present. Calculate the partial pressures of the gases at equilibrium if the total pressure is $2.00 \mathrm{atm}$

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$$\begin{array}{l}P_{\mathrm{PCl}_{3}}=1.11 \mathrm{atm} \\P_{\mathrm{Cl}_{2}}=0.211 \mathrm{atm} \\P_{\mathrm{PCl}_{5}}=0.683 \mathrm{atm}\end{array}$$

Chemistry 102

Chapter 14

Chemical Equilibrium

Carleton College

Rice University

Drexel University

Lectures

10:03

In thermodynamics, a state of thermodynamic equilibrium is a state in which a system is in thermal equilibrium with its surroundings. A system in thermodynamic equilibrium is in thermal equilibrium, mechanical equilibrium, electrical equilibrium, and chemical equilibrium. A system is in equilibrium when it is in thermal equilibrium with its surroundings.

00:54

In chemistry, chemical equilibrium (also known as dynamic equilibrium) is a state of chemical stability in which the concentrations of the chemical substances do not change in the course of time due to their reaction with each other in a closed system. Chemical equilibrium is an example of dynamic equilibrium, a thermodynamic concept.

01:02

For the reaction PCl(g)

03:01

For the reaction PCl_5(g) …

00:58

The equilibrium constant $…

04:06

04:58

(a) Calculate $\Delta G^{\…

So we want to find the partial pressures at equilibrium for the falling balanced chemical equation. So when we hear at equilibrium, the immediately want to think ice table. So we're gonna plug in the values that we know. You know, we have to one then no products initially because that's what we were told and from the story geometry, you know, we subtract one x tracked one x and add when exes were making product. So that means this is x one minus X and two minus x. So if we look at total moles, if we were to add all of our equilibrium columns together, we would get three minus x, and I just really want to do is find the mole fractions. So in order to find the mole fractions, let's start with our first reactant Ian to find the mole fraction What? We're going to dio this take how many moles we have over the total number of moles, and then we're gonna do the same for our second reactant. We know that is one minus X over three minus X and therefore higher product. We have next over three minus x. So once we have the mole fractions. We also confined partial pressure equations in terms of six. So if we look at that, we know partial pressure. Let's start with our product. It's going to be X over three minus X times. We always do the mole fraction times Thedc It'll pressure. And we were We were told that was to a t M. We could do the next. Were first reacted. This is I and that is two minus X over three minus x times the total pressure. And then for our final reactant, we know it is one minus X who are three minus X times to total pressure. So since we were told the KP value, we can go ahead and plug it in there. You know that KP equals 2.93 So we're going to do our whole products. Partial pressure equation. We're gonna do the same for the reactant. It's medicated in brackets, not because this concentration, but just that he tell them apart a little bit better. We have two minus x over three minus X times two and one minus X over three minus X times so we can go ahead and simplify this a little bit. Try polio exes in crossing out any to the total pressures that we can. And when the bottom we're going to see we have you like this tu minus x one minus x But then that last remaining total pressure value and then we can simplify this further. It saves in time. I'm going to give you the X value that when we calculated out, you should get 0.7 64 So now that we have the X value the remaining opponents to find the partial pressure, it's very easy. So we're looking at the partial pressure. Ah, key c l five partial pressure of P c 03 And now that more partial pressure of P. C. L. And just to make thistle more clear, thes Arthuis partial pressures of thes So an extra PT just that we can see that this is partial pressure And this was there partial pressure original equations in terms of X. So now we're going to do them out completely. Since we know what X is so you can do 0.764 That was our X who her three minus 0.764 times the total pressure, which is to we're gonna dio tu minus x so minus at seven 0.764 in total moles. Now that we know that next animals white again by the total pressure then we have six maybe a little bit here, There we go. One minus 0.764 over three minus 0.764 Multiply that by two. So here we find this is a pilot. Choose your a 0.6 83 a. T m. 1.11 a t m. And 0.21 1 a.m. and I major to use the same amount of significant figures and all these just so that we can keep it.

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