The equilibrium constant (KP) for the reaction PCl3(g)+Cl2(g) ⇌PCl5(g) is 2.93 at 127^∘ C Initia

The equilibrium constant (KP) for the reaction...

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 $2.00 \mathrm{atm}$

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs when a reversible reaction reaches a state where the rates of the forward and reverse reactions are equal, resulting in constant concentrations or pressures of the reactants and products. It forms the basis for understanding how systems adjust to changes and how equilibrium compositions are determined.

Equilibrium Constant (Kp)

The equilibrium constant, expressed as Kp for gaseous reactions, is a ratio of the product of the partial pressures of the products to that of the reactants, each raised to the power of their stoichiometric coefficients. This constant is crucial for quantifying the position of equilibrium and predicting the composition of a system under a given set of conditions.

Reaction Stoichiometry

Reaction stoichiometry involves using the balanced chemical equation to relate the amounts of reactants and products. It is essential for determining how the quantities of substances change as a reaction proceeds toward equilibrium, allowing for the calculation of the extent of reaction.

ICE Table Method

The ICE table method (Initial, Change, Equilibrium) is a systematic approach for tracking the initial amounts, the changes that occur, and the final equilibrium amounts or pressures of species in a reaction. This tool helps organize the calculation process in equilibrium problems.

Partial Pressure

Partial pressure is the pressure exerted by an individual gas in a mixture, proportional to its mole fraction. It is a key concept in problems involving gaseous equilibrium, as it directly relates to how each gas contributes to the overall pressure in the system.

Transcript

00:01 So we want to find the partial pressures at equilibrium for the following balanced chemical equation.

00:06 So when we hear at equilibrium, we immediately want to think ice table.

00:12 So we're going to plug in the values that we know.

00:14 We know we have two, one, then no products initially, because that's what we were told.

00:21 And from the stoichiometry, we know we subtract 1x, extract 1x, and add 1x because we're making product.

00:27 So that means this is x, 1 minus x, and 2 minus x.

00:34 So if we look at total moles, if we were to add all of our equilibrium columns together, we would get 3 minus x.

00:54 And next one we want to do is find the mole fractions.

01:01 So in order to find the mole fractions, let's start with our first reactant.

01:20 And to find the mole fraction, what we're going to do is take how many moles we have over the total number of moles.

01:35 And then we're going to do the same for our second reactant.

01:40 We know that is 1 minus x over 3 minus x.

01:45 And then for our product, we have over 3 minus x.

01:57 So once we have the mole fractions, we also can find partial pressure equations in terms of.

02:07 So if we look at that, we know partial pressure.

02:12 Let's start with our product.

02:16 It's going to be x over 3 minus x.

02:23 Times, we always do the mole fraction times the total pressure, and we were told that was 2 atm.

02:33 And we can do the next, our first reactant.

02:36 This is a 5.

02:38 And that is 2 minus x over 3 minus x times the total pressure.

02:48 And then for our final reactant, we know it is.

02:55 1 minus x or 3 minus x times the total pressure.

03:04 So since we were told the kp value, we can go ahead and plug it in there.

03:12 So we know that kp equals 2 .93.

03:17 So we're going to do our whole products partial pressure equation.

03:29 And we're going to do the same for the reactants.

03:32 I'm going to put it in brackets, not because it's a concentration, but just so that we can tell them apart a little bit better...

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