   Chapter 13, Problem 85AE

Chapter
Section
Textbook Problem

# Suppose K = 4.5 × 10−3 at a certain temperature for the reaction PCl 5 ( g ) ⇌ PCl 3 ( g ) + Cl 2 ( g ) If it is found that the concentration of PCl5 is twice the concentration of PCl3, what must be the concentration of Cl2 under these conditions?

Interpretation Introduction

Interpretation: The equilibrium constant value for a decomposition reaction of PCl5 is given. The concentration of PCl5 is given to be twice the concentration of PCl3 . The concentration of Cl2 is to be calculated.

Concept introduction: The state when the reactants involved in a chemical reaction and the products formed in the reaction exist in concentrations having no further tendency to change is known as an equilibrium state of the reaction. When the equilibrium constant is expressed in terms of concentration, it is represented K .

To determine: The concentration of Cl2 under the given conditions.

Explanation

Given

The stated reaction is,

PCl5(g)PCl3(g)+Cl2(g)

The concentration of PCl5 is twice the concentration of PCl3 .

The value of the equilibrium constant (K) is 4.5×103 .

The concentration of Cl2 is assumed to be yM .

The concentration of PCl3(g) is assumed to be xM .

Therefore, the concentration of PCl5(g) is (2x)M .

At equilibrium, the equilibrium ratio is expressed by the formula,

K=ConcentrationofproductsConcentrationofreactants

Where,

• K is the equilibrium constant.

The equilibrium ratio for the given reaction is,

K=[Cl2][PCl3][PCl5]

Substitute the given concentration values in the above expression

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