Sample Exercise 15.1 Writing Equilibrium-Constant Expressions

1 2012 Pearson Education, , The Central Science, 12th EditionTheodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardSample Exercise Equilibrium-Constant ExpressionsSolutionAnalyze We are given three equations and are asked to write an Equilibrium-Constant expression for Using the law of mass action, we write each expression as a quotient having the product concentration terms in the numerator and the reactant concentration terms in the denominator. Each concentration term is raised to the power of its coefficient in the balanced chemical (a) (b) (c)Practice ExerciseWrite the Equilibrium-Constant expression Kcfor (a) ,(b).

2 Answer: (a) (b)Write the equilibrium expression for Kcfor the following reactions:(a)(b)(c) 2012 Pearson Education, , The Central Science, 12th EditionTheodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardSample Exercise between Kcand KpFor the Haber process,Kc= at 300 C. Calculate Kpfor this reaction at this We are given Kcfor a reaction and asked to calculate The relationship between Kcand Kpis given by Equation To apply that equation, we must determine n by comparing the number of moles of product with the number of moles of reactants (Equation ).

3 Solve With 2 mol of gaseous products (2 NH3) and 4 mol of gaseous reactants, (1 N2+ 3 H2), n = 2 4 =2.(Remember that functions are always based on products minus reactants.) The temperature is 273 + 300 = 573 K. The value for the ideal-gas constant, R, is L-atm/mol-K. Using Kc= , we therefore havePractice ExerciseFor the equilibrium , Kc is 10 3at 1000 K. Calculate the value for : 2012 Pearson Education, , The Central Science, 12th EditionTheodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardSample Exercise the Magnitude of an Equilibrium ConstantSolutionAnalyze We are asked to judge the relative magnitudes of three equilibrium constants and then to calculate (a) The more product present at equilibrium, relative to reactant, the larger the equilibrium constant.

4 (b) The equilibrium constant is given by Equation following diagrams represent three systems at equilibrium, all in the same-size containers. (a) Without doing any calculations, rank the systems in order of increasing Kc. (b) If the volume of the containers is L and each sphere represents mol, calculate Kcfor each system. 2012 Pearson Education, , The Central Science, 12th EditionTheodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardSolve(a) Each box contains 10 spheres. The amount of product in each varies as follows: (i) 6, (ii) 1, (iii) 8.

5 Therefore,the equilibrium constant varies in the order (ii) < (i) < (iii), from smallest (most reactant) to largest (most products).(b) In (i) we have mol/L product and mol/L reactant, Kc= = (You will get the same result by merely dividing the number of spheres of each kind: 6 spheres/4 spheres = ) In (ii) we have mol/L product and mol/L reactant, giving Kc= = (or 1 sphere/9 spheres = ). In (iii) we have mol/L product and mol/L reactant, giving Kc= = (or 8 spheres/2 spheres = ). These calculations verify the order in (a).Comment Imagine a drawing that represents a reaction with a very small or very large value of Kc.

6 For example, what would the drawing look like if Kc = 1 10 5? In that case there would need to be 100,000 reactant molecules for only 1 product molecule. But then, that would be impractical to ExerciseFor the reaction , Kp= 794 at 298 K and Kp= 55 at 700 K. Is the formation of HI favored more at the higher or lower temperature?Answer: at the lower temperature because Kp is larger at the lower temperatureContinuedSample Exercise the Magnitude of an Equilibrium Constant 2012 Pearson Education, , The Central Science, 12th EditionTheodore L.

7 Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardSample Exercise an Equilibrium Constant When an Equation is ReversedFor the reactionthat is run at 25 C, Kc= 1 10 this information to write the Equilibrium-Constant expression andcalculate the equilibrium constant for the reactionSolutionAnalyze We are asked to write the Equilibrium-Constant expression for a reaction and to determinethe value of Kcgiven the chemical equation andequilibrium constant for the reverse products over reactants, we haveBoth the Equilibrium-Constant expression and the numerical value of the equilibrium constant are the reciprocals of those for the formation of NO from N2and O2:Plan The Equilibrium-Constant expression is a quotient of products over reactants, each raised to a power equal to its coefficient in the balanced equation.

8 The value of the equilibrium constant is the reciprocal of that for the reverse reaction. 2012 Pearson Education, , The Central Science, 12th EditionTheodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardContinuedPractice ExerciseFor , Kp= 10 3at 300 is the value of Kpfor the reverse reaction?Answer: 102 Comment Regardless of the way we express the equilibrium among NO, N2, and O2, at it lies on the side thatfavors N2and O2. Thus, the equilibrium mixture will contain mostly N2and O2with very little NO Exercise an Equilibrium Constant When an Equation is Reversed 2012 Pearson Education, , The Central Science, 12th EditionTheodore L.

9 Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardSample Exercise Equilibrium ExpressionsGiven the reactions determine the value of Kcfor the reactionSolutionAnalyze We are given two equilibrium equations and the corresponding equilibrium constants and areasked to determine the equilibrium constant for athird equation, which is related to the first We cannot simply add the first two equations to get the third. Instead, we need to determine how to manipulate the equations to come up with the steps that will add to give us the desired equation.

10 2012 Pearson Education, , The Central Science, 12th EditionTheodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick WoodwardSample Exercise Equilibrium ExpressionsContinuedSolveIf we multiply the first equation by 2 and make the corresponding change to its equilibrium constant (raising to the power 2), we getReversing the second equation and again making the corresponding change to its equilibrium constant (taking the reciprocal) givesNow we have two equations that sum to give the net equation, and we can multiply the individualKc values to get the desired equilibrium constant.