Sample Problem Set. Teacher Notes and Answers. Skills Worksheet. EQUILIBRIUM OF ACIDS AND BASES, K a AND K b. Name: Class: Date:

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1 Skills Worksheet Sample Problem Set Teacher Notes and Answers EQUILIBRIUM OF ACIDS AND BASES, a AND b 1. ph.857 a ph a a. [H O M ph 10.1 b b. [B M b ph 10.9 c. [OH M [H O M [B 0.01 M b d. [B initial M b ph b [H NCH CH OH M [OH M ph a. 10 [HB initial M [H O 0.01 M ph [H O M ph a ph.1 1. a M b c M d e. HCN is a fairly weak acid. f M 15. a b c. 1.0 M d. It is moderately weak a M b ph 11.7 b dimethylamine is the stronger base 0. a b c Sample Problem Set 1 Equilibrium of Acids and Bases, a and b

2 Skills Worksheet Sample Problem Set Equilibrium of Acids and Bases, a and b The ionization of a strong acid, such as HCl, will proceed to completion in reasonably dilute solutions. This process is written as follows. HCl( - g) H O( l) H O ( aq) Cl ( aq) goes 100% to the right; NOT an equilibrium process However, when weak acids and weak bases dissolve, they only partially ionize, resulting in an equilibrium between ionic and molecular forms. The following equation shows the equilibrium process that occurs when hydrogen fluoride, a weak acid, dissolves in water. HF( g aq) - ) H O( l) HO ( aq) F ( doesnot go100%totheright;is anequilibrium process Most weak acids react in this way, that is, by donating a proton to a water molecule to form a H O ion. The weak base ammonia establishes the following equilibrium in water. NH ( g ) H O( l) NH ( aq) OH ( aq) Most weak bases react in this way, that is, by accepting a proton from a water molecule to leave an OH ion. You learned to write an equilibrium expression to solve for, the equilibrium constant of a reaction. As with equilibrium reactions, equilibrium constants can be calculated for the ionization and dissociation processes shown above. The equilibrium constants indicate how far the equilibrium goes toward the ionic products. Recall that the concentration of each reaction component is raised to the power of its coefficient in the balanced equation. These concentration terms are arranged in a fraction with products in the numerator and reactants in the denominator. The equilibrium constants calculated for acid ionization reactions are called acid ionization constants and have the symbol a. The equilibrium constants calculated for base dissociation reactions are called base dissociation constants and have the symbol b. From the diagram on the next page and the problems in this chapter, you will see how these constants are calculated and how they relate to concentrations of the reactants and products and to ph. Sample Problem Set Equilibrium of Acids and Bases, a and b

3 General Plan for Solving a and b Problems Sample Problem Set Equilibrium of Acids and Bases, a and b

4 Sample Problem 1 The hydronium ion concentration of a M solution of HF at 5 C is found to be M. Calculate the ionization constant for HF at this temperature. Solution ANALYZE What is in the problem? What are you asked to find? the molarity of the acid solution, the equilibrium concentration of hydronium ions, and the temperature the acid ionization constant, a Items Molar concentration of H O at equilibrium Molar concentration of F at equilibrium Data M? M Initial molar concentration of HF M Molar concentration of HF at equilibrium? M Acid ionization constant, a, of HF? PLAN What steps are needed to calculate the acid ionization constant for HF? Write the equation for the ionization reaction. Set up the equilibrium expression for the ionization of HF in water. Determine the concentrations of all components at equilibrium, and calculate a. Sample Problem Set Equilibrium of Acids and Bases, a and b

5 Write the balanced chemical equation for the ionization of HF in aqueous solution. - HF( aq ) H O( l) H O ( aq) F ( aq) Write the acid ionization expression for a. Remember that pure substances are not included in equilibrium expressions. For this reason, [H O does not appear in the expression for a. a [ H O [ F [ HF From the balanced chemical equation, you can see that one HF molecule ionizes to give one fluoride ion and one hydronium ion. Therefore, at equilibrium, the concentration of F - must equal the concentration of H O. - [F [H O M When the HF ionizes in solution, the HF concentration decreases from its initial value. The amount by which it decreases is equal to the concentration of either the fluoride ion or the hydronium ion. [HF Set up the equilibrium expression. a equilibriu m [HF initial -[H O equilibrium [H [HF O initial calculated above [F [H O COMPUTE a [.0185[ [ [ EVALUATE Are the units correct? Yes; the acid ionization constant has no units. Is the number of significant figures correct? Yes; the number of significant figures is correct because data values have as few as three significant figures. Is the answer reasonable? Yes; the calculation can be approximated as ( )/ , which is of the same magnitude as the calculated result. PRACTICE 1. At 5 C, a 0.05 M solution of formic acid, HCOOH, is found to have a hydronium ion concentration of.0 10 M. Calculate the ionization constant of formic acid. ans: a Sample Problem Set 5 Equilibrium of Acids and Bases, a and b

6 Sample Problem At 5 C, the ph of a 0.15 M solution of nitrous acid, HNO, is 1.9. Calculate the a of nitrous acid at this temperature. Solution ANALYZE What is in the problem? What are you asked to find? the ph of the acid solution and the original concentration of HNO the acid ionization constant, a Items Data ph of solution 1.9 Molar concentration of H O at equilibrium? M - Molar concentration of NO at equilibrium? M Initial molar concentration of HNO 0.15 M Molar concentration of HNO at equilibrium? M Acid ionization constant, a, of HNO? PLAN What steps are needed to calculate the acid ionization constant for HNO? Determine the H O concentration from the ph. Write the equation for the ionization reaction. Set up the equilibrium expression. Determine all equilibrium concentrations and calculate a. Sample Problem Set 6 Equilibrium of Acids and Bases, a and b

7 Calculate the H O concentration from the ph. ph - log [H O ph [H O 10 Write the balanced chemical equation for the ionization of HNO in aqueous solution. HNO ( aq ) H O( l) H O ( aq) NO ( aq) Write the mathematical equation to compute a. a [ NO - [ H O [ HNO Because each HNO molecule dissociates into one hydronium ion and one nitrite ion, [NO [H O the HNO concentration at equilibrium will be its initial concentration minus any HNO that has ionized. The amount ionized will equal the concentration of H O or NO. [HNO equilibrium [HNO initial - [H O - Substitute known values into the a expression. calculated calculated above above [H O [NO a [HNO initial calculated above - [ H O COMPUTE a [H O [. 10 [ [ 0.15 [ EVALUATE Are the units correct? Yes; the acid ionization constant has no units. Is the number of significant figures correct? Yes; the number of significant figures is correct because the ph was to two decimal places. Is the answer reasonable? Yes; the calculation can be approximated as ( )/0. 10, which is of the same order of magnitude as the calculated result. Sample Problem Set 7 Equilibrium of Acids and Bases, a and b

8 Practice 1. The ph of a 0.00 M solution of iodic acid, HIO, is 0.76 at 5 C. What is the a at this temperature? ans: a The ph of a M solution of hypochlorous acid, HClO, is found to be.55 at 5 C. Calculate the a for HClO at this temperature. ans: a Sample Problem Set 8 Equilibrium of Acids and Bases, a and b

9 Sample Problem A 0.50 M ammonia solution has a ph of 11.5 at 5 C. Calculate the [H O and [OH of the solution, and determine the base dissociation constant, b, of ammonia. Solution ANALYZE What is in the problem? the ph of the base solution, the original concentration of NH, and the temperature What are you asked to find? [H O, [OH, and the base dissociation constant, b Items Data ph of solution 11.5 Molar concentration of H O at equilibrium? M Molar concentration of OH at equilibrium? M Molar concentration of NH at equilibrium? M Initial molar concentration of NH 0.50 M Molar concentration of NH at equilibrium? M Base dissociation constant, b, of NH? PLAN What steps are needed to calculate the base dissociation constant for NH? Determine the H O concentration from the ph. Calculate the OH concentration. Write the balanced chemical equation for the dissociation reaction. Write the mathematical equation for b, substitute values, and calculate. Sample Problem Set 9 Equilibrium of Acids and Bases, a and b

10 Determine [H O. Determine [OH. [HO 10 ph - w [H O [OH [ OH w [ H O calculated above Write the equilibrium expression for the ionization reaction. - NH ( aq ) H O( l) NH ( aq) OH ( aq) b [ OH [ NH [ NH Because 1 mol of NH reacts with 1 mol of H O to produce 1 mol of 1 mol of OH : [OH [ΝΗ NH and Sample Problem Set 10 Equilibrium of Acids and Bases, a and b

11 The equilibrium concentration of NH will be the initial concentration minus any NH that has reacted. The amount reacted will equal the concentration of NH or OH. [NH [NH -[OH equilibrium initial Substitute known quantities into the b expression. COMPUTE EVALUATE Are the units correct? b above [ OH [ NH [ NH initial [ OH calculated [H O calculzate above d 1 10 [ OH [.9 10 [.9 10 [ 0.50 [.9 10 b Yes; the equilibrium constant has no units. Is the number of significant figures correct? Yes; the number of significant figures is correct because the ph was to two decimal places. Is the answer reasonable? Yes. The calculation can be approximated as ( )/ / Practice 1. The compound propylamine, CH CH CH NH, is a weak base. At equilibrium, a 0.09 M solution of propylamine has an OH concentration of.7 10 M. Calculate the ph of this solution and b for propylamine. ans: ph 11.57; b Sample Problem Set 11 Equilibrium of Acids and Bases, a and b

12 Sample Problem A 1.00 M iodic acid, HIO, solution has an acid ionization constant of at 5 C. Calculate the hydronium ion concentration of the solution at this temperature. Solution ANALYZE What is in the problem? What are you asked to find? [H O Items Molar concentration of H O at equilibrium Initial molar concentration of HIO Molar concentration of HIO at equilibrium the original concentration of HIO, the temperature, and a Data? M 1.00 M? M Acid ionization constant, a, of HIO PLAN What steps are needed to calculate the acid ionization constant for HIO? Write the balanced chemical equation for the ionization reaction. Write the equation for a. Substitute x for the unknown values. Rearrange the a expression so that a quadratic equation remains. Substitute known values, and solve for x. Write the equilibrium equation for the ionization reaction. HIO ( aq) H O( l) H O ( aq) ( aq) IO Use the chemical equation to write an expression for a. a [ H O [ IO [ HIO Since 1 mol of HIO reacts with 1 mol of H O to produce 1 mol of H O and 1 mol of IO : [ H O [ IO Sample Problem Set 1 Equilibrium of Acids and Bases, a and b

13 The equilibrium concentration of HIO will be the initial concentration minus any HIO that has reacted. The amount reacted will equal the concentration of H O or IO. [ [ HIO [ H O HIO equilibriu m initial Because [H O is an unknown quantity, substitute the variable x for it to solve. [ HIO [ HIO equilibrium a x [ HIO initial initial x x COMPUTE Rearrange the above equation. x x x ( x) x x x 0.169x Notice that this equation fits the form for a general quadratic equation. ax bx c 0 where a 1, b 0.169, c Use the formula for solving quadratic equations. b b ac x a Substitute the values above into the quadratic equation, and solve for x x ( 0.169) ( 1)( 0.169) x () M EVALUATE Are the units correct? Yes; the value has units of mol/l, or M. Is the number of significant figures correct? Yes; the number of significant figures is correct because the data values had three significant figures. Sample Problem Set 1 Equilibrium of Acids and Bases, a and b

14 Is the answer reasonable? Yes; substituting the calculated [H O back into the equation for a yields the value. Practice 1. The a of nitrous acid is.6 10 at 5 C. Calculate the [H O of a M nitrous acid solution. ans:. 10 M Sample Problem Set 1 Equilibrium of Acids and Bases, a and b

15 Additional Problems Equilibrium of Acids and Bases 1. Hydrazoic acid, HN, is a weak acid. The [H O of a 0.10 M solution of hydrazoic acid is M. Determine the ph of this solution, and calculate a at 5 C for HN.. Bromoacetic acid, BrCH COOH, is a moderately weak acid. A 0.00 M solution of bromoacetic acid has a H O concentration of M. Determine the ph of this solution and the a of bromoacetic acid at 5 C.. A base, B, dissociates in water according to the following equation: B H O BH OH Complete the following table for base solutions with the characteristics. Initial [B [B at equilibrium [OH b [H O ph a M NA M?? M? b M? M M? NA? c M? M? M?? M 11.9 d.? M M M? NA?. The solubility of benzoic acid, C 6 H 5 COOH, in water at 5 C is.9 g/l. The ph of this saturated solution is.9. Determine a at 5 C for benzoic acid. (Hint: first calculate the initial concentration of benzoic acid.) 5. A M solution of ethanolamine, H NCH CH OH, has a ph of 10.6 at 5 C. Calculate the b of ethanolamine. What concentration of undissociated ethanolamine remains at equilibrium? 6. The weak acid hydrogen selenide, H Se, has two hydrogen atoms that can form hydronium ions. The second ionization is so small that the concentration of the resulting H O is insignificant. If the [H O of a M solution of H Se is.7 10 M at 5 C, what is the a of the first ionization? 7. Pyridine, C 5 H 5 N, is a very weak base. Its b at 5 C is Calculate the [OH and ph of a 0.10 M solution. Assume that the concentration of pyridine at equilibrium is equal to its initial concentration because so little pyridine is dissociated. 8. A solution of a monoprotic acid, HA, at equilibrium is found to have a M concentration of nonionized acid. The ph of the acid solution is.17. Calculate the initial acid concentration and a for this acid. 9. Pyruvic acid, CH COCOOH, is an important intermediate in the metabolism of carbohydrates in the cells of the body. A solution made by dissolving 8 mg of pyruvic acid in ml of water is found to have a ph of 1. at 5 C. Calculate a for pyruvic acid. Sample Problem Set 15 Equilibrium of Acids and Bases, a and b

16 10. The [H O of a solution of acetoacetic acid, CH COCH COOH, is.8 10 M at 5 C. The concentration of nonionized acid is M at equilibrium. Calculate a for acetoacetic acid at 5 C. 11. The a of -chloropropanoic acid, CH CHClCOOH, is Calculate the [H O and the ph of a M solution of -chloropropionic acid. Let x [H O. The degree of ionization of the acid is too large to ignore. If your set up is correct, you will have a quadratic equation to solve. 1. Sulfuric acid ionizes in two steps in water solution. For the first ionization shown in the following equation, the a is so large that in moderately dilute solution the ionization can be considered 100%. H O H O H SO HSO The second ionization is fairly strong, and a HSO H O H O SO Calculate the total [H O and ph of a M H SO solution. Hint: If the first ionization is 100%, what will [HSO and [H O be? Remember to account for the already existing concentration of H O in the second ionization. Let x [SO. 1. The hydronium ion concentration of a M solution of cyanic acid, HOCN, is found to be M at 5 C. Calculate the ionization constant of cyanic acid. What is the ph of this solution? 1. A solution of hydrogen cyanide, HCN, has a 0.05 M concentration. The cyanide ion concentration is found to be M. a. What is the hydronium ion concentration of this solution? b. What is the ph of this solution? c. What is the concentration of nonionized HCN in the solution? Be sure to use the correct number of significant figures. d. Calculate the ionization constant of HCN. e. How would you characterize the strength of HCN as an acid? f. Determine the [H O for a M solution of HCN. 15. A 1.0 M solution of dichloroacetic acid, CCl HCOOH, at 5 C has a hydronium ion concentration of 0.18 M. a. What is the ph of this solution? b. What is the a of dichloroacetic acid at 5 C? c. What is the concentration of nonionized dichloroacetic acid in this solution? d. What can you say about the strength of dichloroacetic acid? Sample Problem Set 16 Equilibrium of Acids and Bases, a and b

17 16. Phenol, C 6 H 5 OH, is a very weak acid. The ph of a 0.15 M solution of phenol at 5 C is found to be Calculate the a for phenol. 17. A solution of the simplest amino acid, glycine (NH CH COOH), is prepared by dissolving.75 g in 50.0 ml of water at 5 C. The ph of this solution is found to be a. Calculate the molarity of the glycine solution. b. Calculate the a for glycine. 18. Trimethylamine, (CH ) N, dissociates in water the same way that NH does by accepting a proton from a water molecule. The [OH of a M solution of trimethylamine at 5 C is. 10 M. Calculate the ph of this solution and the b of trimethylamine. 19. Dimethylamine, (CH ) NH, is a weak base similar to the trimethylamine in item 18. A M solution of dimethylamine has a ph of 11.0 at 5 C. Calculate the b of dimethylamine. Compare this b with the b for trimethylamine that you calculated in item 18. Which substance is the stronger base? 0. Hydrazine dissociates in water solution according to the following equations: H H NNH NNH HO( l) NHNNH ( aq) OH ( aq) ( aq) H O( l) NH NNH ( aq) OH ( aq) The b of this second dissociation is , so it contributes almost no hydroxide ions in solution and can be ignored here. a. The ph of a 0.10 M solution of hydrazine at 5 C is Calculate b for the first ionization of hydrazine. Assume that the original concentration of H NNH does not change. b. Make the same assumption as you did in (a) and calculate the [OH of a 0.00 M solution. c. Calculate the ph of the solution in (b). Sample Problem Set 17 Equilibrium of Acids and Bases, a and b