Chapter 15Acid-Base Titrations & pH

15.1 Aqueous Solutions & The Concept of pH

Self-Ionization of Water • Autoprotolysis:

H2O (l) + H2O (l) → H3O+ (aq) + OH-

(aq)

• Molarity at 25°C

1.0 x 101.0 x 10-7-7 moles H moles H3300++ per liter of solution per liter of solution

1.0 x 101.0 x 10-7-7 moles OH moles OH-- per liter of solution per liter of solution

Ionization Constant for Water (KW)

• KKWW = [H3O+][OH-] = (1.0 x 10-7M)(1.0 x 10-7M) = 1.0 x 101.0 x 10-14-14MM22

• KW is a constant at ordinary ranges of room temperatures

Neutral: [H3O+] = [OH-]

Acidic: [H3O+] > [OH-]

Basic: [H3O+] < [OH-]

Ion Concentration in Water

Calculating [H3O+] and [OH-]

• Assume that strong acids and bases are completely ionized in solution:

1.0 M H2SO4 = 2.0 M H3O+

1.0 M Ba(OH)2 = 2.0 M OH-

pH Calculations and the Strength of Acids and Bases

• Weak acids and weak bases cannot be assumed to be 100% ionized

• [H30+] and [OH-] cannot be determined from acid and base concentrations, and must be determined experimentally

H+, OH-, and pH

pH Scale

The pH Scale• Due to the variations in soln’s, there are many

possible concentrations of hydronium & hydroxide ions for solutions.

• Usually this spans 10-14 M to 1 M

• In order to compare substances, the pH scale was developed.

• Ex:

6 6 MM sol’n of HCl has a H sol’n of HCl has a H33OO++ molarity of 6 molarity of 6 MM

6 6 MM sol’n of HC sol’n of HC22HH33OO22 has a H has a H33OO++ molarity of 0.01 molarity of 0.01MM

pH• pHpH is a scale in which the concentration of

hydronium ions in solution is expressed as a number ranging from 0 to 14.

• Instead of referring to a scale of 1 to 10-14, the pH scale is much easier to use.

• pH is the negative of the exponent of the hydronium concentration.

Calculating pH & pOH• pH

The negative of the common logarithm of the hydronium ion concentration

pH = - log [HpH = - log [H33OO++]] • pOH

The negative of the common logarithm of the hydroxide ion concentration

pOH = - log [OHpOH = - log [OH--]]

• pH + pOH = 14.0

pH Example

• A solution with a hydronium concentration of 10-11 M has a pH of 11.

• What would be the pH of a solution with a hydronium concentration of 10-6 M?

pH = 6pH = 6

Finding [H3O+], [OH-] from pH, pOH

[H[H33OO++] = 10] = 10-pH-pH [OH[OH--] = 10] = 10-pOH-pOH

Interpreting the pH Scale

• The pH scale is divided into 3 main areas:

• If it is exactly 7, it is neutral.

• If it is less than 7, it is acidic.

• If it is more than 7, it is basic.

pH Scale

Interpreting the pH Scale

• As pH decreases below 7, hydronium ion concentrations increase & hydroxide ion concentrations decrease.

**** pH values differ in factors of 10.pH values differ in factors of 10.

Ex:

An acidic sol’n w/ a pH of 3 has 10 times the hydronium concentration as a sol’n w/ a pH of 4.

Interpreting the pH Scale

• As pH increases above 7, hydroxide ion concentrations increase & hydronium ion concentrations decrease.

Ex: A basic sol’n w/ a pH of 9 has 10 times the hydroxide concentration as a sol’n w/ a pH of 8.

• A neutral sol’n has equal concentrations of hydronium and hydroxide ions.

pH +

pOH = 14

Significant Figures & pH

• Significant digits when calculations involve logarithms are dependant only on the number of digits to the right of the decimal.

• Example:

[H3O+] = 2.5 x 10-3

pH = 2.60

This concentration has 2 significant digits

So the pH will have 2 digits to the right of the decimal point

pH = ?????

Practice1. Determine the [H3O+] & [OH-] in a 0.01 M solution

of HClO4.

2. An aqueous solution of Ba(OH)2 has a [H3O+] of 1 x 10-11 M. What is the [OH-]? What is the molarity of the solution?

3. Determine the pH of a 1 x 10-4 M solution of HBr.

4. Determine the pH of a 5 x 10-4 M solution of Ca(OH)2.

5. What is the pH of a solution whose [H3O+] = 6.2 x 10-9 M?

6. Determine the pH of a 0.00074 M solution of NaOH.

More Practice7. What are the [H3O+] & [OH-] of a solution if its

pH = 9.0?

8. The pH of a solution if 10.0. What is the concentration of hydroxide ions in the solution? If the solution is Sr(OH)2 (aq), what is its molarity?

9. The pH of a hydrochloric acid solution for cleaning tile is 0.45. What is the [H3O+] in the solution?

10.A shampoo has a pH of 8.7. What are [H3O+] & [OH-] in the shampoo?

Practice Answers!1. [H3O+] = 1 x 10-2 M, [OH-] = 1 x 10-12 M

2. [OH-] = 1 x 10-3 M, [Ba(OH)2] = 5 x 10-4 M

3. pH = 4.0

4. pH = 11.0

5. pH = 8.21

6. pH = 10.87

7. [H3O+] = 1 x 10-9 M, [OH-] = 1 x 10-5 M

8. [OH-] = 1 x 10-4 M, [Sr(OH)2] = 5 x 10-5 M

9. [H3O+] = 0.35 M

10.[H3O+] = 2 x 10-9 M, [OH-] = 5 x 10-6 M

Chapter 15Acid-Base Titrations & pH

15.2 Determining pH & Titrations

Indicators and pH Meters• Acid-Base Indicators

Compounds whose colors are sensitive to pH

• Transition Interval

pH range over which an indicator color change occurs

• Indicators are useful when they change color in a pH range which includes the endpoint of the reaction

Using Indicators to Measure pH• A pH meter is the most accurate

way to measure pH. • Measures voltage difference

between two electrodes • It will determine the exact pH of a sol’n.

• There are also colored dyes that will change in a predictable way according to a standard chart. These are called indicators.

pH Indicators and theirranges

Acid-Base Titration • Titration

Controlled addition of the measured amount of a solution of a known concentration required to react completely with a measured amount of sol’n of unknown concentration

• Equivalence Point The point at which the solutions used in a titration are present in chemically equivalent amounts

• Titration Curves: End point The point in a titration at which the rxn is just completed

Titration Curves

Molarity and Titration• Standard Solution

A solution that contains the precisely known concentration of a solute, used in titration to find the concentration of the solution of unknown concentration

• Primary Standard

A highly purified solid compound used to check the concentration of the known solution in a titration

Calculations with Molar Titrations1. Start with the balanced equation for the

neutralization reaction and determine the chemically equivalent amounts of the acid and base

2. Determine the moles of acid (or base) from the known solution used during the titration

3. Determine the moles of solute of the unknown solution used during the titration

4. Determine the molarity of the unknown solution

Titration Calculations

More Practice!1. How many moles of HCl are in 31.15 mL

of a 0.688 M solution?

2. How many moles of NaOH would neutralize 20.0 mL of a 13.9 M solution of H2SO4?

3. How many milliliters of a 2.76 M KOH solution contain 0.0825 mol of KOH?

More Practice!4. A 25.00 mL sample of a solution of RbOH is

neutralized by 19.22 mL of a 1.017 M solution of HBr. What is the molarity of RbOH?

5. If 29.96 mL of a solution of Ba(OH)2 requires 16.08 mL of a 2.303 M solution of HNO3 for complete titration, what is the molarity of the Ba(OH)2

solution?

6. You have a vinegar solution believed to be 0.83 M. You are going to titrate 20.00 mL of it with a NaOH solution known to be 0.519 M. At what volume of added NaOH would you expect to see an endpoint?

Answers!1. 2.14 x 10-2 mol HCl

2. 5.56 x 10-2 mol NaOH

3. 29.9 mL

4. 0.7819 M RbOH

5. 0.6180 M Ba(OH)2

6. 32 mL NaOH

BuffersBuffers• Buffers have many Buffers have many

important biological important biological functions. They keep a functions. They keep a solution solution at a constant pHat a constant pH, , when manageable amounts when manageable amounts of acid of base are added. of acid of base are added.

• Ex: Your blood is a buffer! Its pH is very Ex: Your blood is a buffer! Its pH is very slightly basic at 7.4. Even though you may eat slightly basic at 7.4. Even though you may eat many different types of foods or medicines, many different types of foods or medicines, your blood pH stays relatively stable, varying your blood pH stays relatively stable, varying only about 0.1only about 0.1. That means your blood . That means your blood controls its own pH!controls its own pH!

BuffersBuffers• Buffers contain ions or molecules that Buffers contain ions or molecules that

react with hydronium or hydroxide if they react with hydronium or hydroxide if they are added to the solution. That means, are added to the solution. That means, even if you add an acid or a base, your pH even if you add an acid or a base, your pH will stay the same. will stay the same.

• To make a buffer, you To make a buffer, you combine a weak combine a weak acid or a weak base with its corresponding acid or a weak base with its corresponding saltsalt. .

BuffersBuffers• Example: Ammonia is combined with its Example: Ammonia is combined with its

salt, NHsalt, NH44Cl, in sol’n:Cl, in sol’n:

• If If acidacid is added to this solution, ammonia is added to this solution, ammonia reacts with the Hreacts with the H+ + ::

NHNH3 (aq)3 (aq) + H + H+ + (aq)(aq) → NH → NH44

+ + (aq)(aq)

• If a If a basebase is added to this solution, the NH is added to this solution, the NH44++

from the dissolved salt will react with the from the dissolved salt will react with the OHOH- - ::

NHNH44+ +

(aq)(aq) + OH + OH-- (aq)(aq) → NH → NH3 (aq)3 (aq) + H + H22O O (l)(l)

BuffersBuffers• Blood’s pH is regulated by many systems, Blood’s pH is regulated by many systems,

but dissolved CObut dissolved CO22 is a very important is a very important method. Carbonic acid, Hmethod. Carbonic acid, H22COCO33, and the , and the hydrogen carbonate ion, HCOhydrogen carbonate ion, HCO33

--, are both , are both dissolved in your blood. dissolved in your blood.

COCO22 (g)(g) + H + H22O O (l)(l) → H → H22COCO3 (aq)3 (aq)

• If you add OHIf you add OH- - : :

HH22COCO3 (aq)3 (aq) + OH + OH-- → HCO → HCO33- -

(aq)(aq) + H + H22O O (l)(l)

• If you add HIf you add H+ + ::

HCOHCO33- -

(aq)(aq) + H + H++ → H → H22COCO3 (aq)3 (aq)

BuffersBuffers• Your lungs control the amount of Your lungs control the amount of

carbon dioxide in your body. If your carbon dioxide in your body. If your body takes in too much carbon body takes in too much carbon dioxide, your blood may become too dioxide, your blood may become too acidicacidic so you may yawn to lower the so you may yawn to lower the concentration of carbonic acid by concentration of carbonic acid by expelling COexpelling CO22..

BuffersBuffers

• If you hyperventilate, too much COIf you hyperventilate, too much CO22 is is expelled, which causes the concentration expelled, which causes the concentration of carbonic acid to become too low, and of carbonic acid to become too low, and your blood may become too your blood may become too basicbasic. . Breathing into a paper bag will increase Breathing into a paper bag will increase the concentration of COthe concentration of CO22 in your lungs in your lungs and restore the proper pH. and restore the proper pH.