Acids - Base Equilibria Part I: pH and Acidity

Jespersen Chap. 17 Sec 1 & 2

Dr. C. Yau Spring 2013

Autoionization of Water

H 2 O + H 2 O H 3 O + 2 H 2 O H 3 O + + OH  + OH  K = c 3 + [H O ][OH ] [H O] 2 2 With H 2 O as a solvent, [H 2 O] becomes a constant. We rearrange the equation to give Kc [H 2 O] K 2 w = [H 3 O + ][OH  ] = [H 3 O + ][OH  ] For simplicity, we write

K w =

[H + ][OH 

] At 25 ° C, K w = 1.0x10

-14

= [H + ][OH

Know well! Note: 2 sig. fig. for 1.0



]

K w = 1.0x10

-14

= [H + ][OH  ] As usual, changes in concentration does not change K w . They only cause shifts in the equilibrium. Only T can change K w .

Table 17.1 p. 775 3

K w = 1.0x10

-14 = [H + ][OH



]

Neutral solutions: [H + ]=[OH  ] Acidic solutions: [H + ]>[OH  ] Basic solutions: [H + ]<[OH  ] Note how small K w is.

This means water is a VERY weak acid.

This is why it is considered

nonelectrolytic .

It does not conduct electricity unless it is contaminated with ionic compounds.

Tap water IS electrolytic because it is not pure water and contains salts.

4

H 2 O auto-ionization occurs in any solution

• When other ions present –

[H + ]



[OH



]

– But

K w

= [H + ]·[OH



] = 1.0 x 10



14

• • • In aqueous solution,

Product of [H + ] and [OH



] equals K w [H + ] and [OH



]

may not actually equal each other 5

In a sample of blood at 25 °C, [H + ] is 4.6x10

-8 M. Find the molar concentration of OH , and decide if the sample is acidic, basic, or neutral.

[H + ][OH  ]= 1.0x10

-14 -14 [OH ]  1.0x10

+ [H ] = 1.0x10

-14 4.6x10

-8

Compare

=2.2x10

-7

Ans. [OH ] = 2.2x10

-7 M OH (very slightly basic, more OH than H + ) Pract Exer 17.1 & 17.2 p. 776

6

pH Scale

When we have a dilute solution of acid, the H + concentration is very small, such as 0.0001M, and it becomes cumbersome to be talking about H + concentration of 0.0001 M or 1x10 -4 M.

The pH scale was invented to make it easier to communicate the acidity of a solution.

KNOW THIS WELL:

pH = - log [H + ]

or

pH = - log [H 3 O + ]

7

e.g. [H + ] = 2.43x10

 4 pH =  =  =  log [H + ] M, what is the pH?

log 2.43x10

 4

(3 sig.fig.)

(  3.614)

(3 decimal places)

= 3.614

e.g. pH = 8.71, what is the [H + ]?

pH =  8.71=  log [H  8.71 = log [H + ] + ] log [H + ] Antilog(-8.71) = antilog log [H + ] 10 -8.71 = [H + ]

(2 decimal places) Ans.

[H + ] = 1.9x10

-9 M

(2 sig. fig.) REMEMBER: 10 -pH =

[H + ] 8

We see that the pH and H + concentration has an inverse relationship: As H + concentration increased, the pH decreases.

The smaller the pH, the more acidic it is.

The larger the pH, the more basic it is.

So, if the swimming pool water has a pH that is too high, that means it is too basic.

9

pOH =



log [OH ]

e.g. If [OH  ] = 4.2x10

 3 M, what is the pOH?

pOH =  log 4.2x10

 3

(2 sig.fig.)

=   2.38 = +2.38

(2 decimal places)

e.g. If pOH = 12.3, what is the hydroxide conc?

[OH  ] = 10  12.3

(1 decimal place)

= 5x10  13 M

(1 sig. fig.) THIS IS HOW pH AND pOH ARE RELATED: Remember that [H + ] [OH



] = 1.0x10



14 Finding the log of both sides of the equation gives us… log [H + ] + log [OH



] = log 1.0x10



14 Multiply both sides of equation by



1.



( log [H + ] + log [OH



]) =



( log 1.0x10



14 ) (



log [H + ] )+(



log [OH



]) =



(



14.00) pH + pOH = 14.00

REMEMBER THIS!

10

Practice Exer. 17.4 p. 778 Because rain washes pollutants out of the air, the lakes in many parts of the world have undergone pH changes. In a New England state, the water in one lake was found to have a hydrogen ion conc of 3.2x10

-5 mol L -1 . What are the calculated pH and pOH? Is it acidic or basic?

Ans. pH = 4.49 (acidic) pOH = 9.50

11

What is the pH of a NaOH soln at 25 o C in which the hydroxide ion concentration equals 0.0026 M?

Ans. pH = 11.41 (basic, as expected).

Practice Exercises 17.3 & 17.5 p. 778

12

Calculate the values of pH, pOH and [OH ] for the following solutions: a) 0.020M HCl b) 0.00035 M Ba(OH) 2 .

You must first note that HCl is a strong acid. Only because this is so can you assume 0.020M HCl means 0.020 M H + .

Ans. a) pH = 1.70, pOH = 12.30, [OH ]=5.0x10

-13 M b) 0.00035M Ba(OH) 2 means [OH ] = ?

Ans. [OH ] = 0.00070M, pOH = 3.15, pH = 10.85

13

Acid or basic solutes suppress the ionization of water.

H 2 O + H 2 H 2 2 O H O H 3 3 O O + + + OH  + OH  Remember Le Chatelier’s Principle: If an acidic solute (e.g. HCl) is added to water, it shifts the equilibrium to the left, thus suppressing the ionization of water.

This means that in an acidic solution the only source of H + is from the acid and essentially no contribution from water.

In the same way, in a basic solution the only source of OH is from the base, none from the dissociation of 14 water.

Calculating without a calculator

Often we do not need a calculator to calculate pH or [H + ].

[H + ] = 10  8 [OH  ] = 10  6 What is the pH?

What is the pH?

pH = 4 What is the pOH?

pOH = 3 What is the pH?

15

A soln was made by dissolving 0.837 g Ba(OH) 2 in 100 mL final volume. What is the molar conc of OH in the soln? What are the pOH and the pH? What is the hydrogen ion concentration in the solution? MM(Ba(OH) 2 ) = 171.3 g mol -1 Ans. [OH ] = 0.0977 M, pOH = 1.010

pH = 12.990, [H + ] = 1.02x10

-13 M

Practice Exer 6, 7, & 8 p. 779

16

What is the pH of 0.00000001 M HCl?

[H + ] =1x10  8 M pH = 8 (basic) How can a solution of HCl be basic??

Answer: Its pH will NOT be 8. At very dilute solutions, the H + will NOT suppress the dissociation of water.

Water will contribute to the H + concentration and keep it from becoming basic!

Ans. pH = 7 (stays neutral) 17