pH

REVIEWING SOME THINGS:

Arrhenius Theory of Acids and Bases

An acid is a substance that produces H+ ions in solution A base is a substance that produces OHˉ ions in solution

Neutralization can be represented by:

Arrhenius theory does not recognize the contribution of the solvent in the ionization of the solute

It fails to explain weak bases such as carbonate (CO32-), and ammonia

(NH3)

HCl(g) H+(aq) + Clˉ(aq)H2O

NaOH(s) Na+(aq) + OHˉ(aq)H2O

H+(aq) + OHˉ(aq) H2O(l)

Brønsted Lowry Acid/Base Theory

NaOH(s) + H2O(l) Na+(aq) + OHˉ(aq)

HBr(g) + H2O(l) H3O+(aq) + Brˉ(aq)

For our purposes H3O+and H+ can be considered equivalent terms

Neutralization can be represented by:

H3O+(aq) + OHˉ(aq) 2 H2O(l)

Brønsted Lowry Acid/Base Theory

The main advantage of the Brønsted Lowry Theory is in its treatment of weak bases

An acid is a proton (H+) donor A base is a proton (H+) acceptor

Since NH3 is a weak base, the reverse reaction should also be considered

This reversible reaction may be written as follows:

NH4+ + OHˉ NH3 + H2O

baseacid

NH3 + H2O NH4+ + OHˉ

conjugate acid

conjugate base

acidbase

NH3 + H2O NH4+

+ OHˉ base acid

Review Question

Identifying Brønsted-Lowry Acids and Bases and their Conjugates

Question: For each of the following chemical equations, identify the acids and bases in both the forward and reverse reactions.

i) HClO2 + H2O ClO2ˉ + H3O+

ii) OClˉ + H2O HOCl + OHˉ

iii) NH3 + H2PO4ˉ NH4+ + HPO4

2ˉ

conjugate acid

conjugate base

acidbase

conjugate acid

conjugate base

acidbase

conjugate acid

conjugate base

acidbase

Last two things

Concentration – how much of something is contained in a certain amount of solution

Molarity – a chemical means of measuring concentration

Concentration is measured in M

A. [C6H12O6] = 5M “Five Molar glucose”

B. [C6H12O6] = 2M “Two Molar glucose”

C. [C6H12O6] = 0.5M “0.5 Molar glucose”

D. [C6H12O6] = 0.2M “0.2 Molar glucose”

E. Which of these is the most concentrated?

F. Which of these is the least concentrated?

What happens when the concentration gets really small?

A. [C6H12O6] = 0.00001M

B. [C6H12O6] = 0.00000001M

C. [C6H12O6] = 0.00000000000001M

We bring back SCIENTIFIC NOTATION!!!

A. 0.00001M = 1 x 10-5 M

B. 0.00000001M = 1 x 10-8 M

C. 0.00000000000001M = 1 x 10-14 M

Let’s apply this concentration & scientific notation stuff to Acids/Bases

A. [HCl] = 0.00001M

B. [CH3COOH] = 0.00000000000001M

A. [HCl] = 1 x 10-5 M

B. [CH3COOH] = 1 x 10-14 M

Let’s apply this concentration & scientific notation stuff to Acids/Bases

[HCl] & [CH3COOH] are acids Acids generate H+

So,

a) [HCl] = 1 x 10-5 M [H+] = 1 x 10-5 M

b) [CH3COOH] = 1 x 10-14 M [H+] = 1 x 10-14 M

Now, let’s use the scientific notation…

Rank the following from least to greatest concentration of Hydrogen ions

l[HCl] = 1 x 10-6 M

l[CH3COOH] = 1 x 10-14 M

l[HNO3] = 1 x 10-2 M

l[HBr] = 1 x 10-12 M

l[HClO3] = 1 x 10-3 M

l[HF] = 1 x 10-13 M

1. [CH3COOH] = 1 x 10-14 M

2. [HF] = 1 x 10-13 M

3. [HBr] = 1 x 10-12 M

4. [HCl] = 1 x 10-6 M

5. [HClO3] = 1 x 10-3 M

6. [HNO3] = 1 x 10-2 M

Regardless of the acid’s identity, the concentrations of H+ ions rank as follows:

1. [H+] = 1 x 10-14 M

2. [H+] = 1 x 10-13 M

3. [H+] = 1 x 10-12 M

4. [H+] = 1 x 10-6 M

5. [H+] = 1 x 10-3 M

6. [H+] = 1 x 10-2 M

It means the same thing!!

So, we might as well just write…

Now, for the NEW idea: pH

See if you can figure out what is going on in the next slides…

Part 1: Define a logarithmPart 1: Define a logarithm

When the [H+] = 1 x 10-14 M -141 x 10-13 M -131 x 10-12 M -121 x 10-11 M -111 x 10-10 M -10

1 x 10-9 M -91 x 10-8 M -81 x 10-7 M -71 x 10-6 M -61 x 10-5 M -51 x 10-4 M -41 x 10-3 M -31 x 10-2 M -21 x 10-1 M -1

The logarithm of [H+] =

Part 2: How do we change the log result into a positive number?

Multiply the log by -1 to change it to positiveWhen [H+] = Log [H+] = - Log [H+] =1 x 10-14 M -14 141 x 10-13 M -13 131 x 10-12 M -12 121 x 10-11 M -11 111 x 10-10 M -10 101 x 10-9 M -9 91 x 10-8 M -8 81 x 10-7 M -7 “times -1” 71 x 10-6 M -6 61 x 10-5 M -5 51 x 10-4 M -4 41 x 10-3 M -3 31 x 10-2 M -2 21 x 10-1 M -1 1

It’s LOG!!!!

So, what does a log do?It changes a number that is written in scientific

notation into the EXPONENT of the scientific notation

What does -log do?It changes a number that is written in scientific

notation with a NEGATIVE EXPONENT into a POSITIVE NUMBER ALONE

Part 3: pHPart 3: pH

When the [H+] = 1 x 10-14 M 141 x 10-13 M 131 x 10-12 M 121 x 10-11 M 111 x 10-10 M 10

1 x 10-9 M 91 x 10-8 M 81 x 10-7 M 71 x 10-6 M 61 x 10-5 M 51 x 10-4 M 41 x 10-3 M 31 x 10-2 M 21 x 10-1 M 1

The pH =

So, what is pH?

A mathematical operationJust like Sum, Difference, Product, etc.

It does the same thing that taking the –log of a number does!!!The “p” means ‘take the negative log of’The H stands for [H+]

Thus, pH = -log [H+]

Find the pH of each of the following

Concentration

a) [HCl] = 1 x 10-6 M

b) [CH3COOH] = 1 x 10-14 M

c) [HNO3] = 1 x 10-2 M

d) [HBr] = 1 x 10-12 M

e) [HClO3] = 1 x 10-3 M

f) [HF] = 1 x 10-13 M

pH

6

14

2

12

3

13

What did you notice about the pH scale compared to

concentration?

The smaller the pH the higher the concentration of the [H+]

Let’s try our using pH to rank acid strength

Now, let’s use the scientific notation…

Rank the following from least to greatest concentration of Hydrogen ions

a)pH of HCl = 6

b)pH of CH3COOH = 2

c)pH of HNO3 = 3

d)pH of HBr = 11

e)pH of HClO3 = 8

f)pH of HF = 10

The following are ranked from LEAST to GREATEST [H+]

a) pH of HBr = 11

b) pH of HF = 10

c) pH of HClO3 = 8

d) pH of HCl = 6

e) pH of HNO3 = 3

f) pH of CH3COOH = 2

The smaller the pH the higher the concentration of the [H+]

Why use pH?

It’s much more convenient way of measuring [H+] than using scientific notationIt transforms the negative exponents into

positive numbers

We can use pH to talk about acid strength

The pH scale

1 2 3 4 5 6 7 8 9 10 11 12 13 14

The Acid Concentration Scale

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14

When [H+] = 1 x 10 to the…

Let’s see if the pH concept makes sense to youWhat does the “H” part of pH mean?What does the “p” part of pH mean?What does taking the log of a number do?What does taking the –log of a number

do?Could pH work for ions other than [H+]?

Could we take a pOH perhaps???

pOH: the flip-side of pH

Works JUST LIKE pH, except we are talking now about the [OH-] instead of [H+]

What is the pOH of a NaOH solution that is 1 x 10-3 M?

pOH = 3

The pOH scale

1 2 3 4 5 6 7 8 9 10 11 12 13 14

The Base Concentration Scale

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14

When [OH-] = 1 x 10 to the…

Find the pOH of each of the following

Concentration

a) [NaOH] = 1 x 10-6 M

b) [KOH] = 1 x 10-14 M

c) [LiOH] = 1 x 10-2 M

pOH

6

14

2

What’s the relationship between pH and pOH?

pH + pOH = 14 ALWAYS!!!

pH and pOH

The potential of the hydrogen ion was defined in 1909 as the negative of the logarithm of [H+].

pH = -log[H3O+]

pOH = -log[OH-]

[H3O+][OH-]= 1.0x10-14

pH + pOH = 14

Sample Question

Calculate the pH and pOH of 0.10 M HBr

HBr + H2O H3O+ + Brˉ

For our purposes H3O+and H+ can be considered equivalent terms

pH = -log [H+]

pH = -log (0.1)

pH = 1.0

Since pH + pOH = 14

1.0 + pOH = 14

pOH = 13

Another Sample Question

Calculate the pH of 0.10 M KOH

KOH is a strong base and will fully dissociate; [OHˉ] = 0.10M

Method # 2

Calculate pOH pOH = -log [OHˉ]

pOH = -log (0.1)pOH = 1.0

pH + pOH = 14

pH + 1 = 14

pH = 13

Calculate pH

Why pH/pOH?? Autoprotolysis of Water

H2O + H2O H3O+ + OH-

base acid

Kc= [H2O][H2O]

[H3O+][OH-]

KW= Kc[H2O][H2O] = = 1.0x10-14

[H3O+][OH-]

KW= = 1.0x10-14

[H3O+][OH-]

c. acid c. base