Acids & BasesLesson 5pH scale

H and OH

There is a way we can connect both H and OH together, using what we already know about them.

We know: Kw = [H+][OH-] = 1.0 x 10-14

H and OH• We can create a scale for the concentrations of

H+

[H+] or [H3O+]

• We can choose to make this scale go from 100 to 10-14

remember; 100 = 1

This represents [H+] going from 1.0 M to 1.0 x 10-14 M. In other words, going from 1.0 M strong acid to 1.0 M strong base.

[OH-] = 1.0 x 10-14 = 1.0 x 10-14 = 1.0 M [H+] 1.0 x 10-14

Let us simplify those powers of 10 and get them into whole numbers!

HCl

1 MH+ H2O

NaClOH- NaOH

1 M

100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14

What if we take the log of -[H+]? We can call this pH.

pH = -Log10[H+]

*p comes from “potenz” in German, which means “power” Hence, pH represents powers of 10 of [H+]

We will always use logs to the base 10, and so we will not keep writing 10 as a base anymore.

HCl

1 MH+ H2O

NaClOH- NaOH

1 M

100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14

pH = -Log[H+] Ex: pH = -Log [10-2] = -2 log10= 2 x 1= 2

If I take -Log[H+] for every value of [H+], I get the new scale in blue called the pH scale, going from 0 - 14

“Nice easy whole numbers”

This is the pH scale that goes from 0-14 ( strong acids strong bases)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14

pH = -Log[H+]

For each 1 unit change of pH, the [H+] changes by a factor of 10 x. This is the nature of the logarithm.

1. If [H+] increases by 100 x pH decreases by 22. If [H+] decreases by 1000 x the pH increases by 33. If the pH increases by 2 units the [H+] decreases by 100 x

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14

The pH Scale pH

If the pH is lower than 7, the solution is acidic!If the pH is greater than 7, the solution is basic!If the pH is exactly 7, the solution is neutral!

The pH scale has three important end points. pH  0 Strong Acid 1.0 M HCl 7 Neutral H2O or NaCl

14 Strong Base 1.0 M NaOH

pH 0 7 14

pH 0 7 14

A B C D E

Match each letter with a formula. All are 1.0 M NH3

 HCl KOH HF H2O

weak base D

strong acid A

strong base E

weak acid B

neutral C

What do we want to take from all of this??

pH EquationsYou must know the following equations, which are all based on the ionization of water at 250 C! H2O ⇄ H+ + OH-

 Kw = [H+][ OH-] = 1.00 x 10-14   pH = -Log[H+] Or pOH = -Log[OH-]  pH + pOH = pKw = 14.000

Some math stuff!We are gonna get you from here….to here!

Operation Inverse

-

Log x 10x

x÷

+

102Log = 2

All logs have the base 10. It makes your life easy as we deal with powers of 10’s all the time in our calculations. For ex: log(103) = log(0.01)= log (10-2)=

log(10 -5)=

One more piece of info. needed

Log (10M X l0Y ) = Log (10M) + log (l0Y)Very, very important for us…

For ex:Log ( 3.94 x 10-4 )

log ( 3.94 ) + log ( 10-4 )

0.596 + - 4

-3.404

Why so important?Most of our calculations will look like this:

If [H3O+] = 3.51 x 10-12 M, what is pH?

pH= -log [H+] or pH= -log [H3O+]

pH = -log (3.51 x 10-12 )

= - log (3.51) + -log (10-12 )

Sig Figs and pH1.00 x 10-4 M

3 sig figs-Log 1.00 x 10-4

= 4.000 3 sig figs

The 4 is from the 10-4 which does not count for sig figsFor pH or pOH, only digits after the decimal are significant

This can also be summarized as: when taking the log of a number, your final answer will have the same number of decimals places as there are significant figures in the original number

Converting from pH to [H30+] and [OH-]

Remember,

pH= -log [H+], to get [H+] we take the anti-log. [H+] = anti-log (-pH) On your calculator: press 2nd then log, then enter (-pH)

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

Examples:

If pH = 3.405, what is [H+] and [OH-] ??

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

pH + pOH = pKw = 14.000

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M

Calculation

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M

Calculation The number of sig figs are 2 (green)

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M

Calculation pH = -Log[H+] pH = -Log[2.5 x 10-4]pH = 3.60 The digit before the decimal does not

count as a sig fig. Both digits after the decimal count for 2 sig figs.

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 3.60

Calculation pH = -Log[H+] pH = -Log[2.5 x 10-4]pH = 3.60 keep all digits on the calculator- do not

round!

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 3.60

Calculation pH + pOH = 14.0003.60 + pOH = 14.000

pOH = 10.40

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 3.60 10.40

Calculation [OH-] = 10-pOH

[OH-] = 10-10.40

[OH-] = 4.0 x 10-11 M

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

Calculation Note that all of the entries in the last line have two sig figs!

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

9.435

Calculation pH + pOH = 14.0009.435 + pOH = 14.000pOH = 4.565

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

9.435 4.565

Calculation [OH-] = 10-pOH

[OH-] = 10-4.565

[OH-] = 2.72 x 10-5 M

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

2.72 x 10-5 M9.435 4.565

Calculation [H+][OH-] = 1.00 x 10-14

[H+][2.72 x 10-5 ] = 1.00 x 10-14

[H+] = 3.67 x 10-10 M

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

Calculation Note that all of the entries in the last linehave three sig figs!

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

2.6 x 10-4 M TRY

Calculation pOH = -Log[OH-] pOH = -Log[2.6 x 10-4]pOH = 3.59

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

2.6 x 10-4 M 3.59

Calculation pH + pOH = 14.000pH + 3.59 = 14.000pOH = 10.41

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

2.6 x 10-4 M 10.41 3.59

Calculation [H+] = 10-pH

[H+] = 10-10.41

[H+] = 3.8 x 10-11 M

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 3.59

Calculation Note that all of the entries in the last line have two sig figs!

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 3.59

8.40 Try

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 3.59

4.0 x 10-9 M 8.40

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 3.59

4.0 x 10-9 M 8.40

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 3.59

2.5 x 10-6 M 4.0 x 10-9 M 8.40

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 3.59

2.5 x 10-6 M 4.0 x 10-9 M 5.60 8.40

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 3.59

2.5 x 10-6 M 4.0 x 10-9 M 5.60 8.40

Calculation Note that all of the entries in the last line have two sig figs!

pH Calculations [H+] [OH-] pH pOH

2.5 x 10-4 M 4.0 x 10-11 M 3.60 acid 10.40

3.67 x 10-10 M 2.72 x 10-5 M9.435 basic 4.565

3.8 x 10-11 M 2.6 x 10-4 M 10.41 basic 3.59

2.5 x 10-6 M 4.0 x 10-9 M 5.60 acid 8.40

If the pH is lower than 7, the solution is acidic!If the pH is greater than 7, the solution is basic!

Homework

Logs and anti-logs

p.134 #47

p.135 #48

p. 139 #49, 50

p. 141 #55, 56