1. Section 8D Logarithm Scales: Earthquakes, Sounds, and Acids
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2. Logarithmic Scales Earthquake strength is described in magnitude.
Loudness of sounds is described in decibels.
Acidity of solutions is described by pH.
Each of these measurement scales involves exponential growth.
Successive numbers on the scale increase by the same relative amount.
e.g. A liquid with pH 5 is ten times more acidic than one with pH 6.

3. Earthquake Magnitude Scale
The magnitude scale for earthquakes is defined so that each magnitude represents about 32 times as much energy as the prior magnitude.
The magnitude M is related to the released energy E by the following formulas:
log10(E) = M or E = (2.5 x 104) x 101.5M
Energy is measured in joules.
Magnitudes have no units.

4. ex1/521 Calculate precisely how much more energy is released for each 1 magnitude on the earthquake scale (about 32 times more).
Magnitude 1: E = (2.5 x 104) x 101.5(1)
Magnitude 2: E = (2.5 x 104) x 101.5(2)
Magnitude 3: E = (2.5 x 104) x 101.5(3)
For each 1 magnitude, = times more energy is released.

5. ex2/521 How much energy was released by the magnitude 7
ex2/521 How much energy was released by the magnitude 7.1 earthquake in San Francisco in 1989? by the magnitude 6.9 earthquake in Afghanistan in 1998?
SF in 1989 with M=7.1: E = (2.5 x 104) x 101.5(7.1)
= E15 joules
Afghanistan in 1998 with M=6.9: E = (2.5 x 104) x 101.5(6.9)
= E14 joules
Since E15/5.5968E14 = , we say that:
the SF quake was times more powerful than the Afghanistan quake.

6. Typical Sounds in Decibels
Times Louder than Softest Audible Sound
Example
140
1014
jet at 30 meters
120
1012
strong risk of damage to ear
100
1010
siren at 30 meters 90
109
threshold of pain for ear 80
108
busy street traffic 60
106
ordinary conversation 40
104
background noise 20
102
whisper 10
rustle of leaves 1
threshold of human hearing
-10
0.1
inaudible sound
decibels increase by 10 and intensity is multiplied by 10.

7. Decibel Scale for Sound
The loudness of a sound in decibels is defined by the following equivalent formulas:

8. More Practice
15/527 How many times as loud as the softest audible sound is the sound of busy street traffic?
17/527 What is the loudness, in decibels, of a sound 45 million times as loud as the softest audible sound?
19/527 How much louder (more intense) is a 35-dB sound than a 10-dB sound?

9. pH Scale for Acidity
The pH is used by chemists to classify substances as neutral, acidic, or basic/alkaline.
Pure Water is neutral and has a pH of 7..
Acids have a pH lower than 7.
Bases have a pH higher than 7
Solution pH
Pure water 7
Drinking water
Stomach acid
2-3
Baking soda
8.4
Vinegar 3
Household ammonia 10
Lemon Juice 2
Drain opener
10-12

10. The pH Scale pH = -log10[H+] or [H+] = 10-pH
The pH Scale is defined by the following equivalent formulas:
pH = -log10[H+] or [H+] = 10-pH
where [H+] is the hydrogen ion concentration in moles per liter.

11. Practice
27/527 What is the hydrogen ion concentration of a solution with pH 8.5?
29/527 What is the pH of a solution with a hydrogen ion concentration of 0.1 mole per liter? Is this solution an acid or base?

12. Homework
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# 12,14, 18,20, 28,30