Section 8D Logarithm Scales: Earthquakes, Sounds, and Acids

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Section 8DLogarithm Scales Earthquakes, Sounds,
and Acids

• Pages 519-528

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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.
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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) 4.4
1.5M or E (2.5 x 104) x 101.5M Energy is
measured in joules. Magnitudes have no units.
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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, 101.5 31.623 times more
energy is released.
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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 M7.1 E (2.5 x 104) x
101.5(7.1) 1.11671E15 joules
Afghanistan in 1998 with M6.9 E (2.5 x 104) x
101.5(6.9) 5.5968E14 joules
Since 1.11671E15/5.5968E14 1.99526, we say
that the SF quake was 1.99526 times more
powerful than the Afghanistan quake.
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Typical Sounds in Decibels
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 10 rustle of leaves
0 1 threshold of human hearing
-10 0.1 inaudible sound
decibels increase by 10 and intensity is
multiplied by 10.
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Decibel Scale for Sound
The loudness of a sound in decibels is defined by
the following equivalent formulas
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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?
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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 Solution pH
Pure water 7 Drinking water 6.5-8.2
Stomach acid 2-3 Baking soda 8.4
Vinegar 3 Household ammonia 10
Lemon Juice 2 Drain opener 10-12
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The pH Scale
The pH Scale is defined by the following
equivalent formulas
pH -log10H or H 10-pH
where H is the hydrogen ion concentration in
moles per liter.
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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?
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• Homework
• Pages 526 - 527
• 12,14, 18,20, 28,30