Section 8D Logarithmic Scales: Earthquakes, Sounds, & Acids Pages 519-526

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.

Earthquakes – Relative Energy 8-D Earthquakes – Relative Energy

Approximate number per year (Worldwide average since 1900) Magnitude Scale Category Magnitude Approximate number per year (Worldwide average since 1900) Great 8 and up 1 Major 7-8 18 Strong 6-7 120 Moderate 5-6 800 Light 4-5 6000 Minor 3-4 50,000 Very minor Less than 3 1,000 / 8,000 per day

Earthquakes – Relative Energy 8-D Earthquakes – Relative Energy

The Earthquake Magnitude Scale The scale is designed so that each magnitude (M) represents about 32 times as much energy as the prior magnitude.

Examples: Sumatra: Dec. 26, 2004 magnitude = 9 283,106 deaths Mexico earthquake: Sept. 19, 1985 magnitude = 8 9,500 deaths Since each magnitude increase (of 1) means approximately 32 times as much energy- The December Sumatra released about 32 times as much energy as the 1985 Mexico earthquake, and resulted in almost 30 times as many deaths. 32*9500 = 304,000 --- so in this case there is a relatively close match between magnitude/energy and number of deaths.

The Earthquake Magnitude Scale Where is the ‘almost 32 times as much energy’ coming from? Ah ha!

New Guinea earthquake (June 25, 1976): 8-D New Guinea earthquake (June 25, 1976): magnitude = 7.1 energy = 1.1167×1015 joules # deaths = 422 Afghanistan earthquake (May 30, 1998): magnitude = 6.9 energy = 5.5968×1014 joules # deaths = 4000 Energy New Guinea = 1.1167×1015 = 1.995 Energy Afghanistan 5.5968×1014 New Guinea earthquake was about twice as strong as the Afghanistan earthquake.

Another way: New Guinea earthquake: 7.1 magnitude Afghanistan earthquake: 6.9 magnitude Difference in magnitude = 7.1-6.9 = .2

8-D Measuring Sound The decibel scale is used to compare the loudness of sounds. Designed so that 0 dB represents the softest sound audible to the human ear.

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 Table 8.5 from text decibels increase by 10 and intensity is multiplied by 10.

8-D Measuring Sound The loudness of a sound in decibels is defined by the following equivalent formulas:

8-D Example What is the loudness, in dB, of a sound 25 million times as loud as the softest audible sound?

8-D Example What is the loudness, in dB, of a sound 25 million times as loud as the softest audible sound?

8-D Example How much more intense is a 47-dB sound than a 13-dB sound?

pH Scale 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.

Hydrogen concentration: A mole is Avogadro’s number of particles = 6×1023 particles So [H+] is measured in number of 6×1023 particles per liter

pH Scale The pH scale is defined by the following equivalent formulas: pH = log10[H+] or [H+] = 10pH Pure water is neutral and has a pH of 7. [H+] = 107 = .0000007 moles/liter Acids have a pH lower than 7 Bases (alkaline solutions) have a pH higher than 7.

Typical pH values Solution pH Pure water 7 Drinking water 6.5-8 Stomach acid 2-3 Baking soda 8.4 Vinegar 3 Household ammonia 10 Lemon juice 2 Drain opener 10-12

Example 8-D If the pH of a solution increases from 4 to 6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic? Initial concentration = [H1+] = 10-pH = 10-4 =.0001 moles/liter New concentration = [H2+] = 10-pH = 10-6 = .000001 moles/liter So it decreases by a factor of .0001 = 10-4 = 100 .000001 10-6

Example 8-D If the pH of a solution increases from 4 to 6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic? Pure water is neutral and has a pH of 7. Acids have a pH lower than 7 Bases have a pH higher than 7. This makes the solution more basic (less acidic).

Example 8-D How much more acidic is acid rain with a pH of 3 than ordinary rain with a pH of 6? We really want to know – how many times larger is the hydrogen concentration of the acid rain than that of ordinary rain? Which means we need to look at the ratio of their hydrogen concentrations:

Example 8-D How much more acidic is acid rain with a pH of 3 than ordinary rain with a pH of 6? Ordinary rain: [H+] = 10-pH = 10-6 mole per liter Acid rain: [H+] = 10-pH = 10-3 mole per liter Ratio: 10-3 = 1000 10-6 That is, this acid rain is 1000 times more acidic than ordinary rain. Normal raindrops are mildly acidic, with a pH slightly under 6. However, the burning of fossil fuels releases sulfur or nitrogen that can form sulfuric or nitric acids in the air which can make raindrops far more acidic than normal. Acid rain in the NE U.S. and acid fog in LA have been observed with a pH as low as 2 – the same acidity as pure lemon juice!

8-D Homework: Pages 526-527 # 10, 12, 16, 19, 20, 26, 28, 34