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Logarithmic Scales

Logarithmic Scales. pH scale, Richter scale, & Decibel Scale. The pH Scale. -ranges from 0-14. -difference of 1pH represents a tenfold difference in the concentration of the hydrogen ion [H+] in mol/L. -the hydrogen ion concentration is a measure of the strength of an acid.

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Logarithmic Scales

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  1. Logarithmic Scales pH scale, Richter scale, & Decibel Scale

  2. The pH Scale -ranges from 0-14 -difference of 1pH represents a tenfold difference in the concentration of the hydrogen ion [H+] in mol/L -the hydrogen ion concentration is a measure of the strength of an acid pH = -log[H+]

  3. Example • All rainwater contains some level of acidity. Normal rainwater has a pH of 5.6. When the pH level of rainwater goes below 5.6, it is considered acid rain. • All of the sea life will die when the water that they swim in gets to be too acidic. For example, all fish will die when the water goes below a pH of 4.5. Most of the frogs and insects that live around the water will also die when the water reaches a pH of 4.5. With a pH of 5.5, all of the bottom-dwelling bacterial decomposers, animals that eat the remains of the food that other animals don’t want, will begin to die. When these decomposers die, they leave the un-decomposed food on the bottom of the water. This pollutes the water by making the water dirty for all of the fish to swim in. All fresh water shrimp die when there gets to be a pH of 6.0. Aquatic plants will grow the best when the water is a pH between 7.0 and 9.2. If acid rain gets to be more of a problem, then all of the sea life will eventually be gone. • Some of the lakes that were once acidic are recovering, but many more are not recovering. Of the 202 lakes that were chosen to be studied in the early 1980s; only 33% of them have become less acidic.

  4. pH = -log[H+] Ex#1] A scientist measured the concentration of Hydrogen ions in a lake and found it to have a concentration of 0.0000265 mol/L. Is this lake detrimental to the aquatic life? Ex#2] The pH of human blood is 8. Calculate the hydrogen ion concentration. Ex#3] How much more acidic is a lake with a pH of 4.3 (detrimental to aquatic life) than a lake with pH 9.2 (ideal growth conditions)?

  5. pH = -log[H+] Ex#1] A scientist measured the concentration of Hydrogen ions in a lake and found it to have a concentration of 0.0000265 mol/L. Is this lake detrimental to the aquatic life? Solution] Given: H+=0.0000265 mol/L pH = - log[0.0000265] pH  4.6  pH>4.5  not all fish die but . . . pH<5.5  all bottom-dwelling bacteria decomposers die which means the water is polluted & dirty for the fish

  6. pH = -log[H+] Ex#2] The pH of human blood is 8. Calculate the hydrogen ion concentration. Solution] Given: pH = 8 8 = - log[H+] -8 = log[H+] H+ = H+ = 0.000 000 01 mol/L

  7. pH = -log[H+] Ex#3] How much more acidic is a lake with a pH of 4.3 (detrimental to aquatic life) than a lake with pH 9.2 (ideal growth conditions)? Solution] Given: Acidic Lake & Ideal Lake & & the Acidic Lake is about 79433 times more acidic than the Ideal Lake

  8. The Richter Scale • named after Charles Richter, 1935 • measures the amount of seismic energy released by an earthquake 100 x more intense M = log [ I ]

  9. A 7.0 magnitude earthquake struck Haiti and devastated Port-au-Prince on January 12, 2010. People in the nation of Haiti are struggling to recover after a powerful earthquake on January 12, 2010 caused massive destruction there. 220 000 people in the Caribbean nation were killed and many more were injured. Hospitals were destroyed, as were countless homes. The disaster added more suffering to people already struggling to cope with everyday life. Haiti is one of the poorest nations in the world. The Haitian earthquake measured 7.0 on the Richter scale.

  10. The epicenter of the quake was just outside the Haitian capital Port-au-Prince.[72] On February 10th the Haitian government gave a confirmed death toll of 230,000 The National Palace, after the 12 January 2010 earthquake

  11. Initially reported as 7.9 MW by the USGS, the magnitude was quickly upgraded to 8.8, then again to 8.9, and then finally to 9.0 The 2011 Tōhoku earthquake, officially named the Great East Japan Earthquake, was a magnitude 9.0 (Mw) underseamegathrust earthquake off the coast of Japan that occurred at 14:46 JST (05:46 UTC) on Friday, 11 March 2011, with the epicenter approximately 72 km (45 mi) east of the Oshika Peninsula of Tōhoku and the hypocenter at an underwater depth of approximately 32 km (20 mi). It was the most powerful known earthquake to have hit Japan, and one of the five most powerful earthquakes in the world overall since modern record-keeping began in 1900.The earthquake triggered extremely destructive tsunami waves of up to 38 meters (124 ft)that struck Japan, in some cases traveling up to 10 km (6 mi) inland The top part of the nuclear reactor containment vessel (yellow) at the fourth reactor building of TEPCO's Fukushima-1 nuclear power plant (AFP Photo/HO/TEPCO) The earthquake moved Honshu 2.4 m (7.9 ft) east and shifted the Earth on its axis by almost 10 cm

  12. Over eight hundred aftershocks of magnitude 4.5 or greater have occurred since the initial quake

  13. M = log [ I ] Example #4 How much more intense was the earthquake in Haiti (measuring 7.3) than anaverage tornado(measuring 4.5) ? Solution] Given: Haitiquake & AvgTornado & &  the Haitiquakewas about 631 times more intense than an average Tornado

  14. The Decibel Scale • Noise is measured in decibel units (named after Alexander Graham Bell) Intensity of sound (watts/m2) I L = 10 log Io loudness Intensity of sound at the Threshold of Hearing = 10-12 W/m2.

  15. Noise Pollution • Any form of unwelcome noise (jet plane, barking dog etc.) • 70 dB is safe for an average 24h day • At 110 dB (sound level of a typical nightclub), the risk of permanent hearing damage can occur after as little of 4 minutes of exposure. • Noise: derived from the latin nausea (seasickness); can lead to problems with hearing loss, stress, increase in blood pressure, decrease in sleep and a decrease in productivity

  16. Example #5 A worker in a factory is exposed to levels of sound reaching 95dB for an 8-12 hour work-shift. How much more intense is this than a normal conversation at 60 dB? Occupational hygiene and safety have not been high on the agenda of industrial management in developing countries for a variety of reasons. A study was undertaken to assess the exposure to noise at a foundry in a developing country. Noise levels were [found to be] high at the foundry, exceeding 95 dB at almost all work units except the fabrication workshop.

  17. Example #5 A worker in a factory is exposed to levels of sound reaching 95dB. How much more intense is this than a normal conversation at 60 dB? Solution] Given: FactoryNoise & NormalConversation & & & Factory Noise is about 3162 times more intense than Normal Conversation

  18. Social Justice and Environmental Issues • Acid rain, Disaster relief and Noise pollution are all areas where help is needed. • Consider looking for ways you can help out. Pick any social justice issue that interests you, research it and decide that there is something you can do to help bring changes.

  19. Now Try READ: Ex#1 & Ex#2 on p.494- Ex#4 on p.497- DO: p.499 #1-4 ,5ab,6ac,7,8,17,10 p.492 #9 Correction: #8) 7.94

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