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Notes 4.7...

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Chapter 4.7 Logarithmic Scales The pH Scale . Log = - log[H] . Where [H] is the concentration of hydrogen ions measured in moles per liter (m). . For Instance, If [H] = 10^-4m than pH=-log10(10^-4)=-(-4)=4 . Solutions with a pH of 7 are defined as neutral; those with a pH < 7 are acidic, and those with a pH> 7 are basic. . When the pH increases by one unit, [H] decreases by a factor of 10. Example 1: . (A) The hydrogen ion concentration of a sample of human blood measured to be [H^+] =3.16x10^-8m. Find the pH, and classify the blood as either acidic or basic. pH -log [ H^+] = -log (3.16x10^-8_=7.5 Blood is basic (B). The most acidic rainfall ever measured occurred in Scotland in 1974; its pH was 2.4. Find the hydrogen ion concentration. Solve for [H^+] log[H^+] = - pH Exponential form : [H^+]=10^-pH In this case pH = 2.4 so [H^+] =10^-2.4 + 4.0x10^-3m. The Richter Scale . m = log i/s . I i s the intensity of the earthquake s is the intensity of a “Standard” earthquake (1 micron + 10^-4cm) . The magnitude of a standard earthquake is M = log s/s =log1=0 Example Solution m= log i/s =8.3 . The intensity of the Columbia Ecuador earthquake was 4i, so its magnitude was M = log4i/s = log4+logi/s = log4+8.3 = 8.9

The Decibel Scale

. B=10log1/10 . The decibel level of the barely audible reference sound is: B=10log io/io = 10log1=dB (A) Find the decibel level of a jet engine at take off if the intensity was measured at 100Wm^2 B10log i/io = 10log10^2/10^-12 = 10log10^14 Decibel level=dB (B) Find the intensity level of a motorcycle engine at full throttle if the decibel level was measured at 90 dB. - We need to solve for 1 in the logarithmic equation - B=10log i/io - B/10 = log1 -log10^-12 . Divide by 10, io = 10^-12 - B/10 = log, + 12 . Definition of Logarithm - B/10 -12 = log1 . Subtract 12 - Log 1 = 90/10 - 12=-3 . B=90 - 1=10^-3 . Exponential Form Thus the intensity is 10^-3Wm^2...