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# find the ph?

. For each substance, find the pH from the given hydronium ion concentration.
(a) coffee, 1.26×?10?^(-5)
(b) milk, 2.51×?10?^(-7)
(c) lutefisk, 5.01×?10?^(-12)

pH = - log [H3O+]

a) pH = - log [1.26×10^(-5)] = - log(1.26) - log(10^(-5)) = - log(1.26) + 5
≈ 4.89962945488244 ≈  4.900

Check: 10^(-4.900) ≈ 0.000012589254118 ≈ 0.0000126

(see http://www.ndt-ed.org/GeneralResources/SigFigs/SigFigs.htm for a good description of how to determine the significant figures of a logarithm. Thanks to Andre for helping me to fix my knowledge base! I tried to add this note as a comment but it vanished.)

b) pH = - log [2.51×10^(-7)] = 7 - log(2.51) ≈ 6.60032627851896 ≈ 6.600

Check: 10^(-6.600) ≈ 0.000000251188643 ≈ 0.000000251

c) pH = - log [5.01×10^(-12)] = 12 - log(5.01) ≈ 11.30016227413275 ≈ 11.300

Check: 10^(-11.300) ≈ 0.000000000005012 ≈ 0.00000000000501

Since the power of ten is not part of the original significant figures, only the fractional part of the logarithm (mantissa) is rounded to 3 significant figures, so the answers should be 4.900, 6.600, and 11.300.
Not true.

See http://www.usca.edu/chemistry/genchem/sigfig.htm; esp. “write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant.”

So the power of 10 part of a number in scientific notation does not contribute to the significant figures of the whole number.

To see why your answers are wrong, find the pH value of the concentration 5.02x10-12 and compare to your answer to (c). Based on your rounding you would get the same pH value, which can't be.

Andre, you are absolutely right. Thanks for helping me fix a misunderstanding in my knowledge base.

I found this site, http://www.ndt-ed.org/GeneralResources/SigFigs/SigFigs.htm, where there is a very good description of the rules for significant figures when taking logarithms.

So, as you stated in your first comment, the answers to this problem should be 4.900, 6.600, and 11.300.

Checks:
10^(-4.900) ≈ 0.00001258925412 ≈ 0.0000126
10^(-6.600) ≈ 0.000000251188643 ≈ 0.000000251
10^(-11.300) ≈ 0.000000000005012 ≈ 0.00000000000501

Thanks again,
-Steve