Chem 101 with Math Reactivation
It will be assumed that students in this class have no understanding of logarithms since this topic is not covered in the prerequisite math course (Math 80-Elementary Algebra). An introduction of logarithms, especially common logarithm, is necessary to define pH in the chemistry course.
LOGARITHMS
Consider the following mathematical sentence:
23 = 8
Assume that the base the power is unknown Assume that the exponent is unknown
and find the base: and find the exponent:
x3 = 8 2y = 8
x= 8 y=log28
x=2 y=3
The logarithm to base 2 of 8 is the exponent to which 2 is raised to give 8.
1. Find the exponent. Use correct logarithmic notation first.
a) 2y = 32 b) 2y = 1/8
c) 7y = 1/49 d) 5y = 25
2. Find the value of each logarithm.
a) log264 b) log39
c) log2(1/4) d) log(1/3)27
(In this class, mainly logarithms to base 10 will be used.)
3. Find the value of each logarithm.
a) log10100 b) log1010000000
c) log10(1/1000) d) log100.000001
Convention:
The logarithm to base 10 is called the common logarithm and is denoted
log10A= log A
e) log 0.01 f) log 10000
g) log 107 h) log 1023
i) log 10-9 j) log 4
Definition of pH:
pH= -log[H3O+]
What is the pH of …
a) a black coffee whose concentration is 1×10-5M?
b) a soft drink 1×10-2M?
c) Which drink is more acidic?
How much more?