1.
Find the logarithms of the following numbers:
a. 8.16
b. 1.652
c. 0.004918
d. 1.0 x 10-6
e.
4.5 x 10-10
2.
Find the numbers whose logarithms are
a. 0.8831
b. 1.743
c. -3.161
d. -6.918
e.
-126
3.
Calculate the value of y in each case:
a. y
5
-6.14 x 100 x log 0.0360
b.
c.
-1.614 5
(300y) log (2.0 x 103)
4.
Calculate y in each case:
a.
b.
c.
5.
Find the value of log y if
a. y
5
1.6 x 10-4
b. y 2
5
1.6 x 10-4
c. y1/2
5
1.6 x 10-4
6.
Express in terms of log x and log y:
a.
log x/y b. log xy c. log xy2
7.
Given that
x
5
y 2/z1/2
obtain a relation between log x,
log y, and log z.
8.
Consider the equation
y
5
12.4 - 2.0 log x 8/5
a.
What is y when x 5
3.0?
b.
What is x when y 5
1.0?
9.
Find the natural logarithms of
a.
6.023 b. (2.718)2
c.
6.18 x 10-5
10.
Find the value of
a. e1.00
b. e-2.50
c. e12.92
11.
Calculate the pH of solutions which have the following concentrations
of H+:
a. 1.0 x 10-6
b. 2.61 x 10-2
c. 3.0 x 10-9
d.
6.0
12.
Calculate the concentration of H+ in solutions with
the following pH:
a. 4.0
b. 12.60
c. 3.14
d.
-1.0
13.
In a water solution saturated with H2S;
(conc. H+)2 x (conc.
S2-) 5
1 x 10-21
What is the concentration of S2-
in a solution of this type which has a pH of 4.0?
14.
In any water solution at 258C;
(conc. H+) x (conc. OH-)
5
1.0 x 10-14
Show, using this equation, that
pH 1
pOH 5
14.00
where pOH 5
-log (conc. OH-).
15.
For a water solution of acetic acid, the following relation holds:
where Ka is the ionization
constant of acetic acid, HAc. Starting with this equation, obtain
a relation between log Ka, pH, and log (conc.
HAc).
16.
In a certain electrical cell, the voltage, E, is given
by the expression
a.
Write an equation relating E to pH.
b.
Calculate E when pH 5
3.0.
c.
Calculate pH when E 5
0.50 V.
17.
The fraction, f, of molecules with energy equal to or greater
than the activation energy, Ea, is given by
the equation
What is f when Ea
5
1.00 x 104J, T 5
298 K, R 5
8.31 J/K?