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right.
1.
Express the following numbers in exponential notation:
a.
1000
b.
one billion
c.
0.000 001
d.
16,220
e.
212.6
f.
0.189
g.
6.18
h.
0.000 000 078 46
2.
Express as ordinary numbers:
a.
1.2 x 10-3
b.
6.4 x 101
c.
3.0 x 100
d.
4.1 x 105
e.
1.4 x 10-6
3.
In each of the following pairs, select the number which is larger:
a.
3 x 103 ;
3 x 10-3
b.
3 x 103 ;
10,000
c.
0.0001;
2 x 10-4
d.
6 x 107 ;
4 x 108
e.
9.6 x 10-3 ;
1.5 x 10-2
f.
21 x 103;
2.1 x 104
4.
Arrange the following numbers in increasing order, starting with
the smallest:
2.0 x 10-5, 4.6 x 103,
3.6 x 10-1, 7.1 x 10-5, 6.0 x 10-2
5.
Carry out the indicated operations, citing answers in standard
exponential notation:
a.
(6.20 x 104) x (1.50
x 108)
b.
(4.2 x 10-3) x (1.50
x 108)
c.
(3.62 x 104) x (2.91
x 10-7)
d.
(8.16 x 10-4) x (4.78
x 1019)
e.
(1.39 x 107)/(1.10
x 104)
6.
Carry out the indicated operations:
a.
(3.48 x 103) / (6.72 x 105)
b.
(7.2 x 10-3)/(3.6 x 10-4)
c.
(2.60 x 104)/(7.70 x 10-12)
d.
7.
Evaluate
a.
(2.16 x 10-3)2
b.
(4.9 x 104)3
c.
(6.0 x 10-21)2
d.
(9.0 x 106)1/2
e.
(8.4 x 105)1/2
8.
Find the value of
a.
(6.2 x 10-2)1/2
b.
(1.62 x 10-7)1/2
c.
(2.14 x 1010)1/3
d.
(6.0 x 104)2 x (3.0 x 10-7)1/2
e.
(3.0 x 107)1/5
9.
Carry out the indicated operations:
a.
3.02 x 104 + 1.69 x 104
b.
6.10 x 104 + 1.0 x 103
c.
8.17 x 105 - 1.20 x 104
d.
9.68 x 104 + 7.01 x 102
10.
Find the value of
a.
4.18 x 10-2 + 1.29 x 10-2
b.
5.9 x 10-5 + 1.86 x 10-4
c.
6.49 x 10-10 - 1.23 x 10-11
d.
6.02 x 10-23 - 1.0 x 102
11.
A helium atom has the following properties:
Mass = 0.000 000 000 000 000 000 000 006
65 g
radius = 0.000 000 004 6 cm
average speed at 25_ C = 136,000 cm/s
Express these quantities in standard exponential
notation.
12.
Complete the following table, giving the solubilities of several
different compounds as ordinary numbers (first column) or exponential
numbers (second column).
AgCl _______ =1.3 x 10-5
PbCl2 0.016 =
_______
AgC2H3O2
0.045 = _______
13.
Three different reactions have the following rates:
Reaction A: 2.4 x 10-4
moles per liter per second
Reaction B: 3.6 x 10-4
moles per liter per second
Reaction C: 6.5 x 10-5
moles per liter per second
Which of these reactions is the fastest?
the slowest?
14.
The solubility products (Ksp) of several ionic
compounds are listed below. Arrange these compounds in order of
increasing Ksp.
Compound Ksp
Al(OH)3 5 x 10-33
Cr(OH)3 1 x 10-30
Fe(OH)2 1 x 10-13
Fe(OH)3 5 x 10-38
Mg(OH)2 1 x 10-11
15.
The masses of atoms of four different elements are listed below.
In each case, calculate the mass of 6.022 x 1023 atoms
(one mole):
He 6.647 x 10-24 g
N 2.325 x 10-23 g
Sr 1.455 x 10-22 g
Which of these atoms is the heaviest? the
lightest?
16.
In water at 25_ C, the concentrations of H+ and OH-
are related by the equation
(conc. H+) x (conc. OH-)
5
1.0 x 10-14
Using this relation, complete the table
below:
conc. H+ conc. H-
______ 2.5 x 10-4 ______
3.6 x 10-8 ______ ______
______ ______ 102
17.
According to the Bohr theory of the H atom, the orbital radius
is given by
where r is the radius in centimeters, h
= 6.6 x 10-27, e = 4.8 x 10-10, m
= 9.1 x 10-28, p
= 3.14, and n is the socalled quantum number which
can have any integral positive value. Calculate r when
n = 1; n = 2; n = 3.
18.
When hypochlorous acid, HOCl, is dissolved in water, the following
relation exists:
(conc. H+)2 = (3.2
x 10-8) x (conc. HOCl)
Complete the following table:
conc. HOCl conc. H+ 
1.0 ______ ______
0.10 ______ ______
0.010 ______ ______
19.
Dalton's Law tells us that the total pressure of a mixture of
hydrogen and helium is the sum of the partial pressures of the
two gases. If the total pressure is 1.224 x 103 mm
Hg and the partial pressure of helium is 9.80 x 102
mm Hg, what is the partial pressure of hydrogen?
20.
A certain reaction is carried out in a bomb calorimeter. Part
of the heat evolved in the reaction is absorbed by the water,
part by the bomb. If the water absorbs 12.02 kJ and the bomb absorbs
650 J, what is the total amount of heat evolved? (1 kJ = 103
J)