Burdge/Overby, Chemistry: Atoms First, 2e FM | Page 10

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PREFACE

Chapter 9—In Section 9.5, we now introduce the concept of pH in the context of acid-base
chemistry and have students learn to perform relatively simple pH calculations for strong acids
and bases. The benefits of introducing pH early are twofold: It requires students to become
reacquainted with the logarithmic functions on their calculators in a relatively simple context, with
straightforward conversions between hydronium ion concentration and pH. Later, in the context of
equilibrium, proper use of these calculations should be a ready tool—rather than another layer of
complication amid a chapter with a large volume of new material. A second benefit of introducing
the pH scale and pH calculations early is that it facilitates the inclusion of more experiments in the
laboratory portion of the course—a perennial concern for the atoms-first curriculum.
Se C ti On 9.5

Concentration of Solutions

353

the pH Scale
The acidity of an aqueous solution depends on the concentration of hydronium ions [H3O+]. This
concentration can range over many orders of magnitude, which can make reporting the numbers
cumbersome. To describe the acidity of a solution, rather than report the molar concentration of
hydronium ions, we typically use the more convenient pH scale. The pH of a solution is defined as
the negative base-10 logarithm of the hydronium ion concentration (in mol/L).
pH = –log [H3O+] or pH = –log [H+]

Equation 9.5

Student Annotation: Equation 9.5 converts numbers that can span an enormous
range (~10–1 to 10–14) to numbers generally
ranging from ~1 to 14.

The pH of a solution is a dimensionless quantity, so the units of concentration must be removed
from [H3O+] before taking the logarithm. Because [H3O+] = [OH–] = 1.0 × 10–7 M in pure water
Chapter pure water at the is
at 25°C, the pH of12—With 25°C movement of intermolecular forces to an earlier position in the textbook,

this chapter is now more –log (1.0 × 10–7) = 7.00 the nature of liquids and solids. We have rearranged
tightly focused on
Student Annotation: A word about
significant
When we take the
the sections for neutral solution has pH 7.00. An acidic solution flow, and we have aincluded afigures:two section log the
what we believe is a more logical has pH < 7.00, whereas
new significant figures,
on
At 25°C, therefore, a
of a number with
we report the result to two places past
basic solution has pH > 7.00. Table 9.7 shows the calculation of pH for solutions ranging from
vapor pressure of solids. As before, the chapter culminates with phase changes and phase diagrams.
the decimal point. Thus, pH 7.00 has two
0.10 M to 1.0 × 10–14 M.
significant 14 was
Chapter 14—In the first edition of Chemistry: Atoms First, Chapter figures, not three. Chemical
In the laboratory, pH is measured with a pH meter (Figure 9.13). Table 9.8 lists the pH values
Kinetics. of common fluids.our vision pH of true fluids varies greatly, dependingandthe the result of discussion with
of a number However, in Note that the of a body atoms-first approac h, on as
users of our text, we reasoned that it would be advantageous to introduce thermodynamics as the
predecessoreof chemical equilibrium. Thus,Range of Hydronium is now presented earlier in the second
Benchmark pH Values for a thermodynamics
ta B l 9.7
Ion Concentrations at 25°C
half of the text. We believe that the earlier coverage of entropy and Gibbs free energy will enable
students toOdevelop a more robust understanding of the origins of chemical equilibrium.
pH
[H ] (M)
–log [H O ]
3

+

3

–log (1.0 × 10–1)

0.10
0.010
Ta b L E 14.4

and ????????S is
–4

1.0 × 10
Negative
Positive
1.0 × 10–5
Positive
Negative
1.0 × 10–6
Negative × 10–7
Negative
1.0
1.0 × 10–8
Positive
Positive
1.0 × 10–9
1.0 × 10–10

S E C TI oN 14.5

1.00

Predicting Spontaneity

589

–log (1.0 × 10
Predicting the Sign of) ?G Using 2.00
Equation 14.10 and the Signs of ?H and ?S

1.0 × 10–3

when ????????H is

+

–2

–log (1.0 × 10–3)

3.00

–log (1.0 × 10–4)
Negative
–log (1.0 × 10–5)

4.00

????????G will be

and the process is

5.00 Always spontaneous
Positive
–6
–log (1.0 × 10 )
6.00 Always nonspontaneous
Acidic
Negative× 10–7)
when T?S < ?H 7.00 Spontaneous at low T
–log (1.0
Neutral
Positive when T?S > ?H
Nonspontaneous at high T
–log (1.0 × 10–8)
8.00
Basic
Negative× 10–9)
when T?S > ?H 9.00 Spontaneous at high T
–log (1.0
Positive when T?S < ?H
Nonspontaneous at low T
–log (1.0 × 10–10)
10.00

Example

2H2O2(aq)
3O2(g)

2H2O(l) + O2(g)
2O3(g)

H2O(l)

H2O(s)
(freezing of water)

2HgO(s)

2Hg(l) + O2(g)

figure 9.13 A pH meter is commonly
used in the laboratory to determine the
–log (1.0 × 10–11)
11.00
1.0 × 10–11
Water freezes spontaneously at temperatures below 0°C, and ice melts spontaneously at temperapH of a solution. Although many pH
–12
12.00
1.0 × 15—This –log ice ×remains equilibrium. The temperature that divides
tures above 0°C. At –12 a system of (1.0and10 ) is at focused solely on equilibrium asmeters have a range of 1 to 14,edition,
Chapter10 0°C,
chapter water
with the previous pH values
“high” from “low” depends, though, on the individual reaction. To determine that temperature, we
can actually be less than 1 and greater
–log (1.0
13.00
but now 1.0 ×are–130 in Equation 14.10 equilibrium from the standpoint of its thermodynamic underpinnings.
we 10toable to present × 10–13) equilibrium condition):
must set ?G equal
(i.e., the
than 14.
–log (1.0 × 10–14)
14.00
In this way, 10–14 are able to provide an introduction to equilibrium and the development of the
1.0 × we
0 = ?H ? T?S

equilibrium constant along with the reaction quotient. Then we explore the intimate relationship
Rearranging to solve for T yields
between Gibbs free energypH Values ofreaction quotient, and how Gibbs free energy ultimately is
Typical and the Some Common Fluids
ta B l e 9.8
?H
T = ___
related to the equilibrium constant under standard-state conditions.
?S
fluid
pH
fluid
pH
Chapter 18—With from low for a particular reaction can now be calculated the
The temperature that divides highthe movement of thermodynamics to an ifearlier chapter, the coverage of
Stomach acid
1.0
Saliva
6.4–6.9
values of ?H and ?S are known.
electrochemistry (Formerly Chapter 19) is now moved up. Because electrochemistry is also related
2.0
Milk
6.5
WorkedLemon juice demonstrates the use of this approach.
Example 14.5
to Gibbs free energy and ultimately the equilibrium constant, this provides logical continuity of the
Vinegar
3.0
Pure water
7.0
atoms-first approach with respect to equilibrium.
Grapefruit juice
3.2
Blood
7.35–7.45
Orange juice
Tears
7.4
Chapter 19—Because 3.5
worked Example 14.5 we now have a sequential group of chapters relating thermodynamics
Urine
10.6
and equilibrium, we have 4.8–7.5 the Milk of magnesia
moved
kinetics chapter later in the book. One benefit of this
According to Table 14.4, a air)
be5.5
at
?H
Rainwater
reorganization(inacleanreaction will ?Hspontaneous onlyandhigh=ammonia? mol, determine the
is that students=will be Householdpreparedifto understand the kinetics of reactions in
better temperatures both11.5and
?S are positive. For reaction in which
199.5 kJ/mol
?S 476 J/K
temperature (in °C) above which the reaction is spontaneous.
which there is a fast initial step. Another benefit is that with kinetics in Chapter 19, this material
Strategy The temperature that divides the nuclear temperature (Chapter T?S
is followed immediately byhigh from low is the chapter at which ?H =20), affording students the opportunity
(?G = 0). Therefore, we use Equation 14.10, substituting 0 for ?G and solving for T to determine
to put into in kelvins; we then convert to degrees Celsius. of first-order kinetics—in the context of nuclear decay
temperature timely practice their knowledge
processes.
Setup
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Solution

(

)(

)

476 J
1 kJ
?S = _______ ______ = 0.476 kJ/K ? mol
K ? mol 1000 J
199.5 kJ/mol
?H
T = ___ = ______________ = 419 K
0.476 kJ/K ? mol
?S
= (419 ? 273) = 146°C

Think about It

Spontaneity is favored by a release of energy (?H being negative) and by an increase in entropy (?S being
positive). When both quantities are positive, as in this case, only the entropy change favors spontaneity.
For an endothermic process such as this, which requires the input of heat, it should make sense that
adding more heat by increasing the temperature will shift the equilibrium to the right, thus making it
“more spontaneous.”
bur11184_FM_i-001.indd 10

Practice Problem A t t e m p t A reaction will be spontaneous only at low temperatures if both

9/10/13 12:29 PM