Download Acids, Bases, and pH

Acids, Bases, and pH
by Dr. Lara Baxley
Cuesta College, San Luis Obispo, CA
Outline
I. Acids
II. Acids in Water
III. Strong vs. Weak Acids
IV. Bases
V. The pH Concept
VI. pH of Strong Acid and Strong Base Solutions
VII. Calculating [H+] and [OH–] from pH
VIII. How CO2 makes water acidic
Introduction
You may have heard that cola drinks are acidic, but what about regular
carbonated water with no other additives? It turns out that carbonated water
has a slightly lower pH than still (not carbonated) water. What does it mean
to have a low pH? How is pH measured and how does it relate to the acidity of a solution? Why
is carbonated water acidic? These are all important questions and you will learn how to answer
them, and more, by the end of this chapter.
Not only is acid-base chemistry important in determining the acidity of your drink, it also plays a
crucial role in biology (have you heard of an amino acid?), atmospheric chemistry (acid rain),
health (Vitamin C is a compound called ascorbic acid), and many other aspects of chemistry. In
this mini-chapter you will learn the basics of acids and bases and how they are related to pH.
I. Acids
An Acid is a substance that donates one or more H+ ions (protons) to another
substance (called a base). Some examples of acids are HCl, H2SO4, and
HC2H3O2. Notice that all of these compounds have at least one H atom in
the front of their formulas. This H atom is donated as an H+ ion when the
acid reacts with a base.
A certain class of acids, called carboxylic acids, are organic
compounds that contain C, H, and O atoms. Acetic acid, HC2H3O2,
is an example of a carboxylic acid. The formulas of carboxylic
acids may be written with the H in front like other acids, or with a –
COOH at the end. The –COOH represents a carboxyl group, which
has the structure shown in Fig. 1. This means that acetic acid, shown
in Fig. 2, can be written either as HC2H3O2 or CH3COOH. Other
examples of carboxylic acids are CH3COHCOOH (lactic acid, exists
in milk) and C6H5COOH (benzoic acid, a food preservative).
Acids, Bases, and pH
Dr. Lara Baxley
Fig. 1 A carboxyl
group characterizes
a carboxylic acid.
Fig. 2 The structure of acetic acid
shows that it is a carboxylic acid
with a –COOH group
pg. 1
II. Acids in Water
In 1887 a chemist named Svante Arrhenius proposed that an acid is a substance that produces
H+ ions in water. Therefore, many chemistry textbooks will show an acid ionizing (separating
into ions) in water. For example, the reaction of HCl in water would be,
HCl(aq) → H+(aq) + Cl–(aq)
Arrhenius model (commonly used)
It has subsequently been discovered that when an acid ionizes in water, the H+ (which is a
proton) actually binds to water molecules to form a hydronium ion, H3O+. In essence, the acid
donates a proton to water. This model is often called the Brønsted-Lowry model after the two
chemists who originally proposed the proton-transfer model of acids and bases. Therefore, it is
more correct to write the reaction of HCl in water as,
HCl(aq) + H2O(l) → H3O+ (aq) + Cl–(aq)
Brønsted-Lowry model (more accurate)
The Brønsted-Lowry model is depicted using molecular models in Fig 3.
Fig. 3 When HCl dissolves in water, a proton (H+) is transferred from the acid to water.
The significance of these two models is that you should understand that a chemist will often use
H+(aq) and H3O+(aq) interchangeably.
Practice Problem 1
Problem: Write the chemical equation for the reaction of nitric acid in water using both the
Arrhenius model and the Brønsted-Lowry model.
(Use this space to write your answer. Don’t peak at the answer until you have tried on your own)
Acids, Bases, and pH
Dr. Lara Baxley
pg. 2
Practice Problem 1 continued
Solution Plan
The formula of nitric acid is HNO3. For the Arrhenius model, dissociate the H+ from the anion
NO3–. For the Brønsted-Lowry model, transfer the H+ to a water molecule.
Answer
Arrhenius Model: HNO3(aq) → H+(aq) + NO3–(aq)
Brønsted-Lowry model: HNO3(aq) + H2O(l) → H3O+(aq) + NO3–(aq)
III. Strong and Weak Acids
For simplification, we will use the Arrhenius model for the rest of this chapter. A strong acid
completely ionizes in water such that every molecule of the acid dissociates into H+ and an
anion, with no intact acid molecules left in the solution. The six strong acids that you are to
memorize for this class are HCl, HBr, HI, HNO3, HClO4, and H2SO4. Strong acids are also
strong electrolytes because they completely ionize in water to form ions that can conduct
electricity. For example, since HCl is a strong acid it will completely ionize in water, and the
chemical reaction would look like this,
HCl(aq) → H+(aq) + Cl–(aq)
(100% to products = Strong acid)
Weak acids, on the other hand, only partially ionize in water, producing a small amount of ions,
but most of the molecules stay intact. Because weak acids produce only a small amount of ions,
they are weak electrolytes and will only slightly conduct electricity. The ions of a weak acid are
in equilibrium with the intact molecules. This means that while molecules are reacting to form
ions, some ions are reacting back to form molecules at the same rate. The equilibrium condition
is depicted as a double arrow in the chemical equation. The equilibrium reaction for the weak
acid HF would be shown as,
HF(aq) ⇌ H+(aq) + F–(aq)
(~99% reactants, ~1% products = Weak acid)
The difference between solutions of HCl and HF is shown in Fig. 4, with water molecules
removed for clarity. Notice that the strong acid solution contains more H+ ions.
Fig. 4 Model of a strong acid and a weak acid dissolved in water
Acids, Bases, and pH
Dr. Lara Baxley
pg. 3
Notice that the two acids shown in Fig. 4 both contain the same concentration of acid, that is the
same number of acid molecules were added per unit volume of solution (in this case 6 HCl or
6 HF molecules were added). Also notice that the strong acid contains a higher concentration of
H+, 6 H+ ions for HCl and only 1 H+ for HF (this doesn’t quite agree with only 1% of HF
molecules dissociating, but to show that we’d need a figure with 100 molecules!).
IV. Bases
When Svente Arrhenius experimented with acids, he also determined that a base is a compound
that produces OH– in water. Strong bases are soluble metal hydroxides like NaOH, Sr(OH)2, and
KOH, and metal oxides, such as Na2O, SrO, and K2O (we will not consider the oxides in the rest
of this chapter). Strong bases completely dissociate in water and are strong electrolytes. For
example, NaOH will dissociate in water according to the equation,
NaOH(aq) → Na+(aq) + OH–(aq)
(100% to products = Strong base)
Weak bases, on the other hand, only partially ionize in water to produce only a few OH– ions.
Weak bases contain nitrogen atoms in their formulas, such as NH3 and CH3NH2. Johannes
Brønsted and Thomas Lowry determined that weak bases produce OH– ions in water by
removing (or accepting) H+ from water molecules. The reaction of ammonia, NH3 with water
looks like this,
NH3(aq) + H2O(l) ⇌ NH4+(aq) + OH–(aq)
(~99% reactants, ~1% products = Weak base)
Practice Problem 2
Problem: Identify each of the following as an acid, a base, or neither. (answer in this space,
then look at the solution)
a. H3BO3
b. HOCH2COOH
c. LiOH
d. CH3OH
Solution Plan
I will recognize an acid because it will have one or more H’s at the beginning or –COOH at the
end (or HOOC– at the beginning). I will recognize bases because they will have a metal and
then OH. If it isn’t an acid or a base, I will assume that it is neutral.
Acids, Bases, and pH
Dr. Lara Baxley
pg. 4
Practice Problem 2 continued
Answer
a. H3BO3
This has three H’s in the front, so it is an acid.
This acid is call boric acid and it can be used as an antiseptic and flame retardant. Since
boron gives off a green flame color, boric acid is also sometimes used in fireworks.
b. HOCH2COOH
This has –COOH at the end, so it is an acid (a carboxylic acid, in fact).
This is call glycolic acid. It readily penetrates the skin and is used in chemical peels.
c. LiOH
Lithium is a metal and this compound is a hydroxide, so this is a base.
I don’t have any interesting facts about lithium hydroxide.
d. CH3OH
This is a tricky one. It looks like a hydroxide with an OH, but remember that CH3 is not
a metal, so this is not a metal hydroxide and therefore not a base. This also is not an acid
because it only has OH, no COOH. This compound is neutral.
This compound is called methanol, but has the common name, wood alcohol. Although
this is closely related to ethanol, which is in alcoholic drinks, don’t drink methanol! It
causes blindness and even death.
V. The pH Concept
pH is a measure of how acidic or basic a solution is. The
concept of pH was first introduced in 1909 by a Danish
chemist name Søren Sørensen. The pH scale ranges from
0 to 14, with 0 being the most acidic and 14 being the most
basic. The pH scale, with pH and corresponding H+
concentration (really H3O+) and examples of various
solutions is shown in Fig. 5. The pH can be calculated
from the H+ (or H3O+) concentration using the equation:
(eqn. 1)
pH = –log[H+] or pH = –log[H3O+]
The brackets indicate molar concentration (units of mol/L
or M), so [H+] means “molar concentration of H+.” The
negative sign shows that the higher the [H+], the lower the
pH. Log indicates how many times 10 is multiplied by
itself to result in the number [H+]. This means that for
every increase in 1 pH unit, there is a 10x increase in [H+].
The logarithmic relationship between [H+] and pH is
shown in Fig 6.
Acids, Bases, and pH
Dr. Lara Baxley
Fig. 5 The pH Scale
pg. 5
Fig. 6 pH is a log scale such that for
every 1 pH unit change, the H+
concentration changes 10-fold.
Practice Problem 3
–
Problem: Calculate the pH of a solution with an H+ concentration of 3.20 x 10 3 M (perform this
in your calculator to make sure that you get the right answer).
Solution Plan
Use the pH formula given in eqn. 1, pH = –log[H+]
Solution
pH = –log[H+] = –log(3.20 x 10–3)
pH = 2.49
*note: we will not worry about significant figures for pH in this class. Provide all pH’s to 2 decimal points and all
concentrations with 3 significant figures.
V. pH of Strong Acid and Strong Base Solutions
The example above shows how to calculate the pH of a solution if you know the concentration of
H+, but how do you calculate the H+ concentration of a given acid or base solution? The answer
is that it depends on the compound. In this class, we will only consider the pH of strong acids
and strong bases. Calculations involving weak acids and bases will be covered in Chem 201B.
For a strong acid, since the acid completely dissociates into H+ and an anion, all moles of acid
become H+. Therefore, for a strong acid: [H+] = [strong acid]. For example, Fig. 7 shows that 6
HCl molecules produce 6 H+ ions.
Fig. 7 For every molecule of a strong acid added to water, one H+
ion is formed, so that [H+] = [strong acid].
Acids, Bases, and pH
Dr. Lara Baxley
pg. 6
Practice Problem 4
Problem: Calculate the pH of 0.035 M HClO4 (perform this in your calculator to make sure that
you get the right answer).
Solution Plan
Since HClO4 is a strong acid, it completely dissociates into H+ + ClO4–. Therefore,
[H+] = [HClO4]. This means that the given concentration can be used in eqn. 1 to solve for pH.
Solution
[H+] = [HClO4] = 0.035 M
pH = –log[H+] = –log(0.035)
pH = 1.46
Strong bases completely dissociate into cation and OH– ions. The first step in calculating the pH
of a strong base is to determine concentration of OH– ions. Some strong bases will produce more
than one OH– ion for each formula unit of the base. For example, Ca(OH)2 will dissociate in
water according to the chemical equation,
Ca(OH)2(aq) → Ca2+(aq) + 2 OH–(aq)
The mole ratio in this reaction shows that for every 1 mole of Ca(OH)2 dissolved in water, 2
moles of OH– will be produced. Therefore, for strong bases with 2 OH– ions per formula unit,
[OH–] = 2 x [base]. Hydroxides with 3 OH– ions per formula unit are not soluble in water, so
we do not need to consider them. Once you have determined the [OH–] in the basic solution,
there are two methods for calculating pH. These two methods use the following equations,·
(eqn 2)
pOH = –log[OH–]
(this is just like the pH equation, but with OH–)
(eqn 3)
[H+]•[OH–] = 10–14
(this is a constant for water solutions at 25 °C)
(eqn 4)
pOH + pH = 14
(this is derived by taking –log of both sides of eqn. 3)
If you know [OH–] and you wish to calculate pH, you choose one of the following methods;
Method A
1. Use eqn. 3 to calculate [H+]
2. Then use eqn. 1 to calculate pH
Method B
1. Use eqn. 2 to calculate pOH
2. Then eqn. 4 to calculate pH
Acids, Bases, and pH
Dr. Lara Baxley
pg. 7
Either method will give you the same answer, so the choice is yours. Method B will be
demonstrated in the following examples.
Practice Problem 4
Problem: Calculate the pH the following solutions. (Solve on your own before looking at the
solutions)
a. 2.08 x 10–5 M KOH
b. 0.00755 M Ca(OH)2
Solution Plan
First calculate the [OH–] from the given base concentration and number of OH– ions per formula
unit. Then, use the [OH–] to calculate pOH using eqn 3. Finally, calculate pH from the pOH and
eqn. 4
Answer
a. 2.08 x 10–5 M KOH
KOH has one OH– in the formula, so [OH–] = [KOH] = 2.08 x 10–5 M
pOH = –log(2.08 x 10–5) = 4.6819
pH = 14 – pOH = 14 – 4.6819 = 9.3181 = 9.32
b. 0.00755 M Ca(OH)2
Ca(OH)2 has 2 OH– in the formula, so
[OH–] = 2 x [Ca(OH)2] = 2 x 0.00755 M = 0.0151 M
pOH = –log(0.0151) = 1.8210
pH = 14 – pOH = 14 – 1.82102 = 12.17898 = 12.18
Acids, Bases, and pH
Dr. Lara Baxley
pg. 8
VII. Calculating [H+] and [OH–] from pH
In the previous examples, we learned how to calculate pH given the concentration of a strong
acid or strong base solution. In addition to calculating pH of a solution, one can also measure the
pH of a solution directly using pH strips or a pH meter. Once the pH is measured, one may wish
to use this information to calculate the concentration of H+ or OH– in the solution. This can be
done by taking the anitlog (or 10x) of the pH or pOH equations given in eqns. 1 and 3. The
antilog equations are,
(eqn 5)
(eqn 6)
[H+] = 10–pH
[OH–] = 10–pOH
The method for using these equations is shown in the following example.
Practice Problem 5
Problem: What are the [H+] and [OH–] in a solution with a pH of 11.25? (Solve on your own
before looking at the solutions)
Solution Plan
To calculate [H+], use eqn 5 above. Calculating [OH–] can be done in one of two ways. My
preferred method is to use eqn. 4 (pH + pOH = 14) to calculate pOH and then eqn. 6 to calculate
[OH–].
Answer
Calculate [H+]: [H+] = 10–pH = 10–11.25 = 5.62 x 10–12 M H+
Calculate pOH: pOH = 14 – pH = 14 – 11.25 = 2.75
Calculate [OH–]: [OH–] = 10–pOH = 10–2.75 = 1.78 x 10–3 M OH–
VII. How CO2 makes water acidic
Look at the pH scale in Fig. 5. Notice that rain water has a pH of about 5. This often confuses
people who have been taught that water is neutral and should have a pH of 7. The reason that
rain water is slightly acidic is because CO2 from the atmosphere dissolves in natural water and
Acids, Bases, and pH
Dr. Lara Baxley
pg. 9
makes the water acidic. This is also why carbonated beverages are acidic, even if no other
compound has been added to the water. Earlier in this chapter, you learned that acids can be
identified as have either an H in front of their formula or –COOH at the end of their formula.
CO2 has neither of these, so how can CO2 make water acidic? The reason is that CO2 actually
reacts with the water to make carbonic acid, H2CO3, which is an acid. The chemical equation for
this reaction is,
CO2(aq) + H2O(l) ⇌ H2CO3(aq)
Although this is an equilibrium reaction that will reverse to form the reactants, the product,
carbonic acid, is an acid that will ionize to form H+, which will lower the pH of the water.
Student Learning Outcomes
You now know a little more about acids, bases, and how the acidity of a solution is related to pH.
You not only know how CO2 makes water acidic, but you should also be able to,
1. Identify a compound as being either a strong acid, weak acid, strong base, or weak base
from its formula.
2. Write the chemical equation representing the reaction of an acid or a base in water.
3. Determine which of a pair of solutions will have more ions, a strong acid vs. a weak acid,
or a strong base vs. a weak base.
4. Determine the concentration of H+ ions and OH– ions in a given concentration of a strong
acid or strong base.
5. Calculate the pH of a given solution of a strong acid or strong base.
6. Calculate the concentration of H+ and OH– ions in a solution with a given pH.
Photo credits
Fruit: http://myskin-coach.com/2013/01/14/does-skin-need-fruit-acids-everyday/
pH strips: David Gould, Getty Images (found on about.com)
Baking soda: http://naturesnurtureblog.com/2012/08/13/
Carbonated water: http://www.wisegeek.com/what-is-carbonated-water.htm
Fig. 1: Carboxyl group structure: unknown source
Fig. 2: Acetic acid: wikipedia.com
Fig. 3: HCl in water: modified from http://www.quarkology.com
Fig. 4: Strong vs Weak Acids: Lara Baxley, Cuesta College
Fig. 5: The pH Scale: unknown source
Fig. 6: Relationship between pH and [H+]: Lara Baxley, Cuesta College
Fig. 7: Number of H+ ions formed in a strong acid solution: Lara Baxley, Cuesta College
Acknowledgement
I wish to thank my husband and colleague, Dr. Greg Baxley, for reviewing and editing this
document.
Acids, Bases, and pH
Dr. Lara Baxley
pg. 10