Chapter 8

Acids and Bases

Mathematical Preliminary

• Logarithms – a logarithm is an exponent on some base.

• Two most frequently used bases for logarithms:– 10 (called common logarithms, usually shown as

log10 X or log X)– e (called natural logarithms. e is an irrational number

like usually written as ln Xe = 2.71828…

• In our application of logarithms, we will use the common logarithm (on base 10).

Common Logarithms

• Base 10 works very well with scientific notation.

• Recall scientific notation is of the form

factor x 10p

Where “factor” is a number and < 10.

The number “p” is the power (exponent) of 10.

Logarithms are exponents

• Since “factor” is between 1 and 10, its logarithm is the power of 10 that will generate “factor”. It will be a number that is < 1 but will be

• Example, consider number 4.12 x 104

• Its logarithm will be 4.6149.• How did I get this?• First – review properties of exponents.

Exponent properties

• Multiplying numbers in exponent form – if they have the same base, you add exponents.

• Dividing numbers in exponent form – if they have the same base, you subtract exponents.

• Raising a number to a power (or taking a root) multiply exponent by power (or fraction for a root) and put over the same base.

Examples of exponent arithmetic

How did I find log (4.12 x 104) ?

What if the power of 10 is negative?

How do I handle log(4.12 x 10-4) ?

Antilogs

• An antilog is finding the number corresponding to the given logarithm.

• Suppose we have a value of 5.7743 and it is a logarithm. What is the number corresponding to it?

Another example of antilogs

• Suppose we have number -6.3314, and we are told that it is a logarithm. What is the number corresponding to it?

pH and Logarithms

• We review logarithms because pH is a property based on taking the common logarithm of the hydrogen (hydronium) ion concentration.

• We need to be able to take a concentration and express its pH and do the reverse.

Acid-Base Concepts

Acids and Bases – Arrhenius concept

• Arrhenius (Svante Arrhenius of Sweden was one of the three founding fathers of physical chemistry in the late 1800’s. He along with J.H. van’t Hoff in Holland and Wilhelm Ostwald in Germany are credited with being the founding fathers of physical chemistry).

• Acid produces H+, Base produces OH-

Arrhenius concept -- examples

Acids and Bases – Bronsted Lowry Concept

• Acid donates proton. Base accepts proton.• Leads to concept of conjugate acids and bases

(used for understanding buffers).• When an acid loses a proton, what is left is its

conjugate base.• When a base picks up a proton, the new ion is

its conjugate acid.• Acid-base reactions go from a stronger acid,

stronger base pair to a weaker acid, weaker base pair.

Bronsted Lowry Acid / Base

• Useful for thinking about buffers since a buffer will consist of an acid and its conjugate base or a base and its conjugate acid.

• The stronger the acid, the weaker its conjugate base. The weaker the acid, the stronger its conjugate base.

• The stronger the base, the weaker its conjugate acid. The weaker the base, the stronger its conjugate acid.

Bronsted Lowry examples

Lewis Acid / Base Model

• A large generalization of the idea of acids and bases. Not in the book since it is not as generally useful for talking about aqueous systems.

• Acid is an electron pair acceptor• Base is an electron pair donor• G.N. Lewis is the originator, the same

person who gave us Lewis dot structures of atoms.

Lewis examples

Why is a solution acidic, basic, or neutral?

• Based on the ionization of water.

• Generates an equilibrium constant

• At 25 deg C,

2 2 3H O H O H O OH

143[ ][ ] 1.0 10wK H O OH

Note on chemical equilibrium

• Chemical equilibria are dynamic. This means that the rate of reaction going to the right is exactly balanced by the reverse reaction. There is no net change in composition, although the ions and molecules are continually replacing themselves. If we could tag the atoms and molecules, we would find (1) no net change in population, but (2) changing “actors” in the process (like double casting for an opera or play).

pH and acidity

• Begin with the previous equation

• Take logarithm of both sides

• Multiply through by -1.

143[ ][ ] 1.0 10wK H O OH

143log( ) log( ) log( ) log(1.0 10 ) 14wK H O OH

pH and acidity

• We get

• Or

• pH + pOH = 14

• Where the function p indicates “taking the negative of the logarithm of the quantity”

3log( ) log( ) 14H O OH

pH and acidity

• pH values <7 indicate acid solution. The smaller the pH value, the more acid the solution.

• pH values >7 indicate alkalinity (basic solution). The bigger the pH value, the more basic the solution.

examples