Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 107
Fundamentals of Chemistry
Fall 2008

Lecture Notes: 9 December
© R. Paselk 2005

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*Humboldt State University* ® *Department of Chemistry*

Richard A. Paselk
Chem 107	Fundamentals of Chemistry	Fall 2008
Lecture Notes: 9 December	© R. Paselk 2005

*PREVIOUS*		*NEXT*

The Equilibrium and Mass Action Expressions, cont.

A very common type of reaction is one in which a dissociation takes place.

Example: Consider the gas phase dissociation of carbonyl chloride to carbon monoxide and chlorine @ 100 °C.

If 0.20 moles of carbonyl chloride (COCl₂) is placed in a 2.5 L container at 100 °C calculate the concentrations of all species at equilibrium. K_eq = 2.6 x 10^-10 @ 100 °C. (Notice the very small value of K_eq. This indicates that this reaction will not progress very far towards products, rather it will stay mostly in the form of the initial reactant.)

Heterogeneous Equilibria

So far our discussion has dealt only with homogeneous systems, that is all of the components are in the same phase. What about heterogeneous systems where the components occupy different phases. For example look at the gas/solid system below:

CaO_(s) + CO_{2 (g)} CaCO_{3 (s)}

We can write the equilibrium expression for this reaction as normal:

K = [CaCO_{3 (s)}] / [CaO_(s)][CO_{2 (g)}]

The problem is, what is the concentration of the solids? In a sense each is dissolved in itself and does not change during the reaction (the particles can get larger or smaller, but the concentrations remain constant). It turns out, for theoretical reasons we won't go into, the activity or "behavioral concentration" in the pure state is 1. Thus we can put in the concentration of 1 for each solid:

K_eq = [1] / [1][CO_{2 (g)}]

K_eq = 1/[CO_{2 (g)}]

So the equilibrium expression depends only on the concentration of the gas phase, in this case carbon dioxide, and the amounts of solid reactants and products is inconsequential!

Consider the equilibrium of calcium carbonate dissociating to calcum ion and carbonate ion:

CaCO_{3 (s)} Ca²⁺ + CO₃^2-

Find the solubility if K = 8.7 x 10^-9

Note the solubility will be the amount of calcium or carbonate ion, since that much calcium carbonate must have dissolved to produce them!

K = [Ca²⁺] [CO₃^2-] / [CaCO_{3 (s)}] ; but recall that for a solid, M = 1, so rewriting

K = [Ca²⁺] [CO₃^2-] = 8.7 x 10^-9

and [Ca²⁺] = [CO₃^2-] = (8.7 x 10^-9 )^1/2= 9.3 x 10^-9 M = Solubility

Acids and Bases

What are acids and bases? There are three major definitions. We will look at two in which the proton is a major defining component (the third, Lewis definition, is not needed for our study).

(Although I will signify protons in water as H⁺, you should realize that naked protons do not exist in water - they are always hydrated. At a minimum we see the hydronium ion, H₃O⁺. But hydronium ion is in fact also generally thought to be hydrated, so you will sometimes see hydrogen ion represented as H₅O₂⁺, H₇O₃⁺, etc.)

Arrhenius Definition:

Acids release protons (H⁺) into water.

Bases release hydroxide ions (OH^-) into water.

This is very limited - it only deals with acids and bases in water, and many substances which chemists and others think of as bases (such as ammonia) don't fit the definition. Thus we will focus on the Brønsted-Lowry definition (Brønsted definition in abbreviation):

Brønsted Definition:

Acids are proton donors.

Bases are proton acceptors.

Note that there is no restriction as to solvent, and many substances besides hydroxide ion can contribute basicity.

A consequence of the Brønsted definition is that all acids and bases are related to one or more conjugate bases or acids. That is, when an acid dissociates to give a proton, it also generates a conjugate base which can react with (accept) a proton in the reverse reaction. For example, in the case of water:

H₂O H⁺ + OH^-

acid conj. base

H⁺ + OH^- H₂O

base conj. acid

H₃O⁺ H⁺ + H₂O OH^- + H⁺

conj. acid

acid

base
conj. base

Strong vs. Weak Acids & Bases

These terms have nothing to do with concentration, rather they refer to the degree of dissociation of an acid or base:

A Strong acid is 100% dissociated at all concentrations up to 1M. Common strong acids include:
- Nitric acid (HNO₃)
- Hydrochloric acid (HCl)
- Sulfuric acid (H₂SO₄) for the first dissociation only: H₂SO₄ HSO₄^- + H⁺. The second dissociation is weak, that is it hardly dissociates at 1M.
A Weak acid is only partly dissociated at 1M. The degree of dissociation varies widely, from a few percent to an infinitesimal degree. Common weak acids include:
- Acetic acid (HC₂H₃O₂ or CH₃CO₂H, etc.)
- Formic acid (HCO₂H)
- Hydrofluoric acid (HF)
- Most acids of biological origin such as amino acids, fatty acids, metabolites, nucleic acids etc.
A Strong base is 100% dissociated at all concentrations up to 1M. Common strong bases include:
- Sodium hydroxide (NaOH)
- Potassium hydroxide (KOH)
A Weak base is only partly dissociated at 1M. The degree of dissociation varies widely, from a few percent to an infinitesimal degree. Common weak acids include:
- Ammonia (NH₃)
- Aluminum hydroxide (Al(OH)₃)
- Magnesium hydroxide (Mg(OH)₂)

Aqueous Hydrogen Ion Concentration and pH

The concentration of hydronium ion in water is extremely influential on all kinds of chemistry. The range of hydronium ion concentration in water is also vast, with extremes of about 10M to about 10^-15M, and commonly ranging from 1M - 10^-14M. Imagine plotting [H₃O⁺] vs. volume of acid added to a base solution in a titration. If you had one cm on the graph paper = 10^-14M, then you would need a piece of paper 10⁹ km long (greater than the distance from the Sun to Jupiter) to plot this titration! Obviously a more convenient measure is needed. This is easily accomplished by looking instead at the logarithm of [H⁺] and defining a new term,

pH = -log[H⁺]

Turns out that the concentration of hydrogen ion in water is related to the concentration of hydroxide ion due to the equilibrium dissociation of water:

H₂O

H⁺ + OH^-, so

K = [H⁺][OH^-] / [H₂O]

But the concentration of water remains essentially the same in dilute solution,

so by convention we define the dissociation constant or ion product for water:

K_w= [H⁺][OH^-] = 1.0 x 10^-14 @ 25 °C

pH

Let's look at pH a bit:

Low pH means acidic:
- For 1M strong acid, pH = 0 (log 1 = 0)
- For 0.1M strong acid, pH = 1
- For 10^-7M H⁺, pH = 7
High pH means basic:
- For 1M strong base, pH = 14 ([H⁺] = (1.0 x 10^-14) / [OH^-] = (1.0 x 10^-14) / 1 = 1.0 x 10^-14 and pH = -log(1.0 x 10^-14) = 14.
- For 0.0010M [OH^-], pH = 11.00 (Note significant figures: the digits to the left of the decimal are the power of 10, so are NOT significant, only the digits to the right are significant. Thus the 2 s.f. concentration, 1.0 x 10^-3 gives .00 for 2 s.f.