# Equilibrium Expression Problems, cont.

### Pressure vs. Concentration in Equilibria

In gas phase equilibria we can use either concentrations or pressures, since by the Ideal Gas Law P = (n/V)RT = [ ] RT

So how are the K's for concentration and pressure related? It turns out that this depends on the stoichiometry. If the sums of the coefficients on both sides are equal, then K = KP. More generally (see derivation in Zumdahl 7th, p 602-3), KP = K(RT)n, where n = the number of moles appearing on each side of the stoichiometric equation, and n = nproducts - nreactants.

Example: For the reaction 2 NOCl(g) 2 NO(g) + Cl2(g) , K = 3.75 x 10-6 @ 796°C

Calculate the pressure equilibrium constant, KP.

n = nproducts - nreactants = (2 + 1) - 2 = 1

KP = Kc(RT)n = (3.75 x 10-6){(0.0821)(796 + 273)}1 = 3.29 x 10-4

# Acids and Bases

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

• 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-Lowry or 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.
• 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.
• A consequence of the Brønsted definition is that all acids and bases are related to one or more conjugate bases or conjugate 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.
• (Another common strong acid is Perchloric acid, HClO4 . We do not use this acid in lab however, because of its potential to become explosively unstable.)
• 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)
• All of the other alkali metal hydroxides are also strong, but less common because of their higher cost.
• Alkaline earth hydroxides also tend to be strong, but even though they are 100% dissociated, they are not generally soluble enough to give 1 M hydroxide.
• A Weak Base only partly reacts at 1M. The degree of dissociation varies widely, from a few percent to an infinitesimal degree. Common weak acids include:
• Ammonia (NH3)
• Organic amines (RNH2, where R- is some organic group, e.g. CH3-)
• Metal hydroxide of very low solubility are often included as weak bases, such as:
• Aluminum hydroxide (Al(OH)3), solubility = 1 x 10-8 M
• Magnesium hydroxide (Mg(OH)2), solubility = 3 x 10-4 M

# The pH Scale

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 from 10-14M - 1M. 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+]

Because of the equilibrium dissociation of water to H+ + OH-, the concentration of hydrogen ion in water is related to the concentration of hydroxide ion:

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:

Kw= [H+][OH-] = 1.0 x 10-14 @ 25 °C

Let's look at some general characteristics of pH in aqueous solution.

• Range: pH = -1 to pH = 15 (10M -10-15M)
• for 1 M HCl, pH = 0
• for 1 M NaOH, pH = 14
• At midrange [H+] = [OH-] = 10-7M. The solution is said to be "neutral."
• This follows in aqueous solution from Kw = 1.0 x 10-14 = [H+] [OH-], thus if [H+] = [OH-], then [H+] = (1.0 x 10-14)1/2= 1.0 x 10-7
• Low pH means acidic:
• For 1M strong acid, pH = 0.0 (log 1 = 0)
• For 0.1M strong acid, pH = 1.0
• 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) = 14.0.
• For 0.1 M OH-, (1.0 x 10-14) / 0.1 = 1.0 x 10-13 and pH = -log(1.0 x 10-13) = 13.0.
• For 10-7M OH-, (1.0 x 10-14) / (10-7) = 1.0 x 10-7 and pH = -log(1.0 x 10-7) = 7

Examples:

• What is the pH of a solution of 0.015 M HCl?
Strong acid, so [H+] = 0.015 M
pH = - log [H+]
pH = - log 0.015 = - (- 1.824)
pH = 1.82

Note that the significant figures are correct, 1 is the power of ten, only the figures to the right are significant.

• What is the pH of a solution of 0.067 M NaOH
Strong base, so [OH-] = 0.067 M
Recall that [H+][OH-] = 1.0 x 10-14
Substituting, [H+][0.067] = 1.0 x 10-14
Rearranging, [H+] = (1.0 x 10-14) / 0.067 = 1.493 x 10-13
pH = - log (1.493 x 10-13) = - (- 12.83)
pH = 12.83
Again note the significant figures - 12 corresponds to the power of ten, only the figures to the right are significant.

Note that the "p" has the more general meaning of "-log[]". Thus pOH is -log [OH-], pCa = -log [Ca2+], etc.

## pH of weak acid solutions

Weak acid dissociations involve equilibria. The equilibrium constants have a specific symbol = Ka.

Example: What is the pH of a 0.10 M solution of acetic acid. Ka = 1.8 x 10-5

 HOAc H+ + OAc- Before reaction 0.10 M 0 0 @ Equilibrium 0.10 M- x x x

Ka = [H+][OAc-] / [HOAc]

assume x << 0.1 since Ka =1.8 x 10-5, then [HOAc] = 0.10 M

Substituting, Ka = (x)(x) / 0.10 = 1.8 x 10-5,

x2 = 1.8 x 10-6

x = 1.34 x 10-3M; assumption OK.

pH = - log (1.34 x 10-3) = 2.87

Notice the significant figures. For a log function the number in front of the decimal is the exponent of ten, thus pH = 2.87 is a 2 significant figure number.

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