Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 109 - General Chemistry - Spring 2011

Lecture Notes 38: 27 April

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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)deltan, where n = the number of moles appearing on each side of the stoichiometric equation, and deltan = nproducts - nreactants.

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

Calculate the pressure equilibrium constant, KP.

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

KP = Kc(RT)deltan = (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).

        H2O right arrow  H+  + OH- 
         acid       conj. base
                 
     H+ +  OH-  right arrow  H2O  
        base    conj. acid    
                 
 H3O+
  left arrow
 H+  +  H2O  right arrow  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:

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 equilibrium arrow 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.

Examples:

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  equilibrium arrow 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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© R A Paselk

Last modified 27 April 2011