Concise Physical Chemistry

c13 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

PROBLEMS AND EXAMPLES 215

for the acid. The acidity (ionization) constant is

lnKa=2lnγ±+lnK

lnKa= 2

(

− 1. 172

√

αm

)

+lnK=− 2. 34

√

αm+lnK

or

lnK=− 2. 34

√

αm+lnKa

AplotoflnKvs.

√

αmgives an intercept of lnKaand has a limiting slope of 2.34

asα→1. Asmbecomes very small, the middle term of lnK= 2. 34

√

αm+lnKa

drops out and the measured value ofKapproachesKa.

PROBLEMS AND EXAMPLES

Example 13.1

Suppose you have access to a well-equipped electrochemistry laboratory but you do

not know the value of the faraday. How would you determine the value of the faraday

to four significant figures?

Solution 13.1 To work the problemde novowould be a pretty hard job. Remember,

Faraday was a genius. When you electrolyze different solutions, however, you will

soon find that many metals including silver can be plated out on an electrode by

passage of current through a solution of, for example, silver nitrate. A coulomb is

an ampere second. The idea is this: Measure the current flowItimes the timetin

seconds to force the quantityQof electricity in coulombs through an electrolysis cell

to plate the silver. Then measure the number of moles of silver that have been plated

out. The fractionI×t/moles Ag gives the faraday in coulombs mol−^1. Your first try

at this method will probably be unsuccessful because the faraday is a big number.

It takes more electricity than you might guess to deposit an amount of silver that is

measurable to four figures of accuracy.

Many electrochemical laboratories are equipped with a variety ofpotentiostatsthat

maintain a constant voltage across an experimental cell andamperostatsthat maintain

a constant current. For our purposes, an amperostat would be most convenient because

integration to find the area under anIvs.tcurve would merely be multiplying constant

Iinto the time. Both of these measurements should be possible with high accuracy.

Silver has been known for many years to be plated out in 100%current efficiency,

so if we multiply ourImeasurement into the time of electrolysis, both measured

digitally, we get the number of coulombs passed through the cell. We can then weigh

the silver electrode and find out how much it has increased in weight due to the silver

deposited.

To get a rough idea of the parameters involved, suppose we have a microbalance

sensitive and accurate enough to weigh to±0.01 mg. A silver weight of 0.2 g would