INTRODUCTION:
A weak acid, symbolized HA, is one which is
only slightly ionized in water, i.e., exists in equilibrium with its ions
(equation 1).

HA(aq)
H^{+}(aq) + A^{-}(aq)
(1)

The equilibrium constant for
this reaction is given by the law of mass action:

K_{a} = __[____H__^{+}__]
[A__^{-}__] __
(2)

[HA]

where the square brackets signify
that the concentrations are those existing at equilibrium. A convenient form of
this equation may be derived if one first takes the common logarithm of both
sides:

log K_{a } =
log[H^{+}] + log([A^{-}]/[HA])
(3)

__Definition__: pX = -log_{10}X, where X may be a variable or
a constant. The pH of a solution is thus defined to be equal to -log_{10}[H^{+}]. Substituting into equation
3 now yields

-pK_{a}_{ } =
-pH + log([A^{-}]/[HA])
(4)

Rearrrangement of equation 4 gives the **Henderson-Hasselbalch equation**:

pH = pK_{a}
+ log([A^{-}]/[HA])
(5)

This equation serves as the
basis for the determination of the ionization constant, K_{a}. Inspection of equation 5 reveals that it has
the form of the equation of a straight line, where the pH depends upon the
value of log([A^{-}]/[HA]). We will prepare
solutions with five different values of the ratio [A^{-}]/[HA]. The amounts of the conjugate base and unionized acid
are adjusted by partial neutralization of the acid with standard base solution:

HA(aq)
+ ^{-}^{-}(aq) + H_{2}O(l)
(6)

The pH values of the five
solutions will be measured (read about the use
of a pH meter), and graphical analysis using linear regression techniques
will then be applied to provide a statistically more valid value of pK_{a} than a single determination would provide.
By having five measurements instead of only one and using a best-fit line, the
individual random errors will average out.

PRE-LAB
QUESTIONS:

1. Briefly describe the
electrode and the quantity that is actually measured by the pH meter.

2. What buffer solution is
used in addition to the pH 7 buffer for calibration of the meter when acidic
solutions are to be measured?

3. What are the practical
limits for temperature of solutions when using a pH meter?

4. State two reasons why
it would be inappropriate to use the pH meter to measure the pH of a 12 ** M**
NaOH solution.

EQUIPMENT: 25-mL pipet, 50-mL burette, 10- and 100-mL graduated cylinders, five 150- or 250-mL beakers, wash bottle, pH meter.

EXPERIMENTAL: ** Caution**: KOH is a caustic
substance, and the weak acids are also corrosive. If any of these substances is
spilled on the skin, immediately rinse thoroughly with large amounts of water.
Be sure to wear your goggles.

Record the **identification
code** of your unknown acid and the **concentrations** of all reagents.
Make up the five solutions using the amounts listed in Table I. Measure
carefully, using a __pipet__ to measure the acid,
a __burette__ for the base, and __graduated__ __cylinders__ for the
sodium perchlorate. This last reagent is used to
provide a constant ionic strength, necessary for the pH measurements. Mix all
of the solutions thoroughly.

The pH measurements may be made
in the original beakers. Do not move any controls on the pH meter except as
directed. With the meter on standby (some models of pH meters do not have a
standby mode), rinse the electrode with deionized
water, gently shake off the excess water, and immerse the electrode in the
sample solution. Switch the meter to the pH mode, allow the reading to
stabilize, and record the pH. Switch the meter back to the standby mode, rinse
the electrode again, and leave the electrode immersed in deionized
water. Repeat this procedure for all five solutions.

Solution |
mL HA |
mL KOH |
mL NaClO |

1 |
25.00 |
5.00 |
25.0 |

2 |
25.00 |
10.00 |
20.0 |

3 |
25.00 |
15.00 |
15.0 |

4 |
25.00 |
20.00 |
10.0 |

5 |
25.00 |
25.00 |
5.0 |

CALCULATIONS: Carry out all calculations in terms of
milliliters and millimoles; note that 1 mol/L = 1 mmol/mL. Set up a table showing initial mmols
HA, initial mmols KOH, final mmols
HA, final mmols A^{-}, [A^{-}]/[HA], and log([A^{-}]/[HA]) for each solution. Use
equation 6 to determine the respective values of these quantities. Explain in
detail the calculations for solution 1 in your report, including your reasoning
as well as the actual numerical calculations. The remainder of the calculations
may be done using the spreadsheet software.

Carry out a spreadsheet
regression analysis using Excel to determine the value of pK_{a}.
Report this value **and its uncertainty** and calculate the value of K_{a}.
Use the spreadsheet program to draw a graph of pH vs. log([A^{-}]/[HA]).
Plot the experimental points and the best-fit line. Be sure to scale the
graph such that the data points fill the page as much as possible.

Obtain the identity of your
unknown acid from the instructor. Look up the literature value of K_{a}
(reference it) and determine the percent error in your determination of the K_{a}
and **pK _{a}**. Is the true pK

REPORT: Write a formal report for today’s experiment.