The chemicals   A & B can combine (in solution) to form the compound AB.

<p>A + B &#8652; AB
<p>In 1873 J.W. Gibbs proposed that in an equilibrium of the reaction product AB with the two reactants,
the (Gibbs) free energy was minimized.  Since (for dilute solutions)
the Gibbs free energy is related to the logarithm of concentration,
he derived that

<p>
[AB]/([A] [B]) = constant = <em>K</em>


<p>where [x] denotes the concentration (e.g., in moles/L) of the compound x

<p>In an experiment to test this hypothesis a beaker with a fixed amount
of B is prepared and incremental amounts of A are added.
The fraction of B in the bound state (<em>y</em>) is then measured (by colorimetry)
as a function of the A concentration (<em>x</em>).
The bound-fraction measurements
have an accuracy of 0.02&nbsp;; the measurements of [A] are believed to have negligible error.

<p>If Gibbs hypothesis is correct, a bit of algebra shows:


<p>
<em>y</em> = [AB]/([AB]+[B]) = 1/(1+1/(<em>K x</em>))

<p>or


<p>1/<em>y</em> = 1 + 1/(<em>K x</em>)

<p>So Gibbs predicts that the data can be fit by an "inverse <em>x</em> &amp; <em>y</em>"
relationship where <em>A</em> is expected to be 1 and <em>B</em> is expected to be
<em>1/K</em>.

<ol>
<li>Fit this data with an  "inverse <em>x</em> &amp; <em>y</em>" relationship.
<li>Consider Gibbs scientific claim for his equilibrium law.
Does this evidence (data) confirm or contradict this claim?  Support
your answer quantitatively.
<li>Properly report (sigfigs, error, units) the <em>A</em> and <em>B</em>
parameters of the best-fit relationship.
<li>Use a spreadsheet to calculate the equilibrium constant <em>K</em>.
Find the error in <em>K</em> using the "high-low" method.
<li> Properly report 
(sigfigs, error, units) the value for <em>K</em>. 
<li>Self-document the spreadsheet and turn in a hardcopy of the page.
<li>Make a hardcopy plot of the data with best-fit curve.
Make an additional hardcopy plot
with scales chosen so as to linearize the curve.
</ol>
<p><table style="text-align: center; width: 300px;" border=1 cellpadding=2 cellspacing=2>
 <tr><th>X<br>(nM/L)<th>Y<br>unitless
 <tr><td>10<td>0.13
 <tr><td>20<td>0.25
 <tr><td>50<td>0.45
 <tr><td>100<td>0.52
 <tr><td>200<td>0.74
 <tr><td>500<td>0.90
 <tr><td>1000<td>0.91
 <tr><td>1500<td>0.96
 </table>