Experimentally, we can exploit the relationship between 
and 
to measure 
and 
for a reaction. Recall from Section 4.2 that, at constant temperature,
and
.
Equating these two formulae gives
.
Dividing both sides by -RT and rearranging gives
(Equation 1).
Thus, if we measure the equilibrium constant, , for a reaction at different temperatures, 
, and plot 
as the y values and 
as the x values, the result should be a straight line. Such a plot is called a van't Hoff plot. The generic equation for a straight line is 
, where 
is the slope and 
is the y intercept. Comparing this generic equation with Equation 1, above, shows that when 
and 
, the slope of the line is
and the y-intercept is
.
Van't Hoff plots are useful ways to experimentally measure 
and 
using the slope and intercept of the line.
Note that both and vary with temperature and yet van't Hoff plots are constructed using a range of temperatures. The values of and are much less sensitive to temperature than 
, so it is reasonable to assume that and are approximately constant over reasonable temperature ranges. We will know if the temperature range of a van't Hoff plot is not 'reasonable' enough to make this assumption if the experimental data points connect to form a curve rather than a straight line. In CHEM 123, the temperature ranges given with van't Hoff plots will always be 'reasonable'.
Example: What are
and
for a van't Hoff plot with a best fit line of
?