26.07.2021 Views

General Chemistry Principles, Patterns, and Applications, 2011

General Chemistry Principles, Patterns, and Applications, 2011

General Chemistry Principles, Patterns, and Applications, 2011

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

It is important to remember that when a graphical procedure is used to calculate a slope, the scale on each axis must<br />

be of the same order (they must have the same exponent). For example, although acceleration is a change in velocity<br />

over time (Δv/Δt), the slope of a linear plot of velocity versus time only gives the correct value for acceleration (m/s 2 )<br />

if the average acceleration over the interval <strong>and</strong> the instantaneous acceleration are identical; that is, the acceleration<br />

must be constant over the same interval.<br />

Log-Linear Graphs<br />

A log-linear plot is a representation of the following general mathematical relationship:<br />

y = Acmx<br />

Here, y is equal to some value Ac when x = 0. As described in Essential Skills 3 inChapter 4 "Reactions in<br />

Aqueous Solution", Section 4.10 "Essential Skills 3", taking the logarithm of both sides produces<br />

log y = log A + mx log c = (m log c)x + log A<br />

When expressed in this form, the equation is that of a straight line (y = mx + b), where the plot of y is on a<br />

logarithmic axis <strong>and</strong> (m log c)x is on a linear axis. This type of graph is known as a log-linear plot. Loglinear<br />

plots are particularly useful for graphing changes in pH versus changes in the concentration of<br />

another substance. One example of a log-linear plot, where y = [HA] <strong>and</strong> x = pH, is shown here:<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

968

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!