diff --git a/science-of-cleaning.tex b/science-of-cleaning.tex
index 0dabbf6..3debeab 100644
--- a/science-of-cleaning.tex
+++ b/science-of-cleaning.tex
@@ -263,10 +263,34 @@ In both of these examples, the values are getting closer to seven, which means t
 
 \subsection{The Chemistry of pH}
 
+From a chemical point of view, pH is the inverse logarithm of the concentration of \ch{H+} ions. If you survived high school or college chemistry, you might remember this equation:
 
+\begin{align*}
+\text{pH} = -\log_{10}[\text{H}^+]
+\end{align*}
+
+The square brackets around the \ch{H^+}—that is, \ch{[H^+]}—just mean ``the concentration of \ch{H^+} ions''. Of course, we need to talk about what \ch{H^+} actually means. 
+
+\ch{H^+} just means ``a hydrogen atom with an electron removed'' but because hydrogen is just a single proton surrounded by an orbiting electron, this means that it's just a single proton floating around. 
+
+In reality, protons don't do all that well on their own, and tend to bond to water molecules. The actual chemical equation looks like this: 
+
+\begin{center}
+\ch{!(water)( H2O ) + !(hydrogen\ ion)( H+ ) <-> !(hydronium\ ion)( H3O+ )}
+\end{center}
+
+The real question is now ``where do those protons (i.e., hydrogen ions) come from?'' One of the places they come from is from water itself, which tends to self-ionize, like this: 
+
+\begin{center}
+\ch{!(water)( 2 H2O ) <=> !(hydronium\ ion)( H3O+ ) + !(hydroxide\ ion)( OH- )}
+\end{center}
+
+Notice the \ch{<=>} arrows in the middle, which indicate equilibrium. That means that this is not a one-way reaction. Instead, some water molecules are always reacting to form hydronium and hydroxide ions, and some hydronium ions and hydroxide ions are always reacting to form water molecules.
 
 \chapter{Acid Cleaners}
 
+\section{Acetic Acid (Vinegar)}
+
 The most common acidic cleaner, and also the cheapest, is good old white vinegar. Scientists usually call it \textit{acetic acid}, although its official name\footnote{according to IUPAC, that is} is \textit{ethanoic acid}. Its chemical formula is \ch{CH3COOH} and as you can probably guess, it's a small molecule that looks like this:
 
 \begin{wrapfigure}[10]{l}[0pt]{30mm}
@@ -275,7 +299,9 @@ The most common acidic cleaner, and also the cheapest, is good old white vinegar
 \caption{Chemical structure of acetic acid}
 \end{wrapfigure}
 
-Most commercial white vinegar available in your local grocery store contains 4-5\% acidity; that is, most of what you are buying is water and only 4-5\% of it is actually acetic acid.
+Most commercial white vinegar available in your local grocery store contains 4-5\% acidity; that is, most of what you are buying is water and only 4-5\% of it is actually acetic acid. Some specialty vinegars like balsamic vinegar may have an acidity level of 6\%. It's okay that these vinegars have such a small amount of acetic acid in them, since they are meant for cooking purposes more than cleaning anything. 
+
+If you head over to the hardware store, you can find ``cleaning vinegar'' which is usually around 30\% acidity.
 
 
 \chapter{Alkaline Cleaners}