Added sections 1.1 and 1.2 (chemical & physical changes; start of pH section

science-of-cleaning.tex

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 \chapter{Introduction}
 
+I've always enjoyed cleaning, but I didn't get interested in the science behind cleaning until I ready Kate Biberdorf's \textit{It's Elemental: The Hidden Chemistry in Everything} which has an entire chapter \cite[pp.~211-233]{biberdorf2021} devoted to cleaning.\footnote{She also is from the same home town as me.}
+
+My goal here is not to teach you how to clean everything, but how to use commonly available cleaning agents safely and effectively by teaching you how they actually do their work. 
+
+
+\chapter{A Chemistry Primer}
+
+\section{Chemical vs. Physical Changes}
+
+If you remember your high school chemistry, you'll recall that substances can undergo both chemical and physical changes. Acids, bases, surfactants, enzymes, and solvents rely on chemical changes to clean things, whereas abrasives and heat rely on physical changes. However, chemical reactions are heat dependent and tend to happen more quickly at warmer temperatures, which is just one reason we wash things with warm water—it works better. 
+
+\section{A pH Primer}
+
+pH is a rather vague concept for a lot of people, and the internet contains a lot of misinformation and misunderstandings about how it works as a result. Let's get that sorted out. 
+
+pH is a measure of how acidic or alkaline (i.e., basic) a substance is. There is a lot of chemistry and math involved in pH, so let's start with some basic facts before getting into the chemistry and math. 
+
+\begin{enumerate}[noitemsep]
+\item The pH scale goes in two directions: from 7 down to zero, and from 7 up to fourteen.
+\item Substances with a pH of 7 are neutral—they are neither acidic nor basic. (They are also very rare.)
+\item Substances with a pH less than 7 are acidic.
+\item Substances with a pH greater than 7 are basic. 
+\item The further away a substance gets from 7 on the pH scale (meaning the closer it gets to either 0 or 14) the more chemically reactive a substance is. This means that it is \textit{potentially} a better cleaner, but also that it is \textit{definitely} more dangerous to use. 
+\item The pH scale is unitless. That is, it does not have units like centimeters or pounds or degrees. For convenience, scientists will sometimes talk about ``pH units'' when they talk about moving up or down the scale, 
+\end{enumerate}
+
+\subsection{Math and the pH Scale}
+
+The pH scale is logarithmic, rather than linear. That means that each step on the scale is multiplied or divided by a factor of ten. This can be confusing, because in our everyday lives, we are used to dealing with linear values. If one book is an inch thick, then a pile of five books will be five inches high, and a pile of 20 books will be 20 inches high. 
+
+But logarithmic scales don't work this way. They are meant to deal with values that get very large or very small and make it possible to represent them easily on a graph. 
+
+This means that something with a pH of 5 is not \textit{slightly} more acidic than a substance with a pH of 6; it's actually ten times more acidic. Likewise, something with a pH of 4 is ten times more acidic than something with a pH of 5, but it's also a hundred times more acidic than something with a pH of 6. Something with a pH of 3 would look like this:
+
+\begin{align*}
+\text{pH 3} & = 10 \times \text{pH 4} \\
+& = 100 \times \text{pH 5} \\
+& = 1000 \times \text{pH 6}
+\end{align*}
+
+Because the pH scale is bidirectional (that is, acidic in one direction and basic in the other), this principle also holds true for values greater than 7, but in the opposite direction:
+
+\begin{align*}
+\text{pH 11} & = 10 \times \text{pH 10} \\
+& = 100 \times \text{pH 9} \\
+& = 1000 \times \text{pH 8}
+\end{align*}
+
+In both of these examples, the values are getting closer to seven, which means that they are becoming less acidic (in the first example) and less basic (in the second example). They are, in effect, becoming more neutral.
+
+
+\subsection{The Chemistry of pH}
 
 
-\chapter{A pH Primer}
 
 \Chapter{Acid Cleaners}{Vinegar is your friend}
 
+
 \Chapter{Alkaline Cleaners}{When acids just won't cut it}
 
+
 \Chapter{Surfactants}{i.e., Soaps and detergents}
 
+
 \Chapter{Abrasive Cleaners}{Scrub-a-dub-dub}
 
+
 \chapter{Heat}
 
+
 \chapter{Enzymes}
 
 
+\chapter{Solvents}
+
+I am a bit hesitant to talk about solvents here, because commercial solvents can be strong—too strong for everyday household use. Still, there are several that are available if you know where to look, including ethanol, isopropyl alcohol, acetone, mineral spirits, and turpentine.
+
+
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