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What notation and symbols are commonly used here?

Chemistry relies heavily on math. Many posts include mathematical notation, written using LaTeX commands and delimited by dollar signs. If you see dollar signs with what appears to be gibberish between them, it just means that MathJax, the math rendering we use, isn't working properly for you.

Some basics: Inline formulas are surrounded by single dollar signs ($f(x) = ax^2 + bx + c$ renders as $f(x) = ax^2 + bx + c$), and block formulas by double dollar signs so that $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ renders as

$$x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$$

For chemical equations, one can use the \ce{...} function from the mhchem package. This allows one to properly typeset chemical formulae and reactions:

$\ce{HCl}$ dissociates in water as follows: \ce{H2O + HCl <=> H3O+ + Cl-}$$

which gives:

$\ce{HCl}$ dissociates in water as follows: $$\ce{H2O + HCl <=> H3O+ + Cl-}$$

More details on math formatting can be found in this meta post.