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However, the concentration of hydronium and hydroxide ions will be very, very small; in fact, the equilibrium that's established in solution lies so far to the left, that only 18 in 1010 molecules of water will undergo autoionization.

What does "to the left" mean in the extract above? Does it mean the left side of the chemical equation?

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Yes, "to the left" refers to the left side of an equilibrium expression.

Traditionally, the autoionization of water is written as

$$\ce{2H2O <=> H3O+ + OH-}$$

When we talk about equilibrium lying "to the left", it means that the educt/reactant is favored, i.e. more $\ce{H2O}$ than $\ce{H3O+}$ or $\ce{OH-}$.

Conversely, an equilibrium that lies "to the right" is one that favors products. In this case, it would favor the production of $\ce{H3O+}$ and $\ce{OH-}$ over $\ce{H2O}$,

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