= Dilution
<Dilution> lowers a <solute>'s <concentration> by adding <solvent>. For conserved <amount of substance>, <molar concentration> satisfies
$$
n=c_1V_1=c_2V_2,\qquad c_2=c_1\frac{V_1}{V_2}.
$$
Both $V_1$ and $V_2$ are <chemical solution> <volumes>; $V_2$ is the final total, not the added <solvent>.<Chemistry 2e by Paul Flowers and others/3.3 Molarity>[Chemistry 2e, §3.3, Dilution of Solutions: conserved moles and dilution equation]{ref}
The proof is simply the definition $n=cV$ applied before and after. Its useful assumptions are full transfer of the selected portion, no loss or gain of the counted <solute>, and complete mixing. An ideal <chemical solution> approximation is not required for this inventory equation. If <chemical equilibrium> redistributes dissolved <chemical species>, use a conserved <analytical concentration> or <chemical element> inventory rather than assuming each individual species is conserved. This conservation statement does not by itself preserve the <pH>: a <chemical equilibrium> may change as the <chemical solution> is diluted.
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