Similarly, the product of a solution's molarity times its volume in milliliters gives the number of

millimoles $($abbreviated mmol$)$ in the sample:

$M{V}_{mL}=(\frac{\text{m}\text{m}\text{o}\text{l}\text{s}\text{o}\text{l}\text{u}\text{t}\text{e}}{mLsoln})(mL$ soln $)=$mmol solute

These two relationships are used routinely when dealing with solution concentrations in molarity.

Another way of preparing a solution of a certain molarity is to start with a measured volume $($an

aliquot$)$ of a more concentrated solution of known molarity and dilute to the desired

concentration. The number of moles of solute in the aliquot of the concentrated solution can be

calculated from $MV.$ Regardless of the dilution, this will be the number of moles in the new

solution. Therefore, we can write

or more simply

$M_{\text{i}\text{n}\text{i}\text{t}\text{i}\text{a}\text{l}}{V}_{\text{i}\text{n}\text{i}\text{t}\text{i}\text{a}\text{l}}=M_{\text{f}\text{i}\text{n}\text{a}\text{l}}{V}_{\text{f}\text{i}\text{n}\text{a}\text{l}}$

$M_i{V}_i=M_f{V}_f$

Exercises

Describe how you would go about making exactly $500mL$ of $0\mathrm{.}100MNaN{O}_3(aq)$ solution,

using reagent grade f$.$w$.=85\mathrm{.}0u.$

Starting with a $0\mathrm{.}100MNaN{O}_3$ solution, how would you go about preparing exactly $100mL$

of $0\mathrm{.}0250MNaN{O}_3$ solution?

How many milliliters of $0\mathrm{.}0250MCuS{O}_4$ solution contain $1\mathrm{.}75g$ of solute? $($f$.$w$.CuS{O}_4=$

$159\mathrm{.}6u$

Information $($Analytical Concentration vs$.$ Actual Species Concentration$)$

No molecular dissociation occurs when a nonelectrolyte is dissolved in water. In a non$-$

electrolyte solution, the molarity reflects the actual concentrations of solute molecules. Thus a

$0\mathrm{.}10M$ sugar solution contains $0\mathrm{.}10$ mole of sugar molecules per liter of solution. The situation

is different with electrolytes, because they break up to some extent to give ions in solution. The

concentrations of those ions in solution depends upon $($a$)$ the amount of electrolyte that is

dissolved, $($b$)$ whether the solute is a strong or weak electrolyte, and $($c$)$ the formula of the

electrolyte. In order to talk about the concentrations of ions in weak electrolyte solutions, we

will need to have some way of assessing the extent of dissociation of the solute. We will delay

that topic until later. For now we will only consider predicting the concentrations of ions in

solutions of strong electrolytes.

Many chemists call the number of moles of solute dissolved per liter of solution the analytical

concentration of solute, given the symbol $C.$ This is essentially a statement of the moles of

solute per liter of solution that we dissolved, without regard to the concentrations of the species