Determine the final volume, in milliliters, of each of the...

Determine the final volume, in milliliters, of each of the following: a. a $1.5 \mathrm{M}$ HCl solution prepared from $20.0 \mathrm{mL}$ of a $6.0 \mathrm{M} \mathrm{HCl}$ solution b. a $2.0 \%$ (m/v) LiC1 solution prepared from $50.0 \mathrm{mL}$ of a $10.0 \%(\mathrm{m} / \mathrm{v}) \mathrm{LiCl}$ solution c. a $0.500 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}$ solution prepared from $50.0 \mathrm{mL}$ of a $6.00 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}$ solution d. a $5.0 \%(\mathrm{m} / \mathrm{v})$ glucose solution prepared from $75 \mathrm{mL}$ of a $12 \%(\mathrm{m} / \mathrm{v})$ glucose solution

Determine the final volume, in milliliters, of each of the following:
a. a $1.5 \mathrm{M}$ HCl solution prepared from $20.0 \mathrm{mL}$ of a $6.0 \mathrm{M} \mathrm{HCl}$ solution
b. a $2.0 \%$ (m/v) LiC1 solution prepared from $50.0 \mathrm{mL}$ of a $10.0 \%(\mathrm{m} / \mathrm{v}) \mathrm{LiCl}$ solution
c. a $0.500 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}$ solution prepared from $50.0 \mathrm{mL}$ of a $6.00 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}$ solution
d. a $5.0 \%(\mathrm{m} / \mathrm{v})$ glucose solution prepared from $75 \mathrm{mL}$ of a $12 \%(\mathrm{m} / \mathrm{v})$ glucose solution

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Key Concepts

Dilution Equation (M1V1 = M2V2)

This equation is central to dilution problems, relating the initial and final concentrations and volumes. It is based on the conservation of moles of solute: the product of the initial concentration and volume equals the product of the final concentration and volume. It allows one to calculate an unknown variable (usually the final volume) when diluting a solution from a stock concentration.

Conservation of Solute Quantity

In any dilution process, the total amount of solute remains constant. Whether the concentration is expressed in molarity or percent mass/volume, the solute is neither created nor destroyed during dilution. This principle underpins methods to calculate changes in concentration as the solution's volume is altered.

Percentage Concentration (Mass/Volume)

Mass/volume percent concentration represents the mass of solute (in grams) per 100 milliliters of solution. This measure is particularly useful when the quality of the solution is defined by weight per volume, and it is essential for preparing solutions that require a specific percent concentration after dilution.

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