What is the initial volume, in milliliters, needed to...

What is the initial volume, in milliliters, needed to prepare each of the following diluted solutions? (9.5) a. $250 \mathrm{~mL}$ of $3.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{HCl}$ from $10.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{HCl}$ b. $500 . \mathrm{mL}$ of $0.90 \%(\mathrm{~m} / \mathrm{v}) \mathrm{NaCl}$ from $5.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{NaCl}$ c. $350 . \mathrm{mL}$ of $2.00 \mathrm{M} \mathrm{NaOH}$ from $6.00 \mathrm{M} \mathrm{NaOH}$

What is the initial volume, in milliliters, needed to prepare each of the following diluted solutions? (9.5)
a. $250 \mathrm{~mL}$ of $3.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{HCl}$ from $10.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{HCl}$
b. $500 . \mathrm{mL}$ of $0.90 \%(\mathrm{~m} / \mathrm{v}) \mathrm{NaCl}$ from $5.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{NaCl}$
c. $350 . \mathrm{mL}$ of $2.00 \mathrm{M} \mathrm{NaOH}$ from $6.00 \mathrm{M} \mathrm{NaOH}$

Key Concepts

Dilution Equation

The dilution equation, often written as C1V1 = C2V2, is a key relation used to determine the amount of a concentrated solution needed to prepare a diluted solution of a desired concentration and volume. This equation is applicable whether the concentration is given in molarity or as a percentage, as long as the same units are maintained across the calculation.

Percent (m/v) Concentration

Percent (m/v) concentration is a measure that expresses the mass in grams of a solute present in 100 milliliters of the solution. It is a crucial concept when dealing with solutions where the solute’s mass to solution volume ratio is of interest, and it provides a direct way of representing solution concentration without involving moles.

Molarity

Molarity is the concentration unit defined as the number of moles of solute present per liter of solution. It is widely used in chemistry for solution preparation and chemical reactions because it directly relates the quantity of a substance to its reaction stoichiometry and volume of the solution.

Unit Conversion and Volume Measurement

Accurate unit conversion is essential in dilution problems to ensure that volume measurements (e.g., milliliters and liters) and concentration units (e.g., percentages and molarity) are consistent within calculations. This concept underpins the accurate application of the dilution equation and helps avoid errors due to inconsistent units.

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