- Last updated
- Save as PDF
- Page ID
- 222385
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
As stated previously, chemists have defined several types ofconcentrations, which each use a different chemically-acceptable unit, or combination of units, to indicate the amount of solute that is dissolved in a given amount of solvent. The following paragraphs will present and apply the equationthat is used to calculate a mass/volume percent, which is the final type of percent-based concentrationthat will be discussed in this chapter.
Mass/Volume Percent Equation
The mass/volume percent of a solutionis defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole. Because this type of concentrationis expressed as a percentage, the indicated proportionmust bemultiplied by 100, as shown below.
\(\text{Mass/Volume Percent}\) = \( \dfrac{ \rm{m_{solute} \; (\rm{g})}}{\rm{V_{solution} \; (\rm{mL})}} \) ×\({100}\)
As discussed in the previous two sections of this chapter, mass percents and volume percents can be calculated using an alternative equation, in which the masses or volumes, respectively, of the solute and the solvent thatare contained in a solution are added to obtain the mass or volume, respectively, of that solution, as a whole. While mass percents are typically reported for solid- and liquid-phase solutions, and volume percents are usually determinedfor liquid- and gas-phase solutions, a mass/volume percent concentration is most often calculated for solutions that are specifically prepared by dissolvingsolid solutes in liquid solvents. In order to create this type of solution, the solid solute particles must overcomethe attractive forces that exist between the liquid solvent molecules, in order tomove throughout and occupy the "empty" spacesthat are temporarily created during thesolvationprocess. After the solute particles have dispersed throughout the solvent,the solvent molecules interact more strongly with the solvated solute particles than with other solvent molecules and, consequently, exist in closer physical proximity to those solute particles, relative to other solvent molecules. As a result of thesesolute-solvent interactions,the solvated solute particles occupy less space than they had prior to theirsolvation, which causes thevolume of the solution, as a whole,to decrease, relative to the combined volumes of the individual solute and solvent. Because the magnitude of this volumetric contraction varies based on the solute and solvent that are utilized to prepare a solution, calculating the mass/volume percent of a solution by adding the volumes of its components is prohibitively challenging. Therefore, only the equation that is shown above can be applied to reliably determine the mass/volume percent of a solution.
Mass/Volume Percent Calculations
In order to be incorporated into the equation that is shown above, the mass of the solute must be expressed in grams, the volume of the solution must be provided in milliliters, and the chemical formula of each component must be written as the secondary unit on its associated numerical quantity. Therefore, if either of these measurements is reported using an alternative unit, its value would need to be converted to the appropriate unit prior to being incorporated into the mass/volume percent equation.
During the multiplicationand division processes thatare used to solve this equation, no unit cancelation occurs, because the units that are present in the numerator and denominator, "g" and "mL," respectively, do not match one another. Therefore, the unit that results from the division of the indicated quantitiesis "g/mL," which is a unit that is typically utilized to report thedensityof a substance.Because densities and mass/volume percent concentrations have unique definitions and are calculated using different equations, these measurementsare distinctive quantities and, consequently, cannot be expressed using the same unit.Therefore, the mass and volume units are eliminated during the simplification of the mass/volume percent equation,even though "g" and "mL" do not cancel, mathematically, and the calculated concentration is expressed as a percentage. However, as stated previously, the quantity of solute that is present in a given solution can be expressed using three unique percent-based concentrations. In order to distinguish a mass/volume percent, which is calculated by simplifying a mass-to-volumeratio, from the other percent-based concentrations, the unit in which a mass/volume percentconcentration is reported is "% m/v,"and the chemical formula of the solute iswritten as the secondary unit on this calculated quantity.
Finally, because mass/volume percentsare not defined as exact quantities, their values should bereported using the correct number of significant figures. However, "100" is an exact number and, therefore, does not impact the significance ofthe final reported concentration.
