# 3.4 Other units for solution concentrations  (Page 2/8)

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## Calculations using mass percentage

“Concentrated” hydrochloric acid is an aqueous solution of 37.2% HCl that is commonly used as a laboratory reagent. The density of this solution is 1.19 g/mL. What mass of HCl is contained in 0.500 L of this solution?

## Solution

The HCl concentration is near 40%, so a 100-g portion of this solution would contain about 40 g of HCl. Since the solution density isn’t greatly different from that of water (1 g/mL), a reasonable estimate of the HCl mass in 500 g (0.5 L) of the solution is about five times greater than that in a 100 g portion, or 5 $×$ 40 = 200 g. In order to derive the mass of solute in a solution from its mass percentage, we need to know the corresponding mass of the solution. Using the solution density given, we can convert the solution’s volume to mass, and then use the given mass percentage to calculate the solute mass. This mathematical approach is outlined in this flowchart: For proper unit cancellation, the 0.500-L volume is converted into 500 mL, and the mass percentage is expressed as a ratio, 37.2 g HCl/g solution:

$\text{500 mL solution}\phantom{\rule{0.2em}{0ex}}\left(\frac{1.19\phantom{\rule{0.2em}{0ex}}\text{g solution}}{\text{mL solution}}\right)\phantom{\rule{0.2em}{0ex}}\left(\frac{37.2\phantom{\rule{0.2em}{0ex}}\text{g HCl}}{100\phantom{\rule{0.2em}{0ex}}\text{g solution}}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}221\phantom{\rule{0.2em}{0ex}}\text{g HCl}$

This mass of HCl is consistent with our rough estimate of approximately 200 g.

## Check your learning

What volume of concentrated HCl solution contains 125 g of HCl?

282 mL

## Volume percentage

Liquid volumes over a wide range of magnitudes are conveniently measured using common and relatively inexpensive laboratory equipment. The concentration of a solution formed by dissolving a liquid solute in a liquid solvent is therefore often expressed as a volume percentage    , %vol or (v/v)%:

$\text{volume percentage}=\phantom{\rule{0.2em}{0ex}}\frac{\text{volume solute}}{\text{volume solution}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%$

## Calculations using volume percentage

Rubbing alcohol (isopropanol) is usually sold as a 70%vol aqueous solution. If the density of isopropyl alcohol is 0.785 g/mL, how many grams of isopropyl alcohol are present in a 355 mL bottle of rubbing alcohol?

## Solution

Per the definition of volume percentage, the isopropanol volume is 70% of the total solution volume. Multiplying the isopropanol volume by its density yields the requested mass:

$\left(355\phantom{\rule{0.2em}{0ex}}\text{mL solution}\right)\phantom{\rule{0.2em}{0ex}}\left(\frac{70\phantom{\rule{0.2em}{0ex}}\text{mL isopropyl alcohol}}{100\phantom{\rule{0.2em}{0ex}}\text{mL solution}}\right)\phantom{\rule{0.2em}{0ex}}\left(\frac{0.785\phantom{\rule{0.2em}{0ex}}\text{g isopropyl alcohol}}{1\phantom{\rule{0.2em}{0ex}}\text{mL isopropyl alcohol}}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}195\phantom{\rule{0.2em}{0ex}}\text{g isopropyl alchol}$

## Check your learning

Wine is approximately 12% ethanol (CH 3 CH 2 OH) by volume. Ethanol has a molar mass of 46.06 g/mol and a density 0.789 g/mL. How many moles of ethanol are present in a 750-mL bottle of wine?

1.5 mol ethanol

## Mass-volume percentage

“Mixed” percentage units, derived from the mass of solute and the volume of solution, are popular for certain biochemical and medical applications. A mass-volume percent    is a ratio of a solute’s mass to the solution’s volume expressed as a percentage. The specific units used for solute mass and solution volume may vary, depending on the solution. For example, physiological saline solution, used to prepare intravenous fluids, has a concentration of 0.9% mass/volume (m/v), indicating that the composition is 0.9 g of solute per 100 mL of solution. The concentration of glucose in blood (commonly referred to as “blood sugar”) is also typically expressed in terms of a mass-volume ratio. Though not expressed explicitly as a percentage, its concentration is usually given in milligrams of glucose per deciliter (100 mL) of blood ( [link] ).

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