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SOLUBILITY AND CONCENTRATION UNITS FOR AQUEOUS SOLUTIONS

Many chemical reactions and processes occur in the solution state where water is the solvent. Solubility of a substance is an important chemical property, since clearly, not all substances are soluble in water and can use water as a reaction medium. The term “soluble” deserves some clarification. When a salt such as sodium chloride is said to be soluble in water, it means that moderate, visible or measurable amounts will dissolve. Even sodium chloride has an upper limit of about 35 g per 100 mL of water at room temperature. And similarly, even sand or trichloroethylene will dissolve to a limited extent in water, especially if the volume of water is sufficiently large. So it is preferable to say that the salt calcium phosphate is slightly soluble instead of insoluble, though use of the latter term usually outnumbers the former. Solubility rules for most inorganic compounds in water are well known and are summarized in Table 1.2. For organic compounds, whether solid or liquid, it is best to consult the Handbook of Chemistry and Physics or Wikipedia. Solvents other than water, such as acetone, alcohol, or hexane, are usually listed as alternatives.

Table 1.2. General solubility rules of cations and anions

Soluble Compounds

Insoluble Exceptions

Compounds containing alkali metal ions (Na+, K+, Rb+, Cs+) and the ammonium ion (NH4+)

None

Nitrates (NO3-), bicarbonates (HCO3-), and chlorates (QO3-)

None

Halides (Cl-, Br-, I-) Sulfates (SO42-)

Halides of Ag+, Hg22+, and Pb2+

Sulfates of Ag+, Ca2+, Sr2+,

Ba2+, Hg22+, and Pb2+

Insoluble Compounds

Soluble Exceptions

Carbonates (CO32-), phosphates (PO43-), sulfides (S2-), and chromates (CrO42-)

Compounds containing alkali metal ions and the ammonium ion

Hydroxides (OH-)

Compounds containing alkali metal ions and the Ba2+ ion

Several units exist in chemistry to quantify concentrations of aqueous solutions. The reason for the great variety is that different applications and chemical formulas require different units. The term “concentration” always implies the existence of a solute, present as a gas, liquid, or solid, dissolved in a suitable solvent to form a solution. Unless otherwise specified, the solvent for liquid solutions is understood to be water—hence the designation “aqueous solution,” abbreviated as (aq). The common definitions and units are as follows:

Molarity, M = moles of solute/liter of solution.

Molality, m = moles of a solute/kilogram of solvent.

Mole fraction, X = number of moles of component г/total number of moles of all components.

Percent by mass/mass = mass of solute in grams/mass of solution in grams.

Percent by volume/volume = volume of solute in milliliters/total volume of solution in milliliters.

Example 1.8

A chemist wants to prepare 0.500 L of a 1.50 molar solution of sodium chloride. How does he do this?

Solution

It is important to note that the unit of molarity provides the basis of making water-based chemical reactions and their direct stoichiometric calculations much easier, since the unit of all stoichiometric coefficients in balanced chemical reactions is the mole. Thus, use is made of the simple but powerful relationship:

Moles of Solute = Volume of Solution (L) x Molarity (M).

For example, the number of moles in 100 mL of a 2.5 M NaCl solution involved in a chemical reaction would be: moles NaCl = (0.100 L) x (2.5 M) = 0.250 moles NaCl.

Example 1.9

Hospital saline solutions are often labeled as 1.25% KCl (aq) by mass. What does this mean, and how is this calculated?

Solution

Using the definition of percent by mass/mass, this means:

This solution is made by adding 1.25 g of KCl (s) to 98.75 g of water. Note that while masses of solutes and solvents are exactly additive, volumes of different solutions (with different densities) are not.

Example 1.10

A wine bottle has a label that reads 11.5% alcohol (i.e., ethanol) by volume. What does this mean, and how is this calculated?

Solution

Using the last definition above for Percent by volume/volume, this means:

11.5 mL C2H5OH/100mL of wine solution x 100 = 11.5%

Since most wine bottles contain 750 mL of fluid, this would mean there are 86.25 mL of pure ethanol contained in a bottle of wine.

Conversion from one concentration unit to another may occasionally be necessary or useful. The “factor-label method” is the most efficient way to handle this. Note the following example.

Example 1.11

Find the concentration of sulfuric acid solution, H2SO4 (aq), used in car batteries, in molarity (M). The density of battery acid is about 1.265 g soln/mL soln (while pure sulfuric acid stock solution is 1.800 g/mL, for comparison), and it is 35.0% by mass H2SO4.

Solution

Start with the density figure and then proceed as follows:

Note the systematic cancellation of units from left to right to get to moles H2SO4 per liter (L) of solution on the right, that is, the unit of molarity, M. Other unit to unit conversions are performed in much the same way.

 
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