Solutions and Concentration: Solubility, Percent Composition, and Molarity

Solutions and Concentration

Learning Objectives

• Calculate percentage concentration (m/m, v/v, m/v), ppm, and ppb.

• Calculate the molarity of a solution.

• Use concentration units to calculate the amount of solute in a solution.

• Use molarity to determine quantities in chemical reactions.

• Determine the limiting concentration of a diluted solution.

Solubility

Definition and Importance

Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature. It is usually expressed as grams of solute per 100 mL of solvent. Solutions with a solute concentration equal to the solubility limit are called saturated; those with less are unsaturated.

• Saturated solution: Contains the maximum amount of dissolved solute at equilibrium.

• Unsaturated solution: Contains less than the maximum amount of solute.

• Supersaturated solution: Contains more solute than is stable at equilibrium (rare and unstable).

Solubility varies with temperature and solvent type.

Solubility Table

The following table summarizes the solubility of various substances in water at 25°C (except as noted):

Substance	Solubility (g in 100 mL H2O)
AgCl(s)	0.019
BaSO4(s)	0.0023
CuSO4(s)	0.073
CaCO3(s)	0.0015
Ca(OH)2(s)	0.16
CaCl2(s)	74.5
KBr(s)	63.0
NaCl(s)	36.0
NaNO3(s)	84.0
C6H12O6 (glucose)	120.4 (at 30°C)
C12H22O11 (sucrose)	204.0 (at 20°C)

Percent Composition of Solutions

Types of Percent Concentration

Percent composition expresses the ratio of solute to solution in percentage terms. The three main types are:

• Mass/Mass Percent (m/m): $\frac{\text{mass of solute}}{\text{mass of solution}} \times 100\%$

• Volume/Volume Percent (v/v): $\frac{\text{volume of solute}}{\text{volume of solution}} \times 100\%$

• Mass/Volume Percent (m/v): $\frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \times 100\%$

These units are used for different types of solutions (solid in solid, liquid in liquid, solid in liquid).

Examples

• Example (m/m): A solution with 35.6 g NaCl in 355 g solution: $\frac{35.6}{355} \times 100\% = 10.0\%$ m/m.

• Example (m/v): A solution with 2.00 L water and 15.8 g glucose: $\frac{15.8}{2000} \times 100\% = 0.79\%$ m/v.

Using Percent Composition in Calculations

Percent concentration can be used as a conversion factor between the amount of solute and the amount of solution. For example, a 5% v/v solution of alcohol means 5 mL alcohol in 100 mL solution.

• Conversion factor: $\frac{5\,\text{mL alcohol}}{100\,\text{mL solution}}$

This allows calculation of the amount of solute in any volume of solution.

Parts per Million (ppm) and Parts per Billion (ppb)

Definition and Use

These units are used for very dilute solutions, such as environmental samples.

• ppm: $\frac{\text{mass of solute}}{\text{mass of solution}} \times 1,000,000$

• ppb: $\frac{\text{mass of solute}}{\text{mass of solution}} \times 1,000,000,000$

For aqueous solutions, 1 ppm ≈ 1 mg/L, 1 ppb ≈ 1 μg/L.

• Example: A body contains 0.012 g Ni in 65 kg. $\frac{0.012}{65,000} \times 1,000,000 = 0.18$ ppm.

Molarity

Definition and Calculation

Molarity (M) is the number of moles of solute per liter of solution. It is the most common unit for expressing concentration in chemistry, especially for reactions in solution.

• Formula: $\text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}}$

To calculate molarity, first convert mass of solute to moles, then divide by volume of solution in liters.

• Example: 2.50 g NaOH in 750 mL solution. Moles NaOH = $\frac{2.50}{40.00} = 0.0625$ mol. Volume = 0.750 L. $\frac{0.0625}{0.750} = 0.0833$ M.

Using Molarity in Calculations

Molarity is used to relate volume and amount of solute in chemical reactions. Conversion factors:

• $\frac{\text{moles solute}}{1\,\text{L solution}}$

• $\frac{1\,\text{L solution}}{\text{moles solute}}$

For example, to find moles of sucrose in 0.10 L of 3.0 M solution: $0.10 \times 3.0 = 0.30$ mol.

Summary Table: Concentration Units

Unit	Definition	Formula	Typical Use
Mass/Volume Percent (m/v)	g solute per 100 mL solution	$\frac{\text{g solute}}{\text{mL solution}} \times 100\%$	Medical, IV solutions
Mass/Mass Percent (m/m)	g solute per 100 g solution	$\frac{\text{g solute}}{\text{g solution}} \times 100\%$	Solid mixtures
Volume/Volume Percent (v/v)	mL solute per 100 mL solution	$\frac{\text{mL solute}}{\text{mL solution}} \times 100\%$	Liquid mixtures
ppm	mg solute per kg solution (or L for aqueous)	$\frac{\text{mg solute}}{\text{kg solution}}$	Environmental, trace analysis
Molarity (M)	mol solute per L solution	$\frac{\text{mol solute}}{\text{L solution}}$	Chemical reactions

Key Terms

• Solubility: Maximum amount of solute that can dissolve in a solvent at a given temperature.

• Saturated solution: Contains the maximum amount of dissolved solute.

• Unsaturated solution: Contains less than the maximum amount of solute.

• Supersaturated solution: Contains more solute than is stable at equilibrium.

• Percent composition: Ratio of solute to solution, expressed as a percentage.

• ppm/ppb: Parts per million/billion, used for very dilute solutions.

• Molarity (M): Moles of solute per liter of solution.

Additional info:

• In practice, solubility depends on temperature, pressure (for gases), and the nature of both solute and solvent.

• Percent composition is commonly used in medicine (IV solutions), food chemistry, and environmental science.

• Molarity is essential for stoichiometric calculations in chemical reactions.