Composition of Substances and Solutions

OpenStax Chemistry, 2nd edition

Chapter 3: Compositions of Substances and Solutions

Learning Objectives

3.1 Formula Mass and the Mole Concept

•  Calculate formula masses for covalent and ionic compounds

•  Define the amount unit mole and the related quantity Avogadro’s number Explain the relation between mass, moles, and numbers of atoms or molecules, and perform calculations deriving these quantities from one another

3.2 Determining Empirical and Molecular Formulas

•  Compute the percent composition of a compound

•  Determine the empirical formula of a compound

•  Determine the molecular formula of a compound

3.3 Molarity

•  Describe the fundamental properties of solutions

•  Calculate solution concentrations using molarity

•  Perform dilution calculations using the dilution equation

3.4 Other Units for Solution Concentrations

•  Define the concentration units of mass percentage, volume percentage, mass-volume percentage, parts-per-million (ppm), and parts-per-billion (ppb)

•  Perform computations relating a solution’s concentration and its components’ volumes and/or masses using these units

Resources

3.1 Formula Mass and the Mole Concept

·  Calculate formula masses for covalent and ionic compounds

·  Define the amount unit mole and the related quantity Avogadro’s number Explain the relation between mass, moles, and numbers of atoms or molecules, and perform calculations deriving these quantities from one another

The formula mass of a substance is the sum of the average atomic masses of all the atoms in the substance’s formula.

Covalent substances exist as discrete molecules. 

The formula mass of a covalent substance may be correctly referred to as a molecular mass.

Ionic substances are composed of discrete cations and anions combined in ratios to yield electrically neutral bulk matter. 

Ionic compounds do not exist as molecules. 

The formula mass for an ionic compound may not correctly be referred to as a molecular mass.

The average atomic masses of the ions can be approximated to be the same as the average atomic masses of the neutral atoms. 

Some examples:

The average mass of an aspirin molecule is 180.15 amu. The model shows the molecular structure of aspirin, C9H8O4.

Table salt, NaCl, contains an array of sodium and chloride ions combined in a 1:1 ratio. Its formula mass is 58.44 amu.

The mole is an amount unit similar to familiar units like pair, dozen, gross, etc.

• The mole is defined as the amount of a substance containing the same number of discrete entities (such as atoms, molecules, or ions) as the number of atoms in a sample of pure carbon-12 weighing exactly 12 g. 

• The mole provides a link between the mass of a sample and the number of atoms, molecules, or ions in that sample.

• The number of entities composing a mole has been determined to be 6.02214179 × 1023.

• This constant is named after Italian scientist Amedeo Avogadro and is known as Avogadro’s Number.

• Avogadro’s Number (NA) = 6.022 × 1023 

• The masses of 1 mole of different elements, however, are different, since the masses of the individual atoms are drastically different. 

Sample calculation,

A packet of an artificial sweetener contains 40.0 mg of saccharin (C7H5NO3S). Given that saccharin has a molar mass of 183.18 g/mol, how many saccharin molecules are in a 40.0-mg (0.0400-g) sample of saccharin? How many carbon atoms are in the same sample?

A compound’s empirical formula can be determined from the masses of its constituent elements. 

1. Convert element masses to moles using molar masses.

2. Divide each number of moles by the smallest number of moles.

3. If necessary, multiply by an integer, to give the smallest whole-number ratio of subscripts. 

A compound’s molecular formula can be determined from its empirical formula and its molecular or molar mass. 

The molecular formula is then obtained by multiplying each subscript in the empirical formula by n. 

3.3 Molarity

·  Describe the fundamental properties of solutions

·  Calculate solution concentrations using molarity

·  Perform dilution calculations using the dilution equation

Solutions occur frequently in nature. 

Solutions are another term used for a homogeneous mixture—uniform composition and properties throughout its entire volume. 

The relative amount of a given solution component is known as its concentration.

A solution consists of two components:

• 1. Solvent: component with a concentration that is significantly greater than that of all other components.

  2. Solute: component that is typically present at a much lower concentration than the solvent.

  3. A solution in which water is the solvent is called an aqueous solution.

Molarity (M): the number of moles of solute in exactly 1 liter (1 L) of the solution:

Example of calculation of molarity of a solution:

A 355 mL soft drink sample contains 0.133 mol of sucrose (table sugar). What is the molar concentration of sucrose in the beverage?

Dilution is the process whereby the concentration of a solution is lessened by the addition of solvent. 

Since the dilution process does not change the amount of solute in the solution, the molarity times the volume of each solution can be set equal to one another to derive the dilution equation:

or with other units of concentration (C) and volume (V)

3.4 Other Units for Solution Concentrations

·  Define the concentration units of mass percentage, volume percentage, mass-volume percentage, parts-per-million (ppm), and parts-per-billion (ppb)

·  Perform computations relating a solution’s concentration and its components’ volumes and/or masses using these units

The mass percentage of a solution component is defined as the ratio of the component’s mass to the solution’s mass, expressed as a percentage:

The concentration of a solution formed by dissolving a liquid solute in a liquid solvent is often expressed as a volume percentage.

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.

Very low solute concentrations are often expressed using appropriately small units such as parts per million (ppm) or parts per billion (ppb).

The mass-based definitions of ppm and ppb:

    and