1. Chapter 3: Composition of Substances and Solutions
OpenStax
Chemistry
Joseph DePasquale

2. Chapter Outline 3.1: Formulas Mass and the Mole Concept
3.2: Determining Empirical and Molecular Formulas
3.3: Molarity
3.4: Other Units for Solution Concentrations

3. Problem solving This chapter will involve many quantitative problems.
Always start with what you know
Choose a single quantity to start with
Systematically define all relationships
Apply conversions one at a time, keeping units in check
Report your final answer with the correct number of significant figures and proper unit(s).

4. 3.1: Formulas Mass and the Mole Concept
Atomic mass (Ch. 2) – The average mass of an atom of a particular element.
Takes into consideration the abundances of all naturally occurring isotopes of that element.
Formulas Mass – The mass of a molecule or compound, which is found by summing the atomic masses of all the atoms represented in the substance’s chemical formula.

5. Formula Mass for Covalent Molecules
For covalent molecules the molecular formula represents the number and types of atoms composing a single molecule of that substance.
The formula mass is also referred to as molecular mass.
Consider the compound caffeine:

6. Formula Mass for Ionic Compounds
For ionic compounds, the chemical formula represents the types of cations and anions and the ratio in which they combine to achieve electrically neutral matter.
The chemical formula does NOT represent the composition of a discrete molecule.
Consider the compound, sodium chloride (NaCl)

7. The Mole
Reporting the number of atoms, molecules, or ions in a sample is not practical because atoms are so small.
Instead chemists use the unit called the mole.
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 is important! The mole provides an important link between mass and the number of particles (atoms, molecules, or ions). .

8. Avogadro’s Number and the Mole
The number of entities composing a mole has been determine to be x 1023.
Avogadro’s Number (NA) = x 1023
The term “mole” is analogous to the word dozen or gross.
Dozen – A collection of 12 items.
Gross – A collection of 144 items.
Mole – A collection of x 1023 items.
The relationship that 1 mole = x items is an extremely important and useful conversion factor in chemistry!

9. 1 Mole of anything is 6.022 x 1023 items
1 mole H atoms = x 1023 H atoms
1 mole O atoms = x 1023 O atoms
1 mole H2O molecules = x 1023 H2O molecules
1 mole Na+ ions = x 1023 Na+ ions
1 mole electrons = x 1023 electrons
1 mole pennies = x 1023 pennies

10. The mole and Avogadro’s Number allows us to count atoms and molecules by mass
The atomic mass of an element on the periodic table:
Is equivalent to the average mass of one atom of that element in atomic mass units (amu).
But also equivalent to the mass of one mole of that element in grams.
In the lab we rarely work in amu because we deal with large collections of atoms and compounds.
It is much more practical to work in grams.

11. The molar mass (MM), of an element or compound is the mass in grams of 1 mole of that substance.
What is the molar mass of an H atom?
What is the molar mass of an H2 molecule?
What is the molar mass of an H2O molecule?
Molar Mass (MM)

12. One mole of any element contains 6.022 x 1023 atoms of that element.
But the mass of one mole of different elements are not the same because the masses of the individual atoms are different.
Each sample contains × 1023 atoms —1.00 mol of atoms. From left to right (top row): 65.4 g zinc, 12.0 g carbon, 24.3 g magnesium, and 63.5 g copper. From left to right (bottom row): 32.1 g sulfur, 28.1 g silicon, 207 g lead, and g tin. (credit: modification of work by Mark Ott)

13. One Mole Quantities

14. The importance of the mole, Avogadro’s Number, and Molar Mass must be clear!
Atomic mass N =
Mass of 1 mole of N atoms =
Formula mass NaCl =
Mass of a mole of NaCl =
This relationship applies to every single element, ion, and compound (both covalent and ionic)!

15. Just how big is x 1023?
In order to obtain a mole of sand grains (6.022 x 1023 grains of sand), it would be necessary to dig the entire surface of the Sahara desert (which has an area slightly less than that of the United States) to a depth of 6 feet.
If you had a mole of dollars (6.022 x 1023 dollars), and if you spend this money at the rate of one billion (1 x 109) dollars per second, it would take you over 19 million years to spend all of the money.

16. The number of molecules in a single droplet of water is roughly 100 billion times greater than the number of people on earth. (credit: “tanakawho”/Wikimedia commons)

17. Measuring Amounts
The simplest way to measure the amount of an element, molecule, or ion is by weight.
These entities are very small so counting is not practical!
In chemistry we typically express the amount of our substance in grams or moles.

19. 3.2: Determining Empirical and Molecular Formulas
Empirical Formula – Indicates the simplest whole number ratio of the number of atoms in a compound.
Molecular Formula – Indicates the actual number of atoms in a molecule or compound.

20. Percent Composition of Compounds
The percent composition of a compound is specified by citing the mass percent of each element in the compound.
Percent composition from formula
By knowing the formula, the mass percent of each element can be readily calculated.
The subscripts in a formula represent not only the atom ratio in which the different elements are combined but also the mole ratio.

21. Percent Composition of Compounds
Where n is the number of atoms of that element in a molecule or formula unit of the compound.

22. Determination of an Empirical Formula from Percent Composition
The empirical formula of a compound can be determined by knowing its percent composition.
It is useful to assume 100 g of sample.
Consider a compound composed of only elements A and X.
The empirical formula of a compound can be derived from the masses of all elements in the sample

23. Determination of a Molecular Formula from Empirical Formula and Molar Mass
If we know the molar mass of the compound, we can determine the molecular formula by dividing the molar mass by the empirical formula mass.
We then can multiply the empirical formula by this number to obtain the molecular formula.

24. 3.3: Molarity – Unit of Concentration
Solutions are another term used for a homogeneous mixture.
A solutions is made up of two components:
1) Solute – Substance being dissolved.
2) Solvent – Substance that is doing the dissolving.
Typically, present in largest amount
When water is the solvent the solution is called an aqueous solution.

25. Reactions in the Laboratory
Solids often “react” better when they are dissolved in a solvent to produce a solution.
The solid reactant in this case is the solute.
Knowing the concentration of solute in the solution is important if we wish to perform quantitative analysis.
The concentration unit most often used by chemists is Molarity (M).

26. Molarity – Unit of Concentration
Qualitative terms used to describe a solution:
Concentrated – Relatively high concentration of solute, relatively large molarity.
Dilute – Relatively low concentration of solute, relatively small molarity.

27. Concentration of Solutions

28. Volumetric Flasks
A Volumetric flask is designed such that you can accurately make a solution of known molarity and volume.

29. Preparing A Solution of known M
Lets say that you wanted to make 1000 mL of a M potassium chromate (MM = g/mole) solution.
Step 1: Calculate the number of moles of potassium chromate that you need.
Step 2: Calculate the number of grams of potassium chromate that you need.
Step 3: Add this amount of potassium chromate to a 1000 mL volumetric flask, fill to the 1 L mark with water.

30. Preparing a solution of known Molarity

31. Molarity as a Conversion Factor
In Chapter 1 we saw that density can be used as a conversion factor to convert between mass and volume.
Molarity can be used as a conversion factor to convert between moles of solute and liters of solution.

32. An aqueous hydrochloric acid solution has a concentration of 0. 400 M
An aqueous hydrochloric acid solution has a concentration of M. If 25.0 mL of this solution is added to a flask, then how many grams of HCl were added?

33. Dilution of Solutions
Dilution – The process whereby the concentration of a solution is decreased by the addition of solvent.
Concentrated solutions known as stock solutions are commonly used in a lab.
These stock solutions are often diluted to produce a solution of desired concentration.

34. Dilution of Solutions

35. Derivation of Dilution Equation
moles of solute before dilution = moles of solute after dilution

36. 3.4: Other Units for Solution Concentration
Mass percent
For lower concentrations (very dilute solutions, very little solute)
Parts per million (ppm)
Parts per billion (ppb)

37. 3.4: Other Units for Solution Concentration
Volume Percent:
Sometimes used when the solute and solvent are liquids.
Mass-Volume Percent