## Chapter 4

24 September 2013

*Calculations and the Chemical *
*Equation*

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

## The Mole Concept and Atoms

• Atoms are exceedingly small– Unit of measurement for mass of an atom is atomic mass unit (amu) – unit of measure for the mass of atoms

• carbon-12 assigned the mass of exactly 12 amu

• 1 amu = 1.66 x 10-24_{g }

• What is the atomic weight of one atom of fluorine? Answer: 19.00 amu

• What would be the mass of this one atom in grams?

• Chemists usually work with much larger quantities

– It is more convenient to work with grams than amu when using larger quantities

## Mass of Atoms

atom F F g 10 156 . 3 F amu 1 g 10 1.661 atom F F amu 19.00_{} -24

_{} 23

• A practical unit for defining a collection
of atoms is the **mole**

1 mole of atoms = 6.022 x 1023 _{atoms}

## The Mole

• To make this connection we must define
the **mole** as a counting unit

– The mole is abbreviated mol

• A mole is simply a unit that defines an amount of something – Dozen defines 12 – Gross defines 144 – score 20 – ream 500

## The Mole

F
mol
1
F
atom
10
022
.
6
F
amu
1
F
g
10
66
.
1
F
atom
1
F
amu
00
.
19 _{} 24 _{} 23
=19.00 g F/mol F or 19.00 g/mol F

## Atomic Mass

• The atomic mass of one atomof an element corresponds to:

– The average mass of a single atom in amu

– The mass of a mole of atoms in grams

– 1atomof F is 19.00**amu** 19.00 amu/atom F

– 1 moleof F is 19.00**g** 19.00 g/mol F
F
mol
1
F
atom
10
022
.
6
F
amu
1
F
g
10
66
.
1
F
atom
1
F
amu
00
.
19 _{} 24 _{} 23
=19.00 g F/mol F or 19.00 g/mol F
note:

The name of the unit is “mole” The symbol is “mol”

## Calculating atoms, moles, and mass

• We use the following conversion factors: • Density converts grams – milliliters

• Atomic mass unit converts amu – grams

• Avogadro’s number converts moles – number of atoms

• Molar mass converts grams – moles

## Strategy for Calculations

• Map out a pattern for the required conversion • Given a number of grams and asked for

number of atoms

• Two conversions are required • Convert grams to moles

1 mol S/32.06 g S**OR** 32.06 g S/1 mol S

• Convert moles to atoms

## Practice Calculations

1. Calculate the number of atoms in 1.7 moles of boron.

2. Find the mass in grams of 2.5 mol Na (sodium).

3. Calculate the number of atoms in 5.0 g aluminum.

4. Calculate the mass of 5,000,000 atoms of Au (gold)

## Interconversion Between Moles,

## Particles, and Grams

## The Chemical Formula, Formula

## Weight, and Molar Mass

• Chemical formula - a combination of

symbols of the various elements that make up the compound

• Formula unit - the smallest collection of atoms that provide two important pieces of information

– The identity of the atoms

– The relative number of each type of atom

## Chemical Formula

Consider the following formulas:• H_{2}– 2 atoms of hydrogen are chemically bonded
forming diatomic hydrogen, subscript 2

• H_{2}O– 2 atoms of hydrogen and 1 atom of oxygen,
lack of subscript means one atom

• NaCl – 1 atom each of sodium and chlorine

• Ca(OH)_{2} – 1 atom of calcium and 2 atoms each of
oxygen and hydrogen, subscript outside parentheses
applies to allatoms inside

## Chemical Formula

Consider the following formulas:• (NH_{4})_{2}SO_{4}– 2 ammonium ions and 1 sulfate ion
– Ammonium ion contains 1 nitrogen and 4 hydrogen
– Sulfate ion contains 1 sulfur and 4 oxygen

– Compound contains 2 N, 8 H, 1 S, and 4 O
• CuSO_{4}._{5H}

2O

– This is an example of a **hydrate**- compounds containing
one or more water molecules as an integral part of their
structure

– 5 units of water with 1 CuSO_{4}

Homework: What does “sesqui” mean?

## Comparison of Hydrated and

## Anhydrous Copper Sulfate

## Formula Weight and Molar Mass

• Formula weight- the sum of the atomic weightsof all atoms in the compound as represented by its correct formula

– expressed in amu

• What is the formula weight of H_{2}O?
– 16.00 amu + 2(1.008 amu) = 18.02 amu

• Molar mass– mass of a mole of compound in grams / mole

– Numerically equal to the formula weight in amu

• What is the molar mass of H_{2}O?
– 18.02 g/mol H_{2}O

## Formula Unit

• Formula unit – smallest

collection of atoms from which the formula of a compound can be established

• When calculating the formula weight (or molar mass) of an ionic compound, the smallest unit of the crystal is used

What is the molar mass of (NH_{4})_{3}PO_{4}?
3(N amu) + 12(H amu) + P amu + 4(O amu)=

## Molar Mass

• Molar mass - The mass in grams of 1 mole of atoms

• What is the molar mass of carbon? 12.01 g/mol C

• This means counting out a mole of carbon
atoms *(i.e., 6.022 x 10*23_{)} _{they would have a mass }

of 12.01 g

• One mole of anyelement contains the same

number of atoms, 6.022 x 1023_{, Avogadro’s number}

## The Chemical Equation and the

## Information It Conveys

A Recipe For Chemical Change

• Chemical equation- shorthand notation of a chemical reaction

– Describes all of the substances that react and all the products that form, physical states, and experimental conditions

## Features of a Chemical Equation

1. Identity of products and reactants must bespecified using chemical symbols

2. Reactants are written to the left of the reaction arrow and products are written to the right 3. Physical states of reactants and products may

be shown in parentheses

4. Symbol over the reaction arrow means that energy is necessary for the reaction to occur 5. Equation must be balanced

)
(
O
)
2Hg(
)
2HgO(* s*

**

**l**_{2}

**g****Products**

**Products** – written on the right
**Reactants **– written on the left of arrow

Products and reactants must be specified using chemical symbols

– energy is needed