The Mathematics of

Chemistry

Stoichiometry

Dimensional Analysis

Stoichiometry

• Stoichiometry is a branch of chemistry

that deals with the relative quantities of

reactants and products in chemical

reactions.

• Greek root words:

– Stoicheion meaning " element“

– Metron meaning "measure"

What is Dimensional

Analysis?

• Using the units, or dimensions, of

measurements to express and

calculate chemical quantities

What is the relationship?

• Dimensional analysis is a strategy

used for doing stoichiometric

calculations.

What are some common

equivalent measurements?

• 1 inch =______centimeter(s)

• 1 week = ______ day(s)

• 60 seconds = ______minute(s)

• 1 lb =______ ounce(s)

• 1 cup = _____ fluid ounces

• 1 tablespoon = _____ teaspoon(s)

• 4 quarts = _____ gallon(s)

Common Equivalent

Measurements

• 1 mile = _____ feet

• 1 kg = _____ 2.2 lb

• 1 ft = ____ inches

• 365 days = _____ year(s)

• 1 ton = _____ pounds

Dimensional Analysis –

The Plan 1. What is given? Start your calculation with this

quantity with units.

2. What is your goal? What you are solving for is

your goal and should be on top of the last step of

the problem.

3. Set up a series of equivalent measures that

cancels out all units except the goal units.

4. Solve the problem, and remember to mark through

the cancelled units.

5. Record the answer with appropriate units and sig

figs.

Give it a try! How many seconds are there

in 5.5 days?

Follow the steps:

1.What is given? 5.5 days

2.What is your goal, and what are the units?

Determine # of seconds in 5.5 days

3.Set up a series of equivalent measure that

cancels out all units except the goal units.

Give it a try!

5.5 days X 24 hours X 60 minutes X 60 seconds= ? seconds

1 1 day 1 hour 1 minute 1

4.Record the appropriate answer with units.

What are some common

equivalent measurements in

chemistry?

• 1,000 g = _____kg

• 100 cm = ______ m

• 1 m = _____dm

• 1 L = _____ml

• 1 mole = _______ particles/atoms

• molar mass = _____ mole(s)

• Avogadro’s number = _____ mole(s)

Mole equivalents

MOLE

P

A

R

T

I

C

L

E

S

G

R

A

M

S

Avogadro’s

Number Molar

Mass

Give it a try!

• How many grams are in 4.92

moles of calcium carbonate?

Molar Mass

The mass in grams of 1 mole of

the compound calcium carbonate

CaCO3 Ca 1 X 40.078 grams = 40.078 grams

C 1 X 12.011 grams = 12.011 grams

O 3 X 15.999 grams = 47.997 grams

TOTAL = 100.086 grams

Give it a try!

Stoichiometric Calculations

4.92 mol CaCO3 X 100.086g CaCO3 =

1 mol CaCO3

Stoichiometric Calculations – The Plan

1. Write the chemical equation.

2. Balance the chemical equation.

3. *Follow steps to dimensional analysis: Start with what is given.

Set up a series of equivalent measures.

End with your goal.

Solve the problem by cancelling units.

Record the appropriate answer with units.

Stoichiometric Calculations – The Plan

There are three types of equivalent measures for

stoichiometry:

1. moles to grams 1 mole = molar mass

2. moles to moles using the mole ratio from

the balance chemical reaction

3. moles to avogadro’s number 6.02 x 1023

particles = 1 mole

Balancing

Chemical Equations

C2H5OH (l) + O2 (g) CO2 (g) + H2O (g)

C2H5OH (l) + 3O2 (g) 2CO2 (g) + 3H2O (g)

Chemical Equations as

Equivalents

• Coefficients from a balanced equation

represent the number of theoretical

mole equivalents and can be used in

stoichiometric calculations.

Stoichiometric Calculations – The Plan

1. Write the Chemical Equation.

2. Balance the Chemical Equation.

3. Follow steps to Dimensional Analysis: Start with what is given.

Set up a series of equivalent measures.

End with your goal.

Solve the problem by cancelling units.

Record the appropriate answer with units.

Stoichiometric Calculations – The Problem

Lithium hydroxide is used in an outer space environment to

remove excess exhaled carbon dioxide from the living

environment. The products of the reaction are lithium

carbonate and water. If 48.0 grams of lithium hydroxide are

used in a small scale experimental device, how much carbon

dioxide will the device process? The Plan:

1. Write the chemical equation.

2. Balance the chemical equation.

3. Follow steps to dimensional analysis: Start with what is given.

Set up a series of equivalent measures.

End with your goal.

Solve the problem by cancelling units.

Record the appropriate answer with units.

* Remember Significant Figures.

Stoichiometric Calculations – The Plan

LiOH + CO2 (g) Li2CO3 + H2O (g)

2. Balance the chemical equation.

1. Write the chemical equation.

2 LiOH + CO2 (g) Li2CO3 + H2O (g)

Stoichiometric Calculations – The Plan

2 LiOH + CO2 (g) Li2CO3 (g) + H2O (g)

48.0 g LiOH X 1 mole LiOH X 1 mole CO2 X 44.009g CO2 =

1 23.948 g LiOH 2 mole LiOH 1 mole CO2

3. Follow steps to dimensional analysis:

Stoichiometric Calculations – The Answer

When 48.0 grams of lithium hydroxide are available for

use in a reaction, 44.1 grams of carbon dioxide can be

processed by the reaction.

*Remember the significant figures.

Partner Share

Write your own stoichiometry question

for this reaction, and switch with your

table partner:

Barium chloride reacts with sodium

sulfate in a precipitation reaction to

make barium sulfate.