STOICHIOMETRY OF CHEMICAL REACTIONS

(Q3 U2)

STOICHIOMETRY The study of the quantitative relationships

between reactants and products in a reaction It is used to answer questions like; If I have this much

reactant, how much product can I make? If I want this much product, how much reactant do I

need? These questions have real life application,

particularly in manufacturing. It allows us to convert the mass of a substance to

the number of particles (atoms, ions or molecules) it contains.

These numbers can be really large, so they are counted in groups

Much like when we count a lot of pennies we stack them in 10’s and count by 10

The Mole Atoms are very tiny, so small that the grouping we use to count them must be very large MOLE; the group (unit of measure) used to

count atoms, molecules, formula units or ions of a substance

1 mole of a substance has a particular number of particles in it! Much like 1 dozen always means 12; whether it is 12 eggs 12 oranges or 12

gold bars

How many particles are in a mole?

The number of particles in a mole = 6.02 x 10 23 or

602,000,000,000,000,000,000,000 !

This is known as Avogadro’s Number

Using this, We can easily count the number of particles in all kinds of things !

Counting Particles in a MoleThere are 6.02 x 10 23 Carbon atoms in a mole of

carbon There are 6.02 x 10 23 CO2 molecules in a mole of CO2

There are 6.02 x 10 23 sodium ions in a mole of sodium

There are 6.02 x 10 23 marbles in a mole of marbles

That’s a lot of marbles!

The Size of a mole of a substance changes, the bigger the substance the more space a mole of the substance takes up, but the number of particles in a mole is always the same!

A Mole of Water

Molar Mass Chemicals do not come bundled in moles, like a

dozen eggs comes in a 1 dozen or 1 ½ dozen package so we use the mole as a grouping unit.

The mass of 1 mole of a pure substance called it’s molar mass

If I want to produce 500g of methanol using the following equation, CO2 +3H2 CH3OH + H20 how many grams of CO2 and H2 do I need?

These are the questions stoichiometry answers!

What do we need to know to answer this?

If I want to produce 500g of methanol using the following equation;

CO2 +3H2 CH3OH + H20

How many grams of CO2 and H2 do I need?

This equation relates the molecules of reactants and products, NOT THEIR MASSES! 1 molecule of CO2 and 3 molecules of H2 will make 1

molecule of CH3OH

We need to relate the masses to the number of molecules.

Relating Mass to Moles

Remember; The average atomic masses of the elements are found on the Periodic Table!

We can use the atomic masses on the PT to relate the mass of the compound to the mass of a mole!

Molar Mass and Formula Mass

Molar mass: The mass (in grams)of one mole of a molecule or a formula unit

Molecular mass: mass in atomic mass units of just one molecule

Formula Mass: mass in atomic mass units of one formula unit of an ionic compound

Relating the Mass of an Atom to the Mass of a Mole of substance.

Steps

1. Find the average Atomic Mass of the element on the PT. (state it in grams instead of atomic units)

a) Example: molar mass of Fe = 55.847 gb) Example: molar mass of Pt = 195.08 g

2. If the element is a molecule, count the number of atoms in the molecule then multiply the atomic mass by the number of atoms.

a) Example: O2, the mass of O =16.0g There are 2 atoms of O in the O2 molecule , 2 atoms X 16.0g = 32.00g is the molar mass of the molecule.

Let’s Practice

Calculate the molar mass of each of the following:

1. N2

2. Cl23. Br2

4. I25. H2

6. F2

Molar Mass Answers

Calculate the molar mass of each of the following:

1. N2 = 14.007g X 2 =28.014 g/mol

2. Cl2 = 35.453g X 2 =70.906 g/mol

3. Br2 = 79.904g X 2 =159.808 g/mol

4. I2 = 126.904g X 2 =253.808 g/mol

5. H2 = 1.008g X 2 =2.016 g/mol

6. F2 = 18.998g X 2 =37.996 g/mol

Now, let’s do the same for an example reaction!

Steps1. Count the number and type of atoms2. Find the Atomic Mass of each atom type,

on the periodic table. Write it in grams.3. Multiply the mass times the # of Atoms.

Then add the totals

How do we calculate Molar Mass?1. Count the number and type of atomsEthanol (C2H5OH)

2. Find the Atomic Mass of each atom type, on the periodic table. Write it in grams.

3. Multiply The mass X the # of Atoms. Then add the totals.

Atom type Amount of each atom

C 2

H 6

O 1

Atom type Amount of atom

Ave. Atomic Mass in g

C 2 12.0

H 6 1.00

O 1 16.0

Atom type

Amount of atom

Ave. Atomic Mass in g

Total

C 2 12.0 =24.0

H 6 1.00 =6.0

O 1 16.0 =16.0

Molar Mass Of Ethanol (C2H5OH) = 46.0g/mole

How do We Calculate Molar Mass?

Atom Types

Amount of Atoms

Ave. Atomic

Mass in g

Total

Ca 1 40.1 40.1

Cl 2 35.5 71.0

Mass of 1 mol of CaCl2 (molar mass) 111.1 g/mole

Example: Calcium Chloride (CaCl2 )

Now You Do Some

What is the molar mass of each of the following?

1. Fe2 O3

2. H2O

3. CO2

4. NaCl5. NH3

6. BaI2

Molar Mass Answers Fe2 O3 = 55.85g X 2= 111.7 g

16.0g X 3 = 48.0g = 159.7 g/mol_______________________________________________ H2O = 1.01g X 2 = 2.02

16.0g X 1 = 16.0 = 18.02 g/mol_______________________________________________ CO2 = 12.01g X 1 = 12.01

16.0g X 2 = 32.0 = 44.01 g/mol________________________________________________NaCl = 22.99 gX1 = 22.99 35.45g X1 = 35.45 = 58.44 g/mol________________________________________________NH3 =14.01g X 1 = 14.01

1.01g X 3 = 3.03 = 17.04 g/mol________________________________________________BaI2 = 137.33g X 1 = 137.33

126.90g X 2 = 253.80

= 391.13 g/mol

Now that we know how to find Molar Mass What is the next step?

If I want to produce 500g of ethanol using the following equation;

6CO2 +17H2 3C2H5OH + 9H20

How many grams of CO2 and H2 do I need?

The Molar Mass Of Ethanol (C2H5OH)

= 46.0g/mole Now we need to find the number of

atoms in the sample. How many molecules of ethanol are in

500g?

Finding the number of atoms in a given mass

Steps to finding the number of atoms in a given mass of a sample

1. Use PT to find the molar mass of the substance

2. Convert the mass of the substance to number of moles in the sample (convert using mass of one mole as conversion factor)

3. Use the number of atoms in a mole to find the number of atoms in the sample

4. Solve and check answer by canceling out units

Finding the number of atoms in a sample of an element

The mass of an iron bar is 16.8g. How many iron(Fe) atoms are in the sample?Step 1: Use PT to find the molar mass of the substance : The molar mass of Fe =55.8g/moleStep 2: Convert the given mass of the substance to number of moles in the sample: Fe =55.8g/mole

(16.8g Fe) (1 mol Fe) (6.022 X 1023 Fe atoms)= 1.81 X 10

23 Fe atoms

(55.8g Fe) (1 mol Fe)

Step 3: Use the number of atoms in a mole to find the number of atoms in the sample = 1.18 X 1023

Calculate the number of atoms in the given samples

1. 25.0 g silicon, Si

2. 1.29 g chromium, Cr

Answers

(25.0 g Si ) ( 1 mol Si ) (6.02 X 1023 Si atoms ) 1 28.1g Si 1 mol Si = 5.36 X1023 atoms Si

(1.29 g Cr ) ( 1 mol Cr ) (6.02 X 1023 Cr atoms ) 1 52.0g Cr 1 mol Cr= 1.49 X1022 atoms Cr

Practice: Determine the number of Atoms in a given sample

Remember: (given mass X 1 mole per molar mass X atoms per 1 mole)

1. 98.3g mercury, Hg2. 45.6g gold, Au3. 10.7g lithium, Li4. 144.6g tungsten, W

Answers1. (98.3 g Hg ) ( 1 mol Hg )(6.02 X 1023 Hg atoms) 1 200.6g Hg 1 mol Hg = 2.95 X1023 atoms Hg

2. (45.6 g Au ) ( 1 mol Au )(6.02 X 1023 Au atoms) 1 197.0g Au 1 mol Au = 1.39 X1023 atoms Au

3. (10.7 g Li ) ( 1 mol Li )(6.02 X 1023 Li atoms) 1 6.94g Li 1 mol Li = 9.28 X1023 atoms Li

4. (144.6 g W ) ( 1 mol W )(6.02 X 1023 W atoms) 1 183.8g W 1 mol W = 4.738 X1023 atoms W

Determining the Number of formula units in a sample

Steps1. Use the PT to calculate the molar mass

of one formula unit2. Convert the given mass of the compound

to the number of molecules in the sample (use the molar mass as the conversion factor)

3. Multiply the moles of the compound by the number of the formula units in a mole (Avagadro’s number) and solve

4. Check by evaluating the units

The mass of a quantity of Iron(III) oxide is 16.8g. How many formula units in the sample?

1. Calculate the molar mass (Fe2O3)

2 Fe atoms 2X 55.8 = 111.6 3 O atoms 3 X 16.0 = +48.0

molar mass 159.6 g/mol(given mass X 1 mole per molar mass X Form Units per 1

mole)

(16.8 g Fe2O3 ) ( 1 mol Fe2O3 )(6.02 X 1023 Fe2O3 Formula units) 1 159.6g Fe2O3 1 mol Fe2O3

= 6.34 X1022 Fe2O3 Formula units

How many Formula Units in each sample?

1. 89.0g sodium oxide (Na2O)

2. 10.8g boron triflouride ( BF3)

Answers1. 89.0g sodium oxide (Na2O)

Calculate the molar mass (Na2O)

2 Na atoms 2X 23.0 = 46.0 1 O atoms 1 X 16.0 = +16.0

molar mass 62.0 g/mol

(given mass X 1 mole per molar mass X molecules per 1 mole)

(89.0 g Na2O ) ( 1 mol Na2O )(6.02 X 1023 Na2O Form Units) 1 62.0g Na2O 1 mol Na2O

= 8.64 X1023 Na2O Formula units

Answers Continued2. 10.8g boron trifloride ( BF3)

Calculate the molar mass (Na2O)

1 B atom 1X 10.8 = 10.8 3 F atoms 3 X 19.0 = +57.0

molar mass 67.8 g/mol

( given mass X 1 mole per molar mass X molecules per 1 mole)

(10.8 g BF3 ) ( 1 mol BF3 )(6.02 X 1023 BF3 Form units) 1 67.8g BF3 1 mol BF3

= 9.59 X1022 BF3 Formula units

How do we find the number of moles if given the mass?

Steps1. Determine the molar mass2. Change given mass to moles by

using molar mass as the conversion factor. (1/molar mass)

Example of Grams to MolesCalculate the number of moles in 6.84g sucrose (C12H22O11)

12 C atoms 12 X 12.0 = 144.0 22 H atoms 22 X 1.0 = 22.0 11 O atoms 11 X 16.0 = +176.0

molar mass 342.0 g/mol

(given mass/1) X (1 mole/ molar mass)

(6.84 g sucrose ) ( 1 mol sucrose ) 1 342.0g sucrose

= 2.0 X10-02 moles of sucrose

Determine the number of moles in each sample

1. 16.0g sulfur dioxide, SO2

2. 68.0g ammonia, NH3

3. 17.5g copper(II) oxide, CuO

Answers1. 16.0g sulfur dioxide, SO2

(16.0g/1) (1mole/64.1g ) = 0.250 mol SO2

2. 68.0g ammonia, NH3

( 68.0g/1) (1 mole/ 17.0g) = 4.00 mol NH3

3. 17.5g copper(II) oxide, CuO ( 17.5g/1) (1 mole/ 79.1g) = 0.22 mol

CuO

How do we find the mass if given the moles?

Steps:1. Find the molar mass of the compound2. Use the molar mass to convert the given

number of moles to a mass (moles) X (g/mol)

3. Solve4. Check using dimensional analysis (make

sure units cancel and leaves only grams)

Ex: What mass of water must be weighed to obtain 7.50 mol of H2O?

1. Find the molar mass of the compound (H2O)

H - 2 atoms – 1.0 = 2.0 O - 1 atom - 16.0 = 16.0 18.0 g/mol 2. Use the molar mass to convert the given number of

moles to a mass (moles) X (g/mol) (7.5 mol H2O) ( 18.0 g H2O)

( 1 mol H2O)

3. Solve : 7.5 X 18.0g H2O = 135 g H2O

4. Check using dimensional analysis (make sure units cancel and leaves only grams) “mol H2O” cancel each other out, units are correct!

Practice Determining the Mass from the Molar Quantities:

1. 3.52 mol Si2. 1.25 mol aspirin, C9H8O4

3. 0.550 mol F2

4. 2.35 mol Barium Iodide, BaI2

Answers: Molar Quantity Problems

(moles) X (g/mol)

1. What mass of Si = 3.52 mol Si (3.52 mol Si) (28.1g Si) = 98.9g Si 1 (1 mole Si)

2. What mass of C9H8O4 = 1.25 mol aspirin, C9H8O4

C -9 atoms – 12.0 – 108.0

H- 8 atoms – 1.0 - 8.0

O – 4 atoms – 16.0 - 64.0

180.0g/mol

(1.25 mol C9H8O4) (180.0g C9H8O4) = 225.0g C9H8O4

1 (1 mole C9H8O4)

Answers: Molar Quantity Problems, part 2

3. What mass of F2 = 0.550 mol F2

F- 2 atoms – 19.0 = 38.0 g/mol

(0.550 mol F2 ) (38.0 g F2) = 20.9g F2

1 (1 mole F2)

4. What mass of BaI2 = 2.35 mol Barium Iodide, BaI2

Ba-1 atom – 137.3 - 137.3

I – 2 atoms – 126.9 - 253.8

391.1g/mol

(2.35 mol BaI2) (391.1g BaI2) = 919.1g BaI2 1 (1 mole BaI2)

What We Should Know & Be Able To Do At This Point!

Know:1. What stoichiometry is2. What a mole is3. How to calculate molar mass of an element and of a compound4. How to determine the number of atoms or

formula units in a given mass of sample 5. How to determine the number of moles in a

given mass of a sample6. How to determine the mass of a given molar

quantity

Review of Calculation Rules To Find molar mass (g/mol)

(atomic mass of each atom) X (amount of each atom) Then add together mass of all atoms(g/mol)

To Find the # atoms in a given mass

(given mass) X (1mole) /(molar mass(g)) X (# atoms) /(1 mole)

To Find the # moles in a given mass

(given mass) X (1mole)/(molar mass(g)) X (#atom)/(1mole)

To Find the mass(g) of a given molar quantity

(#moles) X (grams/1 mole)(from molar mass)

Using Moles Balanced chemical equations relate

moles of reactants to moles of products Just like when baking, reactants have to be

mixed in the proper proportions to make a certain amount of the desired product

Specific amounts of reactants produce specific amounts of product

We can use balanced chemical equations and moles to PREDICT the masses of reactants or products

Predicting Mass of a Reactant and Product

Steps You can not move directly from the mass

of one substance to the mass of the second1. You MUST convert the given mass to

moles first!2. The coefficients of balanced reactions tell

you the NUMBER OF MOLES of each chemical in the reactant

3. Once you know the number of moles of any reactant or product use the coefficients in the equation to convert the moles of the other reactants and products

Example: Predicting Mass of a Reactant and Product

Ammonia gas is synthesized from nitrogen gas and hydrogen gas according to the balanced equation : N2 + 3H2 2NH3

How many grams of hydrogen gas are required for 3.75g of nitrogen gas to react completely? What mass of ammonia is formed?

Reactants and products are related in terms of moles The amount of H2 needed depends on the moles

of N2 present in 3.75g and the ratio of moles of H2 to moles of N2 in the equation.

The amount of ammonia formed depends on the ratio of moles N2 to moles of ammonia

1. Convert the given mass to moles Find the # of moles of N2 using molar mass(3.75g N2) (1 mol N2)

(28.0 g N2)

2. The coefficients of balanced reactions tell you the NUMBER OF MOLES of each chemical in the reactant

3. Once you know the number of moles of any reactant or product use the coefficients in the equation to convert the moles of the other reactants and products