The mass of particles

Relative isotopic mass, Relative atomic mass, Relative molecular

mass, The mole

Relative isotopic mass

• The relative isotopic mass (Ir) of an isotope is the mass of an atom of that isotope relative to the mass of an atom of 12C taken as 12 units exactly

Relative atomic mass• An element can have several naturally

occurring isotopes.

• These isotopes of a element behave in the same way.

• In calculating the relative atomic mass of an element with isotopes, the relative mass and proportion or percentage of each is taken into account.

Calculating relative atomic massIsotope Relative isotopic mass Relative abundance

(%)

Cl 34.969 75.80

Cl 36.966 24.20

Ar = (relative isotopic mass X1 % abundance) + relative isotopic mass X2 % abundance)

100

Ar (Cl) = (34.969 X 75.8) + ( 36.966 X 24.2) 100

Ar (Cl) = 2650.65 + 894.58 100

Ar (Cl) = 35.45 amu (atomic mass unit)

Your turn• Calculate the relative atomic mass of

Boron to two decimal placesIsotope Relative

abundance (%)Relative isotopic mass

10B 19.91 19.9111B 80.09 11.009

• Significant figures are important because they tell us how good the data we are using is.   

100 grams• This number has only one significant figure  

Because this digit is in the “hundreds” place, this measurement is only accurate to the nearest 100 grams

100. grams• This number has three significant figures (the

decimal makes all three digits significant.  Because the last significant figure is in the “ones” place, the measurement is accurate to the nearest gram.

100.00 grams• The number has five significant

figures.  Because the last significant figure is in the “hundredths” place, the measurement can be considered to be accurate to the nearest 0.01 grams

Significant Figures• The rules for identifying significant digits when

writing or interpreting numbers are as follows:

1. All non-zero digits are considered significant. Example: 1, 20, and 300 all have one significant figure. Their significant figures are 1, 2, and 3 respectively.

• 123.45 has five significant figures: 1, 2, 3, 4 and 5.

2. Zeros appearing anywhere between two non-zero digits are significant.

• Example: 101.12 has five significant figures: 1, 0, 1, 1 and 2.

3. Leading zeros are not significant. For example, 0.00012 has two significant figures: 1 and 2.

4. Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0.

• The number 0.000122300 still has only six significant figures. In addition, 120.00 has five significant figures.

5. Any zero that’s after all of the nonzero digits is significant only if you see a decimal point

20 000 has 1 significant figure 20 000.0 has 6 significant figures.

Scientific Notation

Ordinary decimal notation

300

0.00004

4,570

5,720,000,000

−0.000 000 006 1

Scientific notation

= 3×102

= 4×10-5

= 4.57×103

= 5.72×109

= −6.1×10−9

Scientific Notation is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation.

Relative molecular mass (Mr )• The relative molecular mass of a compound

is the mass of one molecule of that substance relative to the mass of a 12C

• This is calculated by taking the sum of the relative atomic masses of the elements in the molecular formula (i.e. covalent compounds)

• It is called relative formula mass for ionic compounds

Calculating relative molecular mass

Normally to find the relative atomic mass you just look in the periodic table!!

Oxygen (O2)Mr = 2 X Ar(0)

= 2 X 16.0

= 32.0 amu

Carbon Dioxide (CO2)Mr = Ar(C) + 2 X Ar(0)

= 12.0 + (2 X 16.0)

= 44.0 amu

Mass Spectrometer• is an analytical technique that can be used

to determine the chemical composition of a sample

• It Is a machine that separates the individual isotopes in a sample

• From this you can

calculate the relative

atomic mass.

Mass spectrum – graph of a mass spectrometer.

• Number of peaks = number of isotopes

• Position of peaks = relative isotopic mass

• Height of peaks = relative abundance of

the isotope,

in comparison to the

other isotopes of that

element.

Questions from the book

• Pg 59 Question 1,2,3 and 4

• x

The Mole

What is a mole?• What is a dozen?• 12 of something• The mole is like a dozen, it is a fixed number

of something• The mole is the amount of substance of a

system which contains as many elementary entities as there are atoms in 12 g (0.012 kilograms) of carbon 12.

• That number is 6.02 X1023 or• 602000000000000000000000 • a mole is a fixed number of things just like a

dozen.

Why have the mole?• It can become very cumbersome to deal with

such large numbers, especially during calculations.

• To overcome this impracticality, chemists deal with multiples of particles, instead of individually. This is why we have a mole!

Where did the mole come from?• The mole is a unit of measurement based

on work done almost 200 years ago by Amadeo Avogadro as he studied gas behavior.

• His work led to the association of a number, 6.02 x 1023, with the mole.

• 6.02 x 1023, is also called Avogadro’s constant or number

• It allows particles to be "counted.“• The word "mole" is derived from "gram molecular weight"

How big is the mole• The mole can be applied to anything: number of

trucks, number of balloons, number of Twilight fans.

• In a mole we know there are 6.02 X1023 of stuff it can be anything trucks, twilight fans etc• To have one mole of peas, they would have to

be a metre deep around earth and you would need 250 earths to fit them all on

How big is the mole• If you believe the universe is 15 billion

years old we have not yet had a mole of seconds yet!!!

• So the mole is HUGE!• But you can hold a mole of NaCl in your hand because molecules and atoms are so small

Examples of moles• 1 mole of iron contains the same number of

atoms as 1 mole of gold

• 1 mole of sodium chloride contains the same number of molecules as 1 mole of water

• the number of atoms in 1 mole of iron is equal to the number of molecules in 1 mole of water.

• 1 mole of water (H2O) has 1 mole of oxygen and 2 o hydrogen.

Lets deal with that big numbers first

• If I have 3 mol of trucks. How many trucks do I have?

• Its all about setting up your units correctly

• If you look at the units they cancel out

3 mol of trucks x 6.02x1023 trucks

1 mol of trucks

= 1.806 x 1024 trucks

Moles of atoms in molecules

• How many moles of oxygen atoms are in 5 mol of O2 ?

1 mol of O2 contains 2 mol of O atoms

5 mol of O2 contains 10 mol of O atoms

• How many moles of oxygen atoms are in 5 mol of H2SO4?

1 mol of H2SO4 contains 4 mol of O atoms

5 mol of H2SO4 contains 20 mol of O atoms

Atoms to Moles• I have 4.673 x 1011 atoms of Zinc. How many

mole do I have• Is it a mole?• 4.673 x 1011 atoms of Zinc x 1 mol of Zinc 6.02 x 1023 atoms of Zinc

= 7.7 x10-11 mols of zinc• Always check the units have cancelled out• This number is less than one therefore it is less

than one mol as it should be!

Moles to atoms• I have 3.01 x 1023 copper atoms. How

many mole of copper atoms do I have?

• 1 mol = 6.02 x 1023 atoms of copper

• Mol of copper = 3.01 x 1023copper atoms

6.02 x 1023 atoms of copper

mol

Mol of copper = 0.5 mol

Check calculation!

Your turn

• pg 61 Question 5, 6, 7 and 8

• CHALLENGE

How many moles of seconds have we experienced (if the world is 15 billion years old)

Show units and unit cancellation

Molar Mass

Molar Mass

• Molar mass (M) is the mass of one mole of a substance (chemical element or chemical compound).

• The unit of molar masses is:

grams per mole ( g or g/mol or g mol–1)

mol

How do you find the molar mass of an element?

• In general the molar mass of an element is the relative atomic mass of the element expressed in grams.

• The molar mass of a compound is the relative formula mass of the compound expressed in grams.

What is the molar mass of oxygen?What is the molar mass of bromine?

• x

Example• Calculate the molar mass of table sugar,

sucrose (C12H22O11)

Ar Carbon = 12.01

Ar Hydrogen = 1.00

Ar Oxygen = 16.00

M = (12 x 12.01)+ (22 x 1.00)+ (11 x 16.00)

M = 144.12 + 22 + 176

M = 342.12 g/mol

Your turn

• Pg 65 Questions 9

Grams to moles • Use the molar mass it has grams and moles

• How many moles of Zinc chloride do I have in 2.6g ZnCl2?

• Molar mass of ZnCl2 = 65.37 + (2 x 35.45)

= 136.27 g/mol

2.6 g of ZnCl2 x 1mol of ZnCl2 136.27 g ZnCl2

= 0.019 mol of ZnCl2

Grams to moles

• I have 30.0g of NH3. How many moles of NH3 do I have?

• Ar (NH3)= 14.00 +(1.00 x 3)

= 17g/mol

= 30.0g x 1 mol

17g

= 1.76 mol of NH3

Moles to grams

• I have 1.973 mol of I2

• How many grams of Iodine do I have?

• Molar mass of I2 = 126.90 x 2

= 253.8 g/mol

1.973 mol of I2 x 253.8g

1 mol of I2

= 500.75 g

Moles to Grams• I have 0.300 mol of water how many

grams of water do I have?• Ar (H2O) = (1.00 x 2) + 16.00 = 2.00 + 16.00 = 18.00 g/mol

= 0.300 mol H2O x 18.00g of H2O

1 mol of H2O

= 5.4 g of H2O

Moles to Grams1.Find how many moles are given in the problem. 2.Calculate the molar mass of the substance 3.Multiply step one by step two.

Grams to Moles1.Find the number of grams given in the problem. 2.Calculate the molar mass of the substance. 3.Divide step one by step two.

How many atoms of Iron?

• I have 5.5 g of Iron. How many atoms do I have • Ar = 55.45g/mol= 5.5g x 1 mol 55.45g= 0.099 mol= 0.099 mol x 6.02 x 1023 atoms of Iron

1 mol of Iron= 5.96 x 1022 atoms of Iron

Your turn

• Pg 65 Questions 10, 11, 12 and 13

• CHALLENGE

Using your knowledge of mole calculations and unit conversions, determine how many atoms there are in 1 L of petrol. Assume that the molecular formula for petrol is C6H14 and that the density of petrol is approximately 0.85 grams/mL.

Prac - How many moles of chalk does it take to write your name on a path?

• Weigh a piece of ordinary chalk and write your name on a path outside S1. Weigh the chalk again, and determine the number of moles of calcium carbonate that were used.

• Weight of chalk before writing your name: _______________

• Weight of chalk after writing your name: _______________

• Grams of chalk required to write your name: _______________

• Show all working out including unit cancellations

Percentage Composition

Percentage composition

• Percentage composition of a compound is a relative measure of the mass of each different element present in the compound.

• E.g. The percentage of Zn in ZnCl2

or The percentage of Al in Al2O3

Formula and Example% by mass of = mass of element in 1 mole of compound x 100

the element mass of 1 mole of the compound

Example: Calculate the percentage of Al in Al2O3

Step 1: Find the molar mass of the compoundMr (Al2O3) = (2 x 27) + (3 x16)

= 102 g/mol

Step 2: Find the molar mass of the element in the compound mass of Al in Al2O3 = (2 x 27)

= 54g/mol

Step 3 : Determine the % of the element in the compound% Al in Al2O3 = 54g/mol x 100

102g/mol

= 52.9%

Your turn

• Calculate the percentage composition of Zinc (Zn) in ZnCl2

• Calculate the percentage composition of oxygen (O) in Fe(NO3) 3

• Calculate the percentage composition of Carbon in C7H14O2

Empirical Formulas

Empirical formula• The empirical formula is a simple expression of

the relative numbers of each type of atom in it.• A person has two hands and ten fingers, or

H2F10. The empirical formula for that would be HF5

• Benzene, C6H6. The empirical formula is CH.

• This empirical formula tells us that the ratio of C to H is 1 to 1; there is one H atom for every C atom.

Empirical formula

• Write the empirical formula of the following.

• C8H16

• C8H8

• C10H30

How to calculate empirical formulas

A compound of carbon and oxygen is found to contain 27.3% carbon

and 72.7% oxygen by mass.Carbon Oxygen

Calculate the amount in moles 27.3 = 2.27

12.0

72.7 = 4.54

16.0Divide the number of moles by smallest

2.27 = 1

2.27

4.54 = 2

2.27Obtain the simplest whole number mole ratio

1 2

9.0g of a compound of only C,H,O contains 4.8 g of O and 3.6g of C

C H O

m(g) 3.6 9 – (4.8+3.6) = 0.6

4.8

n(mol) 3.6 =0.3

12.0

0.6 = 0.6

1.0

4.8 = 0.3

16.0

Divide by smallest mol

0.3 = 1

0.3

0.6 = 2

0.3

0.3 = 1

0.3

Ratio 1 2 1

Your turn

• Pg 71 Q 40, 41 and 42

Molecular Formulas

• A molecular formula gives the actual number of atoms in one molecule of the compound

• The empirical and molecular formula can be the same

• The molecular formula is always a whole number multiple o the empirical formula

A compound has the empirical formula of CH . The molar mass of the compound is 78 g/mol. What is the molecular formula of the compound?

• The molar mass of CH is 13g/mol

• Compound molar mass is 78g/mol

• No. of CH unit in a molecule = 78g/mol

13g/mol

= 6

CH x 6 = C6H6 = molecular formula

A sample of hydrocarbon was found to contain 7.2g of C and 1.5g of hydrogen. The molar mass of the compound is 58g/mol. What is the molecular formula?

1. Determine empirical formulaC H

7.2 1.5

7.2 = 0.6

12.0

1.5 = 1.5

1

0.6 = 1

0.6

1.5 = 2.5

0.6

2 5

2. Determine the molecular formula

• Empirical formula is C2H5

• The molar mass of C2H5 is 29g/mol• Compound molar mass is 58g/mol• No. of C2H5 unit in a molecule = 58g/mol 29g/mol = 2

• C2H5 x 2 = C4H10 = molecular formula

• Experiment: Percentage composition of Mg In MgO