Download bYTEBoss Chapter 4 Relative atomic mass and the mole

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 mass
Isotope
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 places
Isotope
Relative
abundance (%)
Relative isotopic
mass
10B
19.91
19.91
11B
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 nonzero 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
Scientific Notation is a way of writing numbers
that accommodates values too large or small
to be conveniently written in standard decimal
notation.
Ordinary decimal notation
Scientific notation
300
0.00004
4,570
5,720,000,000
−0.000 000 006 1
= 3×102
= 4×10-5
= 4.57×103
= 5.72×109
= −6.1×10−9
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
12
C
• 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 Grams
1. 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 Moles
1. 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 compound
Mr (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.
Calculate the amount in moles
Divide the number of moles by
smallest
Obtain the simplest whole number
mole ratio
Carbon
Oxygen
27.3 = 2.27
12.0
2.27 = 1
2.27
1
72.7 = 4.54
16.0
4.54 = 2
2.27
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
4.8
n(mol)
3.6 =0.3
12.0
0.3 = 1
0.3
1
9 – (4.8+3.6) =
0.6
0.6 = 0.6
1.0
0.6 = 2
0.3
2
Divide by
smallest mol
Ratio
4.8 = 0.3
16.0
0.3 = 1
0.3
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 formula
C
H
7.2
1.5
7.2 = 0.6
12.0
0.6 = 1
0.6
2
1.5 = 1.5
1
1.5 = 2.5
0.6
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