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Physical chemistry 1
Amount of substance
Relative atomic and molecular masses, the Avogadro constant and the mole
Relative atomic mass Ar
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The mass in grams of any atom or molecule is too small to find by weighing, so the masses of
atoms are compared, and relative masses are used
...
Now 1/12 or Carbon has an Ar of exactly 1
...


•

Ar = (average mass of 1 atom of an element *12) / (mass of 1 atom of carbon-12)
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You find the Mr by adding the Ar of every atom present in the molecule
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g
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Relative formula mass
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This also has the symbol Mr but is used for ionic compounds as they don’t exist as molecules
...


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To count atoms, we weigh large numbers of them
...


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If you weigh out the Mr of a molecule, it will have the same number of molecules
...


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Entities is a general word for a particle
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6
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The mole

Physical chemistry 1
Amount of substance
•

The amount of substance that contains 6
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Mass

Mr * moles
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The Ar of any element (in grams) contains 1 mole of atoms
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Number of moles = Mass * Mr
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To get a solution with a concentration of 1 mol dm-3, add solvent to 1 mole of solvent
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It’s measured in mol dm-3
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of mole (n) / volume (V) (dm3)

Number of moles in a given solution
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It changes with pressure and temperature
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Boyle’s law
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The product of pressure and volume is constant as long as temperature remains constant
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Physical chemistry 1
Amount of substance

Charles’ law
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Volume is proportional to the temperature as long as pressure remains constant
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Volume (V) / temperature (T) = constant
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Pressure (p) α temperature (T)
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Combining these relationships gives:
o

Pressure (p) * volume (V) / temperature (T) = constant for fixed mass of gas
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For n moles of gas:
o

Pressure (p) * volume (V) = no
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o

PV = nRT
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31 Jk-1mol-1
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No gases obey it exactly, but at room temperature and pressure it
holds well for many gases
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Units
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P must be in Pa (Nm-2)
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T must be in K (˚C + 273)
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Using the ideal gas equation

Physical chemistry 1
Amount of substance
•

None of the terms in the equation refer to a particular gas, so the volume will be the same for
any gas
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If you know the number of moles in a given mass of gas, you can find the mass of 1 mole of gas,
telling us the Mr
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o

Stp is standard temperature and pressure which is 35 ˚C and 100 kPa
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1
...

2
...

3
...

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E
...
4
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20g C, 4
...

o

Ca = 4
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1 = 0
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20/12
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10 mol

o

O = 4
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0 = 0
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10:0
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30 = 1:1:3

o

CaCO3

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If the number of moles in each element (step 2) is very close to 0
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2, 0
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you can times
by 2, 5, 3 etc
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Finding the molecular formula
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It gives the actual number of each element in 1 molecule of the compound (this only applies to
substances that exist as a molecule)
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To find the number of units of the empirical formula in the molecular formula: relative
molecular mass / relative mass of the empirical formula
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g
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17% C, 13
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79% O, Mr=46
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Find the empirical formula
o

C = 52
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0 = 4
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04/1 = 13
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79/16 = 2
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348:13
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174 = 2:6:1

o

C2H6O

2
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o

(2*12) + (6*1) + (1*16) = 46

3
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o

46/46=1

o

There’s 1 unit of the empirical formula
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•

It involves burning the unknown compound in excess oxygen and measuring the amount of
water, CO2, and other oxides
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The basic method measures carbon, hydrogen, sulfur and nitrogen, assuming that the oxygen
makes up the difference after the other 4 elements have been weighed
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The sample is burnt completely in oxygen
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The unreacted nitrogen is measured by thermal conductivity
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The molecular formula can be found if the relative molecular mass has been found using a mass
spectrometer
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g
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58 X compound with 1
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54g H2O gave 1
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54g H2O
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The relative molecular mass is 58
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1
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Physical chemistry 1
Amount of substance
o

o

o

C = 1
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32/44 = 0
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03 moles of C
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54g of H2O
▪

Mr = 18

▪

0
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03 mol of H2O

▪

Each mole has H2O has 2 moles of H so there’s 0
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▪

0
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Mass = 0
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36g

▪

0
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Mass = 0
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06g

▪

0
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06 = 0
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C and H
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58 – 0
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16) is O
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0g O (Ar = 16)
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16/16 = 0
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O

o

Sample contains: 0
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06 moles H and 0
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o

C:H:O = 0
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06:0
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o

C3H6O

2
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o

C3H6O

Balanced equations and related calculations
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Equations represent what happens in a chemical reaction
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Reactions → products
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Atoms react together in ratios, called the stoichiometry
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Physical chemistry 1
Amount of substance
Balanced symbol equations
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Use the formulae of reactants and products
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They tell us about the amounts of substances that react together and are produced
...

o

(s) means solid
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o

(g) means gas
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Writing balanced equations
1
...

2
...

3
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4
...

5
...

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E
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Aluminium + oxide → aluminium oxide
1
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1

2

2 3

3
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(4*27) + (3*2*16) → (2*27*2) + (2*3*16)
108 + 96 → 108 + 96
204 → 204
This is balanced
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Sometimes ions don’t take part in the reaction they’re called spectator ions
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g
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The total of charges on each side must be equal
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E
...
0
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Mg(s) + HCl(aq) → MgCl2(aq) + H2(g)
2
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1 mole

2 mole

1 mole

1 mole

4
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3
5
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12g of Mg = 0
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3 = 0
...

o

1 mole of Mg gives 1 mole MgCl2 therefore there’s 0
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o

Mr of MgCl2 = 24
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5) = 95
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o

Mass of MgCl2 = 95
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0049 = 0
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Finding concentrations using titrations
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Need to know concentration of reactant 1 and the equation for the reaction
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1
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2
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3
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Find the number of moles pf reactant 2 (V*conc
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Deduce the moles of reactant 1 (from equation)
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Find the concentration of reactant 1 (moles/V)
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Watch out for dilution, done if the reactants are dangerous or if titration needs repeating
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g
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4mol dm-3 of NaOH in 25cm3, xmol dm-3 of HNO3 in 18
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o

NaOH = 25cm3 = 0
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o

V*conc
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025*0
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01 mole
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01 moles

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Mole/v = 0
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0187 = 0
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Most chemical reactions produce 2 or more products, but usually only 1 is required
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Atom economy
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Found directly from the balanced equation
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Percentage atom economy = (mass of desired product / total mass of reactants)*100
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g
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o

From the equation calculate mass of each reactant and product involved
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o

2*(23 + 16 + 1) = 80g
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o

2*35
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0g
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o

23+16+35
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5g
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0g
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5/151 * 100 = 49
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o

Only 49
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Some reactants, in theory, have no wasted atoms
...

o

The atom economy tells us, in theory, how many atoms must be wasted in a reaction
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The practical process
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As a result of reactants that don’t go to completion
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In practice you never get the amount of product the equation predicts
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of moles of a specified product / theoretical maximum number
of moles of the products *100
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Physical chemistry 1
Amount of substance
•

Another problem is when reactions are reversible and don’t go to completion, which is common
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