Amount of Substance
2.1 Relative atomic and molecular masses, the
21 Relative Atomic, Molecular Masses, Avogadro’s
Constant and the Mole Avogadro constant and the mole
- Relative atomic mass (Ar) ~ The weighted average 2.2 moles in solution
mass of an atom of an element, taking into
account its naturally occurring isotopes, relative to 2.3 the ideal gas solution
1/12th the relative atomic mass of an atom of 2.4 empirical and molecular formulae
carbon-12.
2.5 balanced equations and related calculations
- Relative molecular mass (Mr) ~ The mass of a
molecule compared to 1/12th the relative atomic 2.6 Balanced equations, atom economies and
mass of an atom of carbon-12. percentage yields
!"#$!%# '!(( )* )+# #,#'#+-
- 𝐴𝑟 = !
'!(( )* )+# !-)' .!$/)+012
!"
!"#$!%# '!(( )* )+# '),#.3,#
- 𝑀𝑟 = !
'!(( )* )+# !-)' .!$/)+012
!"
- Avogadro’s constant ~ The number of atoms in 12g of carbon-12.
- Avogadro’s constant is 6.022 × 1024
- Mole ~ The amount of substance that contains Avogadro’s constants number of particles.
- 𝑚𝑎𝑠𝑠 (𝑔) = 𝑚𝑜𝑙𝑒𝑠 (𝑚𝑜𝑙) × 𝐴$ /𝑀$
22 Moles in Solution
- The concentration of a solution is the number of moles of solute dissolved in 1dm3 solvent.
5),#( ('),)
- 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (𝑚𝑜𝑙𝑑𝑚04 ) = #
8),3'# (9' )
e.g. 1.17g of sodium chloride was dissolved in water to make 500cm3 of solution. What is
the concentration of the solution in mol dm-3 Ar Na=23.0 Cl=35.5?
The mass of 1 mole of sodium chloride is 23.0 + 35.5 = 58.5g
𝑚𝑎𝑠𝑠/𝑔 1.17
= = 0.020 𝑚𝑜𝑙
𝑀$ 58.5
+) )* '),#( >.>2>
𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (mol𝑑𝑚04 ) = "),3'# (9'# ) = >.@>> = 0.040𝑚𝑜𝑙𝑑𝑚04
.)+.#+-$!-:)+ ;'),9'$# < × "),3'# (.'# )
- 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑖𝑛 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = 1>>>
- It is often necessary to prepare a solution with a highly accurate concentration. These are prepared in a
volumetric flask. When the bottom of the meniscus touches the line, the volume is 250cm3 with an
error of +/- 0.15cm3.
- Method for a 250cm3 standard solution:
1. Weigh out the desired mass of the solid into a weighing boat.
2. Put the solid into a beaker, rinse the weighing boat and put the washings into the beaker.
3. Add approximately 100cm3 of distilled water to the beaker.
4. Stir until all of the solid has dissolved.
5. Carefully pour all of the solution into the volumetric flask.
6. Rinse the beaker and pour this into the volumetric flask.
7. Add distilled water until it is about 1cm below the line.
8. Using a dropper pipette, carefully continue to add distilled water until the bottom of the meniscus
touches the line.
9. Put the stopper on the flask and invert it to mix
, - You may have to make up a solution with a low concentration. When this happens, you make up a
concentrated solution and then dilute it. This is called serial dilution. You may need to do multiple dilutions
to get the desired concentration.
- To work out the concentration of a serial dilution
o Calculate the concentration of the first solution
"),3'# A:A#--#9
o 𝑁𝑒𝑤 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑜𝑙𝑑 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 × "),3'# )* +#B *,!(C
o For any further dilutions repeat the calculation for each successive solution.
23 The Ideal Gas Solution
- Boyle’s Law
o The pressure multiplied by volume is a constant at a constant temperature.
o P x V = constant
- Charles’ Law
o The volume is proportional to the temperature at constant pressure
o 𝑉 ∝ 𝑇 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
8
o D
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
- Gay-Lussac’s Law
o The pressure is proportional to the temperature at a constant volume
o 𝑃 ∝ 𝑇 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
E
o D = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
- The ideal gas equation is a combination of these laws.
o 𝑃𝑉 = 𝑛𝑅𝑇
o Pressure (Pa) x Volume (m3) = number of moles x gas constant (J K-1mol-1). x temperature (K)
o The Value of R (gas constant) is 8.31
0
- 0 C = 273K
- This can also be represented to include Mr
'FD
o 𝑀$ = E8
- To determine the Mr of a volatile gas you need to know the temperature of the experiment, volume of
gas, mass of the gas and pressure. You use this method:
1. Weigh the mass of the gas canister
2. Allow gas to bubble through the delivery tube until the level of water inside and outside the
measuring cylinder is the same.
3. Measure the volume of the gas
4. Remeasure the mass of the gas canister
5. Measure temperature
6. Pressure will be atmospheric pressure (100kPa)
24 Empirical and Molecular Formulae
- Empirical formula ~ the formula that represents the simplest whole number ratio of the atoms of each
element in a compound.
- To find an empirical formula:
1. Find the masses of each of the elements in compound
2. Work out the number of moles of atoms in each element
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 =
𝑚𝑎𝑠𝑠 𝑜𝑓 1 𝑚𝑜𝑙 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
2.1 Relative atomic and molecular masses, the
21 Relative Atomic, Molecular Masses, Avogadro’s
Constant and the Mole Avogadro constant and the mole
- Relative atomic mass (Ar) ~ The weighted average 2.2 moles in solution
mass of an atom of an element, taking into
account its naturally occurring isotopes, relative to 2.3 the ideal gas solution
1/12th the relative atomic mass of an atom of 2.4 empirical and molecular formulae
carbon-12.
2.5 balanced equations and related calculations
- Relative molecular mass (Mr) ~ The mass of a
molecule compared to 1/12th the relative atomic 2.6 Balanced equations, atom economies and
mass of an atom of carbon-12. percentage yields
!"#$!%# '!(( )* )+# #,#'#+-
- 𝐴𝑟 = !
'!(( )* )+# !-)' .!$/)+012
!"
!"#$!%# '!(( )* )+# '),#.3,#
- 𝑀𝑟 = !
'!(( )* )+# !-)' .!$/)+012
!"
- Avogadro’s constant ~ The number of atoms in 12g of carbon-12.
- Avogadro’s constant is 6.022 × 1024
- Mole ~ The amount of substance that contains Avogadro’s constants number of particles.
- 𝑚𝑎𝑠𝑠 (𝑔) = 𝑚𝑜𝑙𝑒𝑠 (𝑚𝑜𝑙) × 𝐴$ /𝑀$
22 Moles in Solution
- The concentration of a solution is the number of moles of solute dissolved in 1dm3 solvent.
5),#( ('),)
- 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (𝑚𝑜𝑙𝑑𝑚04 ) = #
8),3'# (9' )
e.g. 1.17g of sodium chloride was dissolved in water to make 500cm3 of solution. What is
the concentration of the solution in mol dm-3 Ar Na=23.0 Cl=35.5?
The mass of 1 mole of sodium chloride is 23.0 + 35.5 = 58.5g
𝑚𝑎𝑠𝑠/𝑔 1.17
= = 0.020 𝑚𝑜𝑙
𝑀$ 58.5
+) )* '),#( >.>2>
𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (mol𝑑𝑚04 ) = "),3'# (9'# ) = >.@>> = 0.040𝑚𝑜𝑙𝑑𝑚04
.)+.#+-$!-:)+ ;'),9'$# < × "),3'# (.'# )
- 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑖𝑛 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = 1>>>
- It is often necessary to prepare a solution with a highly accurate concentration. These are prepared in a
volumetric flask. When the bottom of the meniscus touches the line, the volume is 250cm3 with an
error of +/- 0.15cm3.
- Method for a 250cm3 standard solution:
1. Weigh out the desired mass of the solid into a weighing boat.
2. Put the solid into a beaker, rinse the weighing boat and put the washings into the beaker.
3. Add approximately 100cm3 of distilled water to the beaker.
4. Stir until all of the solid has dissolved.
5. Carefully pour all of the solution into the volumetric flask.
6. Rinse the beaker and pour this into the volumetric flask.
7. Add distilled water until it is about 1cm below the line.
8. Using a dropper pipette, carefully continue to add distilled water until the bottom of the meniscus
touches the line.
9. Put the stopper on the flask and invert it to mix
, - You may have to make up a solution with a low concentration. When this happens, you make up a
concentrated solution and then dilute it. This is called serial dilution. You may need to do multiple dilutions
to get the desired concentration.
- To work out the concentration of a serial dilution
o Calculate the concentration of the first solution
"),3'# A:A#--#9
o 𝑁𝑒𝑤 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑜𝑙𝑑 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 × "),3'# )* +#B *,!(C
o For any further dilutions repeat the calculation for each successive solution.
23 The Ideal Gas Solution
- Boyle’s Law
o The pressure multiplied by volume is a constant at a constant temperature.
o P x V = constant
- Charles’ Law
o The volume is proportional to the temperature at constant pressure
o 𝑉 ∝ 𝑇 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
8
o D
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
- Gay-Lussac’s Law
o The pressure is proportional to the temperature at a constant volume
o 𝑃 ∝ 𝑇 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
E
o D = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
- The ideal gas equation is a combination of these laws.
o 𝑃𝑉 = 𝑛𝑅𝑇
o Pressure (Pa) x Volume (m3) = number of moles x gas constant (J K-1mol-1). x temperature (K)
o The Value of R (gas constant) is 8.31
0
- 0 C = 273K
- This can also be represented to include Mr
'FD
o 𝑀$ = E8
- To determine the Mr of a volatile gas you need to know the temperature of the experiment, volume of
gas, mass of the gas and pressure. You use this method:
1. Weigh the mass of the gas canister
2. Allow gas to bubble through the delivery tube until the level of water inside and outside the
measuring cylinder is the same.
3. Measure the volume of the gas
4. Remeasure the mass of the gas canister
5. Measure temperature
6. Pressure will be atmospheric pressure (100kPa)
24 Empirical and Molecular Formulae
- Empirical formula ~ the formula that represents the simplest whole number ratio of the atoms of each
element in a compound.
- To find an empirical formula:
1. Find the masses of each of the elements in compound
2. Work out the number of moles of atoms in each element
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 =
𝑚𝑎𝑠𝑠 𝑜𝑓 1 𝑚𝑜𝑙 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
