4. Chemical Calculations

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Balancing equations
An important principle in chemical reactions is that matter
cannot be created or destroyed. It is important that symbol
equations are balanced.
A balanced equation has the same number of each type of
atom on each side of the equation.
Unbalanced:
Na
+
Cl2
1 sodium 2 chlorine
Balanced:
2Na
+
Cl2
2 sodium 2 chlorine

NaCl
1 sodium 1 chlorine

2NaCl
2 sodium 2 chlorine
This shows that two moles of sodium react with one mole
of chlorine to make two moles of sodium chloride.
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Balancing unfamiliar equations
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Balancing ionic equations
Equations containing ions should have the same overall
charge on each side in order to be balanced.
This can be achieved by balancing the equation in the
normal way:
Unbalanced:
Ca2+
+
Cl-
2 calcium 1 chloride
+1 charge
Balanced: Ca2+
+
2Cl-
2 calcium 2 chloride
no charge
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→
CaCl2
2 calcium 2 chloride
no charge
→
CaCl2
2 calcium 2 chloride
no charge
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Balancing ionic equations problems
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State symbols
State symbols are letters that are added to a formula to
indicate what state each reactant and product is in.
The four state symbols are:
s
solid
l
liquid
g
gas
aq
aqueous
These are added after the formula in brackets and subscript.
For example:
2H2(g)
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+
O2(g) 
2H2O(g)
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Adding state symbols
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Reacting masses
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Calculating reacting masses
To calculate the mass of a product given the mass of a
reactant, use the following steps:
1. Calculate no. moles of reactant:
no. moles = mass / Mr
2. Determine mole ratio of reactant to product:
ensure the equation is balanced
3. Calculate no. moles of product:
use the mole ratio
4. Calculate mass of product:
mass = moles × Mr
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Reacting masses example
What mass of sodium chloride is produced if 2.30 g of
sodium is burnt in excess chlorine?
1. Calculate
no. moles of Na:
no. moles = mass / Mr
= 2.30 / 23.0
= 0.100
2. Determine mole
2Na + Cl2  2NaCl
ratio of Na to NaCl: ratio = 2:2
= 1:1
3. Calculate
0.100 moles Na = 0.100 moles NaCl
no. moles of NaCl:
4. Calculate
mass = moles × Mr
= 0.100 × 58.5
mass of NaCl:
= 5.85 g
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Reacting masses calculations
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More reacting masses calculations
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What is concentration?
The concentration of a solution is a measure of how much
solute is dissolved per unit of solvent.
concentration = amount of solute / volume of solvent

amount of solute is measured in moles

volume of solvent is measured in dm3

concentration is measured in mol dm-3.
Volumes are often expressed in cm3, so a more useful
equation includes a conversion from cm3 to dm3.
concentration = (no. moles × 1000) / volume
mol dm3
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cm3
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Concentration, moles and volume
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Concentration calculations
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Standard solutions
A standard solution is a solution of known concentration.
Standard solutions are made by
dissolving an accurately weighed mass
of solid in a known volume of solvent
using a volumetric flask.
The volumetric flask has a thin neck,
which is marked with a line so it can be
filled accurately to the correct capacity.
The standard solution can then be used to find the
concentration of a second solution with which it reacts.
This is known as volumetric analysis or titration.
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Preparing standard solutions
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What is a titration?
A titration is a procedure used to identify the concentration
of a solution by reacting it with a solution of known
concentration and measuring the volume required for a
complete reaction.
The number of moles in the standard
solution is calculated. Using a
balanced equation for the reaction,
the number of moles in the solution
of unknown concentration can also
be calculated.
Once the number of moles for the
solution is known, the concentration
can be easily calculated.
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Carrying out a titration
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Titration calculations examples
What is the concentration of an NaOH solution if 25.0 cm3
is neutralized by 23.4 cm3 0.998 mol dm-3 HCl solution?
1. Calculate no.
moles HCl:
moles = (conc. × volume) / 1000
= (0.998 × 23.4) / 1000
= 0.0234
2. Determine ratio NaOH + HCl  NaCl + H2O
of NaOH to HCl: ratio NaOH:NaCl = 1:1
3. Calculate no.
0.0234 moles HCl = 0.0234 moles NaOH
moles of NaOH:
4. Calculate conc.
of NaOH:
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conc. = (moles × 1000) / volume
= (0.0234 × 1000) / 25.0
= 0.936 mol dm-3
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Titration calculations
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More titration calculations
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What are the different types of yield?
The percentage yield of a chemical reaction shows
how much product was actually made compared with
the amount of product that was expected.
To calculate the percentage yield, the theoretical yield
and the actual yield must be calculated.
The theoretical yield is the maximum mass of
product expected from the reaction, calculated
using reacting masses.
The actual yield is the mass of product that is
actually obtained from the real chemical reaction.
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Calculating yield
The percentage yield of a reaction can be calculated using
the following equation:
percentage yield = (actual yield × 100) / theoretical yield
Example: What is the percentage yield of a reaction
where the theoretical yield was 75 kg but the actual
yield was 68 kg?
percentage yield = (actual yield × 100) / theoretical yield
= (68 × 100) / 75
= 90.7%
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What is atom economy?
Atom economy is another measure of the efficiency of a
chemical reaction. It is the mass of reactants that end up as
the desired product – this is calculated as a percentage.
This concept is useful to chemical industry, because it
takes into account the atoms that end up in unwanted
waste products as well as the yield of the reaction.
This means a process that produces several worthless
by-products could have a high yield but a low atom economy.
Reactions with a high atom economy tend to be more
environmentally friendly as they tend to produce less waste,
use fewer raw materials and use less energy.
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Calculating atom economy
mass of desired products × 100
atom economy =
total mass of reactants
Example: What is the atom economy of a reaction
where the actual yield was 25 000 tonnes but the mass
of the reactants was 30 000 tonnes?
mass of desired products × 100
atom economy =
total mass of reactants
25 000 × 100
=
30 000
= 83.3%
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Yield and atom economy calculations
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Glossary
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What’s the keyword?
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Multiple-choice quiz
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