Calculating masses of reactants and products.
As mentioned previously, quantitative analysis involves the determination of ‘how much’ is present. The mole is particularly useful for calculating the quantities of substances consumed or produced in a chemical reaction.

Calculations involving excess reactants
Occasionally you are given data for two reactants. In these calculations you must first determine which reactant is ‘controlling’ the reaction (ie which reactant will run out first – called the limiting reagent ).

Scenario:
In a particular experiment 3.0 mL of lead nitrate is added to six test tubes. Different amounts of KI are added to each test tube. (Refer page 20 of textbook Fig 2.5). The reaction is as follows:
Pb(NO3)2 (aq) + KI (aq) 2KNO3 (aq) + PbI2 (s)
The height of the yellow precipitate indicates the amount of PbI2 that has been formed. In the first three test-tubes the height of the precipitate increases, since the amount of KI in each test tube is increasing. In the last two test tubes since the height of the precipitate is remaining constant it indicates that the the reactants have reached their stoichiometric ratio. Therefore no matter how much more KI is added the height of the precipitate will continue to remain constant. The amount of KI added to reach this constant can be used to determine the amount of Pb(NO3)2 present in the solution.

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Empirical Formula

The empirical formula of a compound shows the simplest whole number ratio of the atoms present in a compound. For example ethene, which is made up of molecules of C2H4, has an empirical formula of CH2 because the simplest whole number ratio of the number of carbon to hydrogen atoms is 1 : 2

Molecular Formula

A molecular formula gives the actual number of atoms of each element present in a molecule of a compound.
The molecular formula is always a whole number multiple of the empirical formula. For example benzene which has a molecular formula of C6H6 can be written as (CH)6.

Measuring Water Content
The percentage of water in a sample can be determined by heating the sample to 110 °C until there is no change in mass. This is referred to as heating to constant mass.
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Finding the composition of a mixture - Gravimetric Analysis

Gravimetric analysis is a form of analysis by mass. At it’s simplest it may involve drying or heating a product to determine its water content. Gravimetric analysis can also be a much more sophisticated procedure in which chemical knowledge of chemical reactions, solubilities and stoichiometry is used to determine the amount of substance (A) in a sample. Gravimetric analysis generally falls into three major pathways. The pathway selected depends on the chemical properties of substance A relative to those of the other components of the mixture.

Case 1 - A is the only volatile component of a mixture
To perform the calculation:
  • Measure mass of the sample (Mass 1)
  • Measure the mass of the residue after heating (Mass 2)
  • Calculate the mass of A (Mass 1 – Mass 2)
  • Calculate the % of A in the sample

NB: Detemining the waters of crystalisation is an example of this method of gravimetric analysis.
Case 2 – A is the only component insoluble in a particular solvent.
A suitable solvent is added to a weighed sample of the solid and all other components of the mixture will dissolve. A will be the only solid present and can be filtered off, rinsed, dried and weighed
To perform the calculation:
  • Measure the mass of the sample
  • Measure the mass of residue that remains (pure A)
  • Calculate the % of A in the sample
An example of this type of analysis is the determination of the percentage of gold in a gold bracelet that is an alloy of copper, gold and silver. Nitric acid is added to a weighed sample of the bracelet and the mixture warmed. The copper and silver will dissolve in the acid, leaving the gold as a solid. After filtering out the gold, washng it free of acid and drying it in an oven, it can be weighed to determine the percentage of gold in the alloy.
Case 3 – A is soluble in a particular solvent and is the only chemical that will precipitate out when a suitable chemical is added.
A suitable solvent is added to a weighed sample of the solid. Substance A will be one of the components that will dissolve. Any solid particles will be filtered off. To extract A we react it with a chemical that will form a precipitate. This precipitate is filtered, rinsed, dried and weighed.
To perform the calculation:
  • Weigh the mass of original sample
  • Weigh the precipitate
  • Calculate n (precipitate)
  • Calculate n (A)
  • Calculate mass of A
  • Calculate % of A in original sample
An example of this type of analysis is usd to determine the percentage of iron in some tablets.
Dradrawbacks of Gravimetric Analysis
1. We are assuming that A is the only component that does not dissolve in the solvent in case 2.
2. We are assuming that A is the only component that will react to form a precipitate in case 3.
3. Not all of A may be precipitated out in case 3. To overcome this the filtrate can be tested for the presence of A. If some is still present, we can add more precipitating agent and refilter.
4. The precipiate may not be dried properley and so residual moisture can add to the mass, making our experimental result for the % of A in the original sample slightly higher than the true result.
Sources of errors of Gravimetric Analysis
Action
Effect on analysis result
Reason
Insoluble materials not filtered out before forming the precipitate
Overestimated
The apparent mass of the precipitate will increase
Not enough of the precipitate forming chemical added
Underestimated
Not enough of the precipitate will form as some of the ions that are being analysed will remain in solution.
Forming a precipitate that is too soluble
Underestimated
Not all of the ions being analysed will be in the precipitate
Forming extra precipitate due to the presence of other competing ions
Overestimation
Too much of the precipitate will form
Weighing the precipitate before it is dry
Overestimation
The water present will increase the apparent mass of the precipitate
Not rinsing the precipitate before dying it
Overestimation
As the precipitate dries, other soluble chemicals will begin to crystallise out of the small amount of solution still trapped in the precipitate. These will add to the mass.
Adding too much of the precipitate causing chemical
No effect
This is a necessary part of the method to make sure that all of the required ions are in the precipitate. The chemical must be in excess
Using too much water for the initial dissolving
No effect
This is a practical consideration – the more water you have, the longer the filtering step.