C2.3 Calculations

Atomic Mass tells us protons + neutrons.
Atomic Number tells the number of protons.

Atoms of the same element can have different numbers of neutrons; these atoms are called isotopes of that element.

The mass number of an element tell us the relative atomic mass of that element. The relative atomic mass of an element (A_r) compares the mass of atoms of the element with the ¹²C isotope. It is an average value for the isotopes of the element.

When calculating relative atomic mass both the abundance and the mass of all isotopes are taken into account. It is an average value for the isotopes of the element.

The relative formula mass (M_r) of a compound is the sum of the relative atomic masses of the atoms in the numbers shown in the formula. To work out the Mr of a substance, you add the Ar of the elements in that formula. 

The relative formula mass of a substance, in grams, is known as one mole of that substance.

• 1 mole always contains the same no. of particles (6.02 x 10^23)
• The mass of 1 mole depends on the formula of the element/compound
• 1 mole is the Mr in g
  • mass = mr x moles
  • no. of moles = mass / mr

The molecular formula for glucose is C6H12O6. The molecular formula tells us the actual no. of atoms of each element in a compound. The formula can be simplified to CH2O which is the simplest ratio. We call this the empirical formula. 
By carrying out experiment we can use data to calculate the empirical formula.

Calculating Empirical Formula
THINK TABLE!!!

Worked Example: A compound is made from 72g of carbon and 12g hydrogen. What is the empirical formula?

What mass of ammonia can I get from 1.4g of nitrogen?

What % by mass of CO2 is carbon?

From our reacting masses calculations we are calculating the maximum mass possible e.g. CaO + H2O --> Ca(OH)2. The maximum mass of Ca(OH)2 we can make from 2.00g is 2.6g.

In reality we NEVER actually obtain the maximum mass of product. This could be because:

• There are other reactions taking place
• Product could remain in the reaction vessel
• Not all reactants may reactant
• Some product may escape (g)
• May be a reversible reaction <-->

Calculating % yield
We should get 2.6g of product, but we get 2.15. What is the % yield?

A food colouring might contain one dye or it might contain a mixture of dyes. Here's how you can tell:

• Extract the colour from a food sample by placing it in a small cup with a few drops of solvent (can be water, ethanol, salt water etc.)
• Put spots of the colour solution on a pencil baseline on filter paper. (Don't use pen as it might dissolve in the solvent).
• Roll up the sheet and put it in a beaker with some solvent - but keep the baseline above the level of the solvent.
• The solvent seeps up into the paper, taking the dyes with it. Different dyes form different spots in different places.
• Watch out though - a chromotogram with four spots means at least four dyes, not exactly four dyes. There could be five dyes but two of them could be making a spot in the same place. It can't be three dyes though, because one dye can't split up into two spots. 

• In gas chromotography a small sample of a mixture of compounds is vaporised (turned into gas).
• A carrier gas takes the sample through the column.
• The carrier gas (often nitrogen) must be inert and not react with the sample.
• The column is packed with a solid material which slows the sample down.
• Different compounds travel through the column at different speeds and leave the other end of the column at different times.
• The amount of time a particular compound takes to pass through the instrument is called its retention time.
• The retention time can help identify the compound.
• A recorder draws a graph called a gas chromatograph which shows a peak for each compound.
• The number of peaks show the number of compounds present in the sample and the position of the peaks show the retention time.
• A more accurate way of identifying the different compounds which leave the column can be made by using a mass spectrometer.

• A mass spectrometer can provide a quick and accurate identification of a substance from a very small sample.
• The instrument works by vaporising the sample (turning it into a gas).
• The sample passes through an electron beam which knocks off some electrons from the molecules and turns them into ions.
• The charged ions are accelerated towards a detector.
• A strong magnetic field makes the ions follow a curved path instead of moving in a straight line .
• Ions with a small mass curve the most and ions with a large mass curve the least.
• A recorder draws a graph called a mass spectrograph, usually called a mass spectrum, which shows a peak for each ion detected.
• The position of the peaks shows the mass to charge ratio and this is used to identify the substances which are present in the sample.
• The mass to charge ratio is also used to give the relative molecular mass (Mr) of the substances in a sample.
• A mass spectrometer is sometimes used with gas chromotography to identify the different compounds which leave the column.