1.3 Chemical Calculations

• Relative atomic mass (Ar) of an element is the average mass of one atom relative to one-twelfth of the mass of one atom of carbon-12.
• Relative isotopic mass - the average mass of an isotope relative to one-twelfth of the mass of one atom of carbon-12.
• Relative formula or molecular mass (Mr) - The average mass of one molecule relative to one-twelfth of the mass of one atom of carbon-12.
• $A_r =$$\frac{mass \times abundance}{total ,abundance}$Relative atomic mass equation
• Mass Spectrometer - VIADD:

  Vapourisation

  Ionisation

  Acceleration

  Deflection

  Detection

  
• Mass spectrometry:

  • The sample is vaporised by heating or reducing the pressure.
  • The sample is ionised. High speed electrons bombard the gaseous sample and knock off an electron resulting in positive ions formed.
  • The sample is collimate to a narrow beam slit - which is accelerated by a negatively charged place.
  • The sample enters a magnetic field - particles are deflected according to their mass/charge ratio. Ions of least m/z are deflected most.
  • The sample is Detected - signal amplified and recorded.
  • By changing the strength of the magnetic field all positive ions are detected.
• Acceleration:

  Attracted to both plates equally so goes through split

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  o o o o

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• Mass Spectrometer: Vaporisation

  The sample is heated and the pressure is reduced to vaporise it from a solid/liquid into a gas. Prior to this, a vacuum removes contaminants (e.g. air) to provide an unobstructed path for the gaseous ion.
• Mass Spectrometer: Ionisation

  The electron gun bombards the gaseous sample with electrons. This knocks off an electron making a positive ion.
• Mass Spectrometer: Acceleration

  Negatively charged plates accelerate the positive ions.
• Mass Spectrometer: Deflection

  An electromagnet deflects the ions by their mass:charge (m/z) ratio.
• Mass Spectrometer: Detection

  The ions strike a detector, the electrical impulse is amplified to produce a mass spectrum.
• (Look in booklet for revision on mass spectrum of elements)
• The simplest formulae of a compound is the simplest whole number ratio of atoms within a compound. Also called the "empirical formulae"
• Writing simplest formulae (mass):

  1. Identify the symbol
  2. Mass of element (g)
  3. Identify Ar value
  4. Divide mass by Ar
  5. Divide by smallest number
  6. Ration of atoms
  7. Simplest formulae
• Writing simplest formulae (percentage):

  1. Identify the symbol
  2. % mass of the element
  3. Identify Ar value
  4. Divide % mass by Ar
  5. Divide by smallest number
  6. Ration of atoms
  7. Simplest formulae
• The mole is a unit of measurement. A mole of a substance contains as many partgicles as there are atoms in 12g of carbon-12.
• The avogadro constant is the number of particles in one mole. It is equal to 6.02 x 10^23
• $\frac{mass(g)}{M_r} =$$amount\; in\; moles =$$\frac{number\;of\;particles}{Avogadro\;constant}$

  $\frac{m}{M_r} =$$n =$$\frac{number\;of\;particles\;}{L}$
• Avogadro constant - the number of particles in one mole of a substance (6.02 x 10^23 particles)
• Calculating moles from mass:

  $amount\;(in\;moles)=$$\frac{mass(g)}{M_r}$
• 1 litre = 1000 cm^3 = 1 dm^3
• cm^3 ----> dm^3:

  divide by 1000
• $conc.(mol/dm^3) =$$\frac{moles}{volume (dm^3)}$

  
• $conc.(g/dm^3) =$$\frac{mass(g)}{volume (dm^3)}$

  
• For mole calculation involving solutions, it is essentil to have a value showing the amount of substance dissolved in a fixed volume - its concentration.

  The units for this are (mol dm^-3)
• Standard solution - A solution containing a known concentration of a solute in a solvent
• Making a standard solution from a solid.

  Step 1:

  • Calculate the mass of solid required.
  • Dissolve this solid in a beaker in a small volume of water.
  • Stir using a glass rod until all the solid has dissolved.
• Making a standard solution from a solid.

  Step 2:

  • Select a volumetric flask of the required volume.
  • Using a funnel, pour the contents of the beaker into the flask.
  • Using a wash bottle, rinse the contents of the beaker, the stirring rod and funnel and transfer the washings into the volumetric flask.
• Making a standard solution from a solid.

  Step 3:

  • Add distilled water to just below the graduation mark.
  • Add distilled water drop-wise using a pipette until the base of the meniscus is on the graduation mark.
  • Stopper and invert the flask to mix the contents.
• To calculate the mass of solid required for a standard solution, use conc and volume to find number of moles and use moles and Mr to find mass.
• Accurate titre readings need to be within 0.3cm^3 of eachother, and two readings need to be within 0.1cm^3 of eachother for repeatability.
• Look at 2 practicals in 1.3 booklet
• 1 mole of gas occupies 24.5 dm^3 at 25*c
• 1 mole of gas occupies 22.4 dm^3 ar 0*c
• Volume varies with temperature because gases exhibit random motion, and the speed of their movement increases with temperature.
• Gases move faster at higher temperatures so will cause an increase in pressure during the summer and decrease during the winter (assuming the quantity of the gas inside remains constant).
• $moles =$$\frac{Volume (dm^3)}{Molar\;volume}$

  
• $density (g/cm^3) =$$\frac{Mass(g)}{Volume(cm^3)}$
• The ideal gas equation allows you to establish the link between the pressure or volume of a gas at any given temperature