Maths skills for Chemistry

• Zeros at the end of a number are significant if they come after a decimal point
• Zeros at the start of a number are not significant
• You should round your answer to the same number of significant figures/decimal places as the data value with the fewest sig figs/decimals
• When working with logs, give your answer to the same number of decimal places as there are significant figures in the number you're taking the log of
• If you raise 10 to a power, you should give your answer to the same number of significant figures as there are decimal places in the power
• natural logs are to base e
• the natural logarithm is ln
• kilo (k) means the unit is 1000 times bigger than the basic unit
• deci (d) means the unit is 10 times smaller than the base unit
• centi (c) means the unit is 100 times smaller than the base unit
• milli (m) means the unit is 1000 times smaller than the base unit
• To go from a bigger unit to a smaller unit, multiply by the conversion factor
• To go from a smaller unit to a bigger unit, divide by the conversion factor
• If units are squared, the conversion factor must be squared
• If the units are cubed, the conversion factor must be cubed
• to go from dm3 to cm3, multiply by 1000
• to go from cm3 to dm3, divide by 1000
• to go from m3 to dm3, multiply by 1000
• to go from dm3 to m3, divide by 1000
• To convert from kelvin to celsius, add 273
• The uncertainty is half the smallest division the equipment measures, in either direction (e.g. in a burette with markings every 0.1cm3, uncertainty would by + or - 0.05 cm3)
• percentage error = uncertainty / reading
• your answer shouldn't be more exact than the uncertainty and the uncertainty shouldn't be more exact than the answer value. If so, round
• when adding or subtracting measurements, add their uncertainties
• A wedge shows a bond pointing towards you
• a dotted line shows a bond pointing away from you
• a straight line shows a bond in the same plane as the page
• The presence of nuclear spin makes nuclei behave like bar magnets
• When molecules in solution are placed in a strong magnetic field the nuclei with an odd mass number will line up with the magnetic field
• If molecules in solution with a strong magnetic field are irradiated with a range of radio frequencies the nuclei of specific atoms in the molecule will absorb a specific radio frequency
• like electrons, nucleons are able to spin in opposite directions. Opposite spins pair up. If there is an uneven number of nucleons, there is an overall nuclear spin
• In organic molecules, protons are surrounded by electrons which partially shield them from the applied magnetic field
• The amount of shielding in organic molecules depends on the electron density surrounding the nucleus and varies for protons within a compound
• factors which influence the electron density include bond polarity and the presence of electron donating or electron withdrawing groups:

  • the nucleus is deshielded when the electron density is reduced
  • the nucleus is shielded when the electron density is increased
• Because each chemically distinct hydrogen atom has a unique electronic environment, it gives rise to characteristic resonance
• Chemically equivalent protons are all in the same environment, therefore absorb the same frequency
• For hydrogen atoms the difference in frequencies are small, being recorded as only a few parts per million
• On the NMR spectra the zero point is on the right hand side
• On some spectre there is a peak at zero which is an indication of the comparison took tetramethylsilane (TMS)
• TMS is used to overcome the fact that different spectrometers have different types of magnets and otherwise would cause resonance at different frequencies