1.3 - calculations

• Amount of substance


  The quantity of a chemical species, measured in moles. Used as a way of counting atoms.
• Calculating number of moles

  1. Number of moles = Mass ÷ Mr

  2. Number of moles = (Pressure x Volume) ÷ (Gas constant, R x Temperature)

  3. Number of moles = Concentration x Volume
• Atom economy


  Measure of the proportion of reacting atoms that become part of the desired product in the balanced chemical equation
• Avogadro constant (L)


  The number of atoms, molecules or ions in one mole of a given substance. It is the number of atoms in exactly 12 g of C (6.02 x 1023mol).
• Empirical formula


  Smallest whole number ratio of atoms of each element in a compound
• Empirical formula examples


  • Benzene (C6H6), cyclobutadiene (C4H4) and acetylene (C2H2) are all simply "CH"
• Ideal gas equation


  An equation that relates the number of moles of a gas to its volume, temperature and pressure
• Mass spectrometry


  A technique used to identify compounds and determine their relative molecular mass
• Molar Mass


  Mass of one mole of the substance expressed in gmol−1
• Mole


  The unit for the amount of substance. This is the amount of chemical species found in 12 g of 12C. One mole is 6.02 x 1023.
• Molecular formula


  The actual number of atoms of each element in a molecule
• Molecular ion peak


  The peak on a mass spectrum with the highest m/z value, this is used to determine the molecular mass of a compound
• Percentage error


  The degree of error in taking a measurement, this is estimated to be + or - half the smallest scale division of the apparatus
• Percentage yield


  The percentage ratio of the actual yield of product from a reaction compared with the theoretical yield
• Relative abundance (of isotopes)


  The relative abundance of an isotope is the percentage of atoms found within a naturally occurring sample of an element that has a specific atomic mass
• Relative atomic mass


  Average mass of an atom of an element, relative to 1/12 of the mass of an atom of carbon-12
• Relative formula mass


  Average mass of a compound relative to 1/12 of the mass of an atom of carbon-12. Relative formula mass refers to compounds that have a giant structure.
• Relative isotopic mass


  Average mass of an atom of an isotope, relative to 1/12 of the mass of an atom of carbon-12
• Relative molecular mass


  Average mass of a molecule relative to 1/12 of the mass of an atom of carbon-12
• Relative peak height


  In mass spectra the peak heights show the relative abundances of the substance that made the peak
• Relative atomic mass (Ar)

  The average mass of one atom of the element relative to one-twelfth the mass of an atom of carbon-12
• Most elements exist as two or more different isotopes, so an average mass is used, relating to the relative abundance of all the isotopes present. It has no units as the masses are relative to another mass.
• Relative isotopic mass


  The mass of one atom of an isotope relative to one-twelfth the mass of one atom of carbon-12
• Relative formula mass (Mr)


  The total average mass of all the atoms in the formula relative to one-twelfth the mass of an atom of carbon-12
• Mass spectrometer


  1. Ionisation

  2. Acceleration

  3. Deflection

  4. Detection
• A mass spectrometer can be used to find the relative atomic mass of an element. It measures the relative mass of each different isotope of an element and the relative abundance of each isotope of the element.
• The lighter ions are deflected more than the heavier ones, and ions with two positive charges are deflected more than ones with one positive charge. These two factors are combined in the mass/charge (m/z) ratio.
• Only ions with a given m/z ratio make it right through the machine to the ion detector. Electrons are transferred from the detector plate to the positive ion and this produces a current. The larger the current, the higher the abundance of that isotope. The signal is then amplified and recorded.
• When the magnetic field is varied, each ion stream can be brought in turn onto the detector to produce a current which is proportional to the number of ions arriving.
• Chlorine has two isotopes - chlorine-35 (35Cl) and chlorine-37 (37Cl). 35Cl is three times more common than 37Cl. The mass spectrum therefore consists of two peaks in the ratio 3:1 relating to 35Cl+ (m/z 35) and 37Cl+ (m/z 37) and three peaks in the ratio 9:6:1 relating to Cl2+ ions.
• The probability of an atom being 35Cl is 3/4 and being 37Cl is 1/4, so the ratio of peaks is 9:6:1.
• Mole


  The amount of a substance in grams which has the same number of particles as there are atoms in 12g of carbon-12
• Avogadro constant (NA)


  6.02 × 10^23 particles per mole
• Molar mass


  The mass of one mole of a substance, with the unit g mol-1
• Calculating reacting masses


  1. Step 1: Calculate the number of moles of the substance you have information about

  2. Step 2: Use the balanced equation to find the mole ratio and deduce the number of moles of the product formed

  3. Step 3: Rearrange the equation mass = moles × Mr to calculate the mass of the product formed
• The relative atomic mass of zirconium is closest to 91.3.
• Molecular formula


  The actual number of atoms of each element present in the molecule
• Empirical formula


  The simplest whole number ratio/proportion of elements present
• Hydrocarbon (Mr 58)


  • Contains 4.80 g carbon and 1.01 g hydrogen
• Calculating empirical and molecular formula

  1. Mass of empirical formula = (2 × 12.0) + (5 × 1.01) = 29.05

  2. Number of units in a molecule = 58 / 29.05 = 1.992 ≈ 2

  3. Molecular formula = 2 × empirical formula = C4H10