Using Units, Symbols & Numerical Values in Chemistry (HL IB Chemistry)

International System of Units (SI)

• In science, there are 7 base SI units which are used to measure various physical quantities 

SI Base Units Table

• These base SI units form the foundation for measuring various properties and quantities in chemistry and other sciences
• Other common units can be derived from these base units for specific applications, but they are all based on the International System of Units (SI)
  • Concentration, c [mol dm^–3]
  • Joules, J [N m]
  • Molar mass, M_r [ g mol^–1]
  • Pascals, Pa [kg / m s²]

Table of common units in chemistry

Prefixes

• Measurements of physical quantities can require very large and very small values, for example:
  • The diameter of an atom is about 10^–10 m or 0.0000000001 m
  • One mole of a substance contains 6.02 × 10²³  or 602 000 000 000 000 000 000 000 particles
• Powers of ten are numbers that can be achieved by multiplying 10 times itself
• These come under two categories of units:
  • Multiples e.g. 10², 10³
  • Sub-multiples e.g. 10^-1, 10^-2
• Each power of ten is defined by a prefix, the most common ones used in chemistry are listed in the table below
  • The complete list of prefixes can be found in Section 3 of the data booklet 

Table of common prefixes in chemistry

Example conversions

• A mass of 5.2 kg
  • 5.2 kg = 5.2 kilograms = 5.2 x 10³ = 5200 grams
• The diameter of an aluminium atom is 184 pm
  • 184 pm = 184 picometres = 184 x 10^–12 m
  • Correctly given in standard form, this is a value of 1.84 x 10^–10 m
• The energy required to heat 10 dm³ of liquid water at constant pressure from 0 °C to 100 °C is approximately 4.2 MJ
  • 4.2 MJ = 4.2 megajoules = 4.2 x 10⁶ = 4 200 000 J

Symbols in chemistry

• There is a large number of symbols used in chemistry:
  • State symbols
    • e.g. solid (s), liquid (l), gas (g)
  • Chemical symbols - from the Periodic Table, Section 7 of the data booklet 
    • e.g. lithium = Li, carbon = C, Copper = Cu
  • Physical constants - given in Section 2 of the data booklet
    • e.g. Planck's constant = h, the speed of light in a vacuum = c
  • Terms in equations - relevant equations are given in Section 1 of the data booklet
    • e.g. n = CV, where n is the number of moles, C is the concentration and V is the volume
  • Units for quantities
    • e.g. specific heat capacity measured in J g^–1 K^–1
  • Other abbreviations used in chemistry
    • e.g. STP for standard temperature and pressure

• While the data booklet can assist with using the correct symbols, it is essential to know the symbols specifically linked to physical constants, terms in equations and units for quantities
  • For example, the letter c, depending on capitalisation (c or C), could represent:
    
    • The speed of light in a vacuum in the c = f λ equation
    • The specific heat capacity in the Q = mcΔT equation
    • Concentration in the n = CV equation
    • The units of electrical charge 
    • The prefix centi-, e.g. cm³
    • The centigrade / Celsius units of temperature
    • The chemical symbol for carbon
    • The symbol for combustion in the enthalpy of combustion term ΔH_c^θ term (if subscripts are included)

What are significant figures?

• Significant figures must be used when dealing with quantitative data
• Significant figures are the digits in a number that are reliable and absolutely necessary to indicate the quantity of that number
• There are some important rules to remember for significant figures
  • All non-zero digits are significant
  • Zeros between non-zero digits are significant
    • 4107 (4.s.f.)
    • 29.009 (5.s.f)
  • Zeros that come before all non-zero digits are not significant
    • 0.00079 (2.s.f.)
    • 0.48 (2.s.f.)
  • Zeros after non-zero digits within a number without decimals are not significant
    • 57,000 (2.s.f)
    • 640 (2.s.f)
  • Zeros after non-zero digits within a number with decimals are significant
    • 689.0023 (7.s.f)
• When rounding to a certain number of significant figures:
  • Identify the significant figures within the number using the rules above
  • Count from the first significant figure to the specified number
  • Use the next number as the ‘rounder decider’
  • If the decider is 5 or greater, increase the previous value by 1
• The same approach can be applied to decimal places, although significant figures are more common

An appropriate number of significant figures

• The appropriate number of significant figures depends on:
  • The precision of the measurement
  • The limitations of the equipment used to make the measurement
• When performing calculations involving measured values, it's essential to maintain the proper number of significant figures throughout the calculation to avoid rounding errors
  • An easy way to avoid rounding errors is to continue using the calculator value until the final answer
  • Tip: Avoid rounding any calculation to 1 significant figure during a calculation as this typically introduces rounding errors and can sometimes, automatically, lose you a mark
• In the final result, the number of significant figures should not exceed the value with the least number of significant figures used in the calculation