7.3.2Additional lessons
Using Units, Symbols and Numerical Values in Chemistry — IB Chemistry HL Revision Notes & Topical Questions
5 min read 6 parts Lesson 164 of 172
Part 1 of 6SI Units and Prefixes
A number without a unit has no chemical meaning, so units are part of every answer.
Base units
- Amount of substance is measured in the mole (mol), mass in kilograms (kg), length in metres (m), time in seconds (s) and temperature in kelvin (K).
Derived units
- Energy is measured in joules (J), pressure in pascals (Pa) and concentration commonly in mol dm⁻³ in chemistry.
Prefixes
- Kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶) and nano (10⁻⁹) scale a unit up or down by a power of ten.
Temperature
- Convert °C to K by adding 273.15, and note that a temperature difference of 1 °C equals a difference of 1 K.
| Quantity | Symbol | Unit |
|---|---|---|
| Amount of substance | n | mol |
| Concentration | c or [ ] | mol dm⁻³ |
| Molar mass | M | g mol⁻¹ |
| Volume | V | dm³ or cm³ |
Part 2 of 6Symbols and Notation
Symbols and Notation
Italic symbols
- Quantity symbols such as n, m, V and T are written in italics, while unit symbols such as mol, g and K are upright.
Square brackets
- [X] means the equilibrium or molar concentration of X in mol dm⁻³, which is used in rate and equilibrium expressions.
Delta
- The symbol Δ means a change, found as final value minus initial value, for example ΔH or ΔT.
Negative indices
- Writing mol dm⁻³ rather than mol/dm³ is the standard way to express a compound unit.
Part 3 of 6Converting Units
1
Identify the starting unit and the target unit before doing anything with the numbers.
2
Use 1 dm³ = 1000 cm³ = 10⁻³ m³, so dividing cm³ by 1000 gives dm³.
3
Use 1 kJ = 1000 J, which matters when combining enthalpy changes with entropy in J K⁻¹ mol⁻¹.
4
Multiply or divide by the conversion factor and check that the answer has a sensible size.
5
Write the final answer with the unit and the correct number of significant figures.
Part 4 of 6Units in Equations
Checking
- The units on both sides of an equation must match, which provides a quick check that a formula has been used correctly.
Rate constants
- For rate = k[A][B] the units of k are dm³ mol⁻¹ s⁻¹, found by dividing mol dm⁻³ s⁻¹ by (mol dm⁻³)².
Gas constant
- R = 8.31 J K⁻¹ mol⁻¹ uses joules, so energies in kJ must be converted first.
Dimensionless values
- Equilibrium constants and percentage yields may have no unit, depending on the expression.
Part 5 of 6Worked Example
Question Calculate the amount of NaOH in 250 cm³ of 0.200 mol dm⁻³ solution, and convert the concentration to mol m⁻³.
- Convert the volume250 cm³ ÷ 1000 = 0.250 dm³.
- n = c × V = 0.200 mol dm⁻³ × 0.250 dm³ = 0.0500 mol.What the symbols mean: c = concentration (mol dm−3) · n = amount (mol) · V = volume (dm3; divide cm3 by 1000)
- 1 dm³ = 10⁻³ m³, so 0.200 mol dm⁻³ = 0.200 ÷ 10⁻³ = 200 mol m⁻³.
Answer
- n = 0.0500 mol;
- concentration = 200 mol m⁻³
Part 6 of 6Exam Checklist & Tips
7.3.2 – Key Points for the Exam
- SI unit A unit from the International System of Units used for scientific measurement.
- Derived unit A unit built from base units, such as the joule or the pascal.
- Prefix A letter placed before a unit to show a power of ten, such as k for 10³.
- Kelvin The SI unit of thermodynamic temperature, where 0 K is absolute zero.
- Delta (Δ) A symbol meaning a change in a quantity, final minus initial.
Common Mistakes
- Using the volume in cm³ in c = n/V, which gives a concentration 1000 times too large.
- Mixing kJ and J when using ΔH with ΔS in the same calculation.
- Writing a temperature in °C where kelvin is required in the gas or Arrhenius equations.
- Leaving out units, or writing them wrongly as mol/dm³ in the final answer.
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