Worked examples: HSC Chemistry Data Sheet

Formula index with worked examples

1. Amount · mass to moles

   Formula or reference: n = m/M

   Units and conditions: Use mass in g and molar mass in g/mol to get mol.

   Worked example: A sample of mass 9.00 g and molar mass 180 g/mol contains 9.00/180 = 0.0500 mol.

2. Solutions · molarity

   Formula or reference: c = n/V

   Units and conditions: Amount in mol, volume in litres and concentration in mol/L.

   Worked example: Dissolve 0.015 mol and make the final volume 250 mL. The concentration is 0.015/0.250 = 0.060 mol/L.

3. Gases · ideal gas law

   Formula or reference: PV = nRT

   Units and conditions: Use kelvin, pressure in Pa and volume in m³ with R = 8.314 J/(mol K).

   Worked example: At 300 K and 100,000 Pa, 0.20 mol occupies (0.20 × 8.314 × 300)/100,000 ≈ 0.00499 m³, or 4.99 L.

4. Thermochemistry · heat

   Formula or reference: q = mcΔT

   Units and conditions: With mass in kg and c in J/(kg K), q is in joules. Temperature differences in kelvin and °C have the same numerical value.

   Worked example: Warming 0.10 kg of water by 4.0 K at c = 4180 J/(kg K) transfers 1672 J to the water.

5. Thermochemistry · Gibbs energy

   Formula or reference: ΔG° = ΔH° − TΔS°

   Units and conditions: T in kelvin. Convert ΔS° so that TΔS° and ΔH° use the same energy unit.

   Worked example: At 300 K, ΔH° = −18 kJ/mol and ΔS° = −40 J/(mol K) give ΔG° = −18 − (−12) = −6 kJ/mol.

6. Acids · pH

   Formula or reference: pH = −log₁₀([H⁺]) in the concentration approximation.

   Units and conditions: Use the numerical molar concentration relative to 1 mol/L. pH is unitless.

   Worked example: A dilute solution with [H⁺] = 1.0 × 10⁻³ mol/L has pH 3.00.

7. Acids · pKa

   Formula or reference: pKa = −log₁₀(Ka)

   Units and conditions: Use the stated value of Ka. pKa is unitless.

   Worked example: An acid with Ka = 1.0 × 10⁻⁵ has pKa = 5.00.

8. Visible spectroscopy · Beer–Lambert law

   Formula or reference: A = εℓc = log₁₀(I₀/I)

   Units and conditions: Absorbance is unitless. Use matching path length and absorptivity units.

   Worked example: At the chosen wavelength, transmitted intensity one quarter of the incident intensity gives A = log₁₀(4) ≈ 0.602.

9. Infrared spectroscopy · carbonyl band

   Formula or reference: Compare the measured wavenumber with the C=O range, 1680–1750 cm⁻¹ on this sheet.

   Units and conditions: Wavenumber in cm⁻¹.

   Worked example: A strong peak at 1715 cm⁻¹ is consistent with a carbonyl. Use other peaks or chemical evidence to distinguish a ketone from other carbonyl compounds.

10. Electrochemistry · standard cell potential

    Formula or reference: E°cell = E°cathode − E°anode using the listed reduction potentials.

    Units and conditions: Both potentials in volts.

    Worked example: If E°cathode = +0.40 V and E°anode = −0.20 V, E°cell = +0.60 V.