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7.3.1Additional lessons

Applying General Mathematics in Chemistry — IB Chemistry HL Revision Notes & Topical Questions

5 min read 6 parts Lesson 163 of 172

📚 IB Chemistry HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Section 1 of 6Number Skills

Reliable chemistry depends on handling numbers carefully.

Scientific notation
  • Scientific notation Very large and small values are written as a × 10ⁿ with 1 ≤ a < 10, such as 6.02 × 10²³ mol⁻¹.
Significant figures
  • Significant figures Count from the first non-zero digit, and quote the answer to the same number of figures as the least precise data value.
Decimal places
  • Decimal places For addition and subtraction the answer takes the number of decimal places of the least precise value.
Estimation
  • Estimation A quick approximation checks whether a calculator answer is sensible, for example whether a molar mass is close to expected.

Section 2 of 6Ratios, Proportion and Percentages

Ratios, Proportion and Percentages
Mole ratio
  • Mole ratio The coefficients of a balanced equation give the ratio in which amounts react, which links any two species in the reaction.
Direct proportion
  • Direct proportion If one quantity doubles and so does the other, they are directly proportional and their ratio stays constant.
Percentage
  • Percentage Percentage yield or composition is part divided by whole multiplied by 100.
Rearranging
  • Rearranging Make the required quantity the subject of an equation before substituting numbers, and keep the units in view.

Section 3 of 6Logarithms and Exponentials

1
A logarithm to base 10 answers the question of what power of 10 gives a number, so log 1000 = 3.
2
pH is defined as −log₁₀[H⁺], which converts a very wide range of concentrations to a small scale.
3
To reverse a logarithm, raise 10 to the power: [H⁺] = 10⁻ᵖᴴ.
4
Natural logarithms (ln) appear in rate and Arrhenius equations, and ln x is the reverse of eˣ.
5
For a logarithm, the number of decimal places in the answer equals the number of significant figures in the original value.

Section 4 of 6Checking Results

Order of magnitude
  • Order of magnitude Compare the size of an answer with what is expected, since an error of a factor of 1000 often means a forgotten unit conversion.
Units
  • Units Carry units through each line and confirm that the final unit matches the quantity requested.
Reasonableness
  • Reasonableness A percentage yield above 100 % or a negative concentration signals a mistake somewhere in the working.
Sig fig rule
  • Sig fig rule Do not round intermediate steps, only the final answer.

Section 5 of 6Worked Example

Question Calculate the pH of 0.0250 mol dm⁻³ HCl, then find [H⁺] for a solution of pH 3.45.

  1. HCl is a strong acid, so [H⁺] = 0.0250 mol dm⁻³.
  2. pH = −log(0.0250) = 1.602, which is quoted as 1.60 because 0.0250 has three significant figures.
  3. For pH 3.45, [H⁺] = 10−3.45) = 3.55 × 10⁻⁴ mol dm⁻³.

Answer pH = 1.60; [H⁺] = 3.55 × 10⁻⁴ mol dm⁻³

Section 6 of 6Exam Checklist & Tips

7.3.1 – Key Points for the Exam

  • Significant figures The digits in a number that carry meaning about its precision.
  • Logarithm The power to which a base must be raised to give a number.
  • Mole ratio The ratio of amounts of substances in a balanced equation.
  • Scientific notation A way of writing numbers as a coefficient between 1 and 10 times a power of ten.
  • Direct proportion A relationship in which the ratio of two quantities is constant.

Common Mistakes

  • Rounding too early in a multi-step calculation, so the final answer is inaccurate in the last figures.
  • Giving a pH with the wrong number of decimal places compared with the significant figures of the concentration.
  • Forgetting to convert cm³ to dm³ before using concentration in mol dm⁻³.
  • Using the ratio of masses rather than the ratio of moles from the balanced equation.

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