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
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.
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.
- HCl is a strong acid, so [H⁺] = 0.0250 mol dm⁻³.
- pH = −log(0.0250) = 1.602, which is quoted as 1.60 because 0.0250 has three significant figures.
- 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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