Logarithmic scale: pH scale

Logarithmic scale: pH scale

In this section, we will bridge the gap between chemistry and mathematics by studying one of the many applications of logarithmic functions. We will learn about the pH Scale and explore how this logarithmic scale can be used to measure the acidity or basicity of a solution.
Basic concepts: Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)},
Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

Lessons

  • 1.
    Pure water has a pH of 7. Vinegar has a pH of 3.
    Complete the following 2 sentences:
    (i) Pure water is __________ times as alkaline as vinegar.
    (ii) Vinegar is __________ times as acidic as pure water.
  • 2.
    Lemon juice has a pH of 2.5.
    Stomach acid is 8 times more acidic than lemon juice.
    Tomato juice is 90 times more basic than lemon juice
    Find the pH of:
    (i)
    stomach acid
    (ii) tomato juice
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13.
Applications of Exponential and Logarithmic Functions
13.1
Exponential growth and decay by a factor
13.2
Exponential decay: Half-life
13.3
Exponential growth and decay by percentage
13.4
Finance: Compound interest
13.5
Continuous growth and decay
13.6
Logarithmic scale: Richter scale (earthquake)
13.7
Logarithmic scale: pH scale
13.8
Logarithmic scale: dB scale
13.9
Finance: Future value and present value
AU Year 12 Maths
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