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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6.
Exponential and Logarithmic functions
6.1
Converting from logarithmic form to exponential form
6.2
Evaluating logarithms without calculator
6.3
Common logarithms
6.4
Evaluating logarithms using change-of-base formula
6.5
Converting from exponential form to logarithmic form
6.6
Product rule of logarithms
6.7
Quotient rule of logarithms
6.8
Combining product rule and quotient rule in logarithms
6.9
Solving logarithmic equations
6.10
Evaluating logarithms using logarithm rules
6.11
Continuous growth and decay
6.12
Finance: Compound interest
6.13
Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
6.14
Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
6.15
Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}
6.16
Exponents: Negative exponents
6.17
Exponents: Zero exponent: a0=1 a^0 = 1
6.18
Exponents: Rational exponents
6.19
Graphing exponential functions
6.20
Graphing transformations of exponential functions
6.21
Finding an exponential function given its graph
6.22
Logarithmic scale: Richter scale (earthquake)
6.23
Logarithmic scale: pH scale
6.24
Logarithmic scale: dB scale
6.25
Finance: Future value and present value
Precalculus
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