Logarithm

Definition

A logarithm is a mathematical function that describes the power to which a fixed number, called the base, must be raised to get another number. Logarithms are closely related to the concepts of pH and pOH, which are used to measure the acidity or basicity of a solution.

5 Must Know Facts For Your Next Test

1. The logarithm of a number is the exponent to which a base must be raised to get that number.
2. pH is the negative logarithm of the hydrogen ion concentration in a solution, with a pH of 7 indicating a neutral solution.
3. pOH is the negative logarithm of the hydroxide ion concentration in a solution, and is related to pH by the equation pH + pOH = 14.
4. Logarithms can be used to represent very large or very small numbers in a more compact way, making calculations easier.
5. The common logarithm (base 10) and the natural logarithm (base e) are the most widely used logarithms in chemistry and science.

Review Questions

• Explain how logarithms are used to calculate pH and pOH.
  • Logarithms are used to calculate pH and pOH because they provide a convenient way to represent very small or very large numbers. The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration, while the pOH is the negative logarithm (base 10) of the hydroxide ion concentration. These values are related by the equation pH + pOH = 14, which allows for the determination of one value given the other.
• Describe the relationship between the logarithm, the base, and the exponent.
  • The logarithm of a number is the exponent to which a base must be raised to get that number. For example, if $\log_10 100 = 2$, this means that 10 raised to the power of 2 (10^2) is equal to 100. The base of the logarithm determines the relationship between the logarithm, the base, and the exponent. Common logarithms (base 10) and natural logarithms (base e) are the most widely used in chemistry and science.
• Analyze how the properties of logarithms can be used to simplify calculations in the context of pH and pOH.
  • The properties of logarithms, such as the power rule ($\log_b x^y = y\log_b x$) and the logarithm of a product ($\log_b (xy) = \log_b x + \log_b y$), can be used to simplify calculations involving pH and pOH. For example, the equation pH + pOH = 14 can be derived by recognizing that pH is the negative logarithm of the hydrogen ion concentration, and pOH is the negative logarithm of the hydroxide ion concentration. These properties allow for efficient manipulation and interpretation of pH and pOH values in chemical analyses and problem-solving.

Related terms

Base: The fixed number that a logarithm is calculated with, typically 10 or e.

Exponent: The power to which the base must be raised to get a particular number.

pH:

A measure of the acidity or basicity of a solution, calculated as the negative logarithm of the hydrogen ion concentration.