Acidity and the pH Scale
Acidity and the pH scale is a Grade 7 math application topic from Yoshiwara Intermediate Algebra, connecting logarithms to chemistry. The pH formula pH = -log[H+] uses the common logarithm to compress a wide range of hydrogen ion concentrations into a 0–14 scale.
Key Concepts
Property The pH scale is used by chemists to measure the acidity of a substance. The pH value is defined by the formula: $$\text{pH} = \log {10}[H^+]$$ where $[H^+]$ is the concentration of hydrogen ions. A decrease of 1 on the pH scale corresponds to an increase in acidity by a factor of 10.
Examples If a cleaning solution has a hydrogen ion concentration of $[H^+] = 10^{ 12}$, its pH is calculated as $\text{pH} = \log {10}(10^{ 12}) = ( 12) = 12$. Tomato juice has a pH of about 4. This is 1000 times more acidic than pure water (pH 7), because the difference in pH is $7 4=3$, which corresponds to a factor of $10^3$. To find the hydrogen ion concentration of a liquid with a pH of 3.5, we solve $3.5 = \log {10}[H^+]$. This gives $[H^+] = 10^{ 3.5} \approx 3.16 \times 10^{ 4}$.
Explanation The pH scale simplifies acidity by converting complex hydrogen ion concentrations into simple numbers, usually from 0 to 14. A lower pH means higher acidity, where each whole number step down represents a tenfold increase in acidity.
Common Questions
What is the pH formula?
pH = -log[H+], where [H+] is the concentration of hydrogen ions in moles per liter. A lower pH means more acidic; a higher pH means more basic.
Why is logarithm used in the pH scale?
Because hydrogen ion concentrations span many orders of magnitude, logarithms compress this range into a simple 0–14 scale that is easy to compare and use.
What pH is neutral?
A pH of 7 is neutral, as in pure water. pH below 7 is acidic, and pH above 7 is basic (alkaline).
How do you calculate pH given a hydrogen ion concentration?
Use pH = -log[H+]. For example, if [H+] = 0.001 M = 10^(-3), then pH = -log(10^(-3)) = 3.