How many more times acidic is a solution with a pH of 9 versus a solution with a pH of 12?

Verified step by step guidance

1. Recall that pH is a logarithmic scale that measures the acidity or alkalinity of a solution, defined as \(\mathrm{pH} = -\log_{10}[\mathrm{H}^+]\), where \([\mathrm{H}^+]\) is the concentration of hydrogen ions.
2. Understand that a difference of 1 pH unit corresponds to a tenfold difference in hydrogen ion concentration. Therefore, to find how many times more acidic one solution is compared to another, you calculate the difference in pH and use it as an exponent of 10.
3. Calculate the difference in pH between the two solutions: \(\Delta \mathrm{pH} = 12 - 9\).
4. Use the formula for the ratio of hydrogen ion concentrations: \(\text{Acidity ratio} = 10^{\Delta \mathrm{pH}}\).
5. Interpret the result as how many times more acidic the solution with pH 9 is compared to the solution with pH 12.

Key Concepts

pH Scale

The pH scale measures the acidity or alkalinity of a solution, ranging from 0 to 14. A pH below 7 indicates acidity, 7 is neutral, and above 7 is basic (alkaline). Each whole number change represents a tenfold difference in hydrogen ion concentration.

Logarithmic Nature of pH

pH is a logarithmic scale based on the negative logarithm of hydrogen ion concentration. This means a difference of 1 pH unit corresponds to a tenfold change in acidity or alkalinity, making it essential to calculate differences using powers of ten.

Comparing Alkalinity Between pH Values

To compare how much more alkaline one solution is than another, subtract their pH values and raise 10 to the power of that difference. For example, a solution with pH 12 is 10^(12-9) = 1000 times more alkaline than one with pH 9.