Andy G. answered • 12/14/20
Experienced STEM Tutor for All Ages
Hydrogen ion concentrations can vary by many orders of magnitude, making it inconvenient to express the concentration directly. As a result, pH is a convenient way to measure hydrogen ion concentrations by taking the logarithm, thereby collapsing the very large range of concentrations into a much smaller range of familiar counting numbers.
You can calculate [H+] (that's the symbol for hydrogen ion concentration) with the following formula:
pH = -log([H+]) or conversely, [H+] = 10^(-pH) (the log in the first formula is log base 10)
By dividing the larger concentration by the smaller concentration, we can determine how many times greater the former is than the latter. For example, how many times greater is 10,000 than 10? Well if we divide 10,000 by 10, we get 1,000, so 10,000 is 1,000 times greater than 10. We can check that this is right by multiplying it by the smaller number and seeing if we get the larger. In this case, 10*1,000 = 10,000, so we know that we are right.
Increasing by an order of magnitude means multiplying by 10, or moving the decimal place one spot to the right. So as an example, 10,000 is three orders of magnitude greater than 10. Logarithms essentially tell you what order of magnitude something is; log(10,000) = 4, log(10) = 1. Subtracting the log of the two numbers, we get 4 - 1 = 3, which is the same result we got earlier!
**Check your understanding**: What is the relationship between how many times larger a number is than another and how many orders of magnitude they differ by? In this case, what is the relationship between 1000 and 3? (Hint: think about logs!)
