Question

stem connection
focus on math
sc.8.p.8.8, ma.k12.mtr.2.1
you might be wondering what the numbers on the ph scale mean. a change in one
ph unit represents a tenfold change in the acidity or basicity of a solution. for
example, if one solution has a ph of 1 and a second solution has a ph of 2, then the
first solution is not twice as acidic as the second solution; it is ten times more acidic.
the difference in acidity or basicity between two solutions is represented by 10^n,
where n is the difference between the two ph values.
for example, how much more acidic is a solution with a ph of 1 than a solution with a
ph of 3? first, calculate the difference, n, between the two ph values: n = 3 - 1 = 2.
then use the formula, 10^n, to calculate the difference in acidity: 10^2 = 100. a solution
with a ph of 1 is 100 times more acidic than a solution with a ph of 3.
evaluate using the example, how many times more basic is a solution with a
ph of 11 than a solution with a ph of 8?

Explanation:

Step1: Calculate the difference \(n\)

The formula for the difference in acidity or basicity is \(10^n\), where \(n\) is the difference between the two \(pH\) values.
For \(pH = 11\) and \(pH=8\), \(n = 11 - 8=3\)

Step2: Calculate \(10^n\)

Substitute \(n = 3\) into the formula \(10^n\).
\(10^3=10\times10\times10 = 1000\)

Answer:

A solution with a \(pH\) of \(11\) is \(1000\) times more basic than a solution with a \(pH\) of \(8\).