# Logarithmic Applications: PH

## Essential Question

How does the logarithmic scale help to compare differences in the strength, acidity and concentration of hydrogen ions in different substances?

## What does that mean?

Each pH value under 7 is 10 times more acidic than the last value. If an acid has a pH of 5 it is 10 times more acidic than a pH of 6 and 100 times more acidic than a pH of 7.

## pH and Uses of Log()

The pH scale is a way to measure the concentration of Hydrogen ions in a solutioin, and therefore a scale to acidity or basicity. As explained above, each acid value on the pH scale is consecutively 10 times more acidic than the last. The logarithm's application comes from its unique form of common log. Common log is any log whose base is not given and is understood to be 10. Through the form of common log we can achieve calculations of pH value or Hydrogen Ion concentration from the above equation.

## Question 1

If the pH of lemon juice is 2 what is the concentration of hydrogen ions?

How much less acidic is coffee with a pH of 5?

pH= - log [H+]

2= - log [H+]

-2= log [H+]

H+= 10^-2

H+=o.o1 Hydrogen Ion concentration

The difference in Hydrogen Ion concentration or acidity can be found by using the quotent property.

* Remember you are subtracting a negative log so it is added.

Lemon juice pH - coffee pH = - log(.01) + log(.00001)

Difference in pH = log(.01/.00001)

-3 = log(.01/.00001)

Lemon juice is a 1000 times stronger acid than coffee. Because 10^-3 = 1000

## Question 2

If lemon juice has a Hydrogen Ion concentration of .01 and is 10 times more acidic than battery acid, what is the pH of battery acid?

Lemon Juice pH = X

X = -Log(.01)

-X = Log(.01)

Log(.01) = -2

-X = -2 so X = 2

We know from above that consecutive pH measurements increase 10 times in acidity per unit on the scale. So the pH of battery acid, 10 times less acidic, would be 3.

## Works Cited

Ophardt, Charles E. "PH Scale." Ph Scale. Elmhurst College, 2003. Web. 03 Mar. 2015. <http://www.elmhurst.edu/~chm/vchembook/184ph.html>.