Course:MATH110/Archive/2010-2011/003/Teams/Uri/Homework/13 Part3
Homework
Explain in your own words what it means that these concepts work on a logarithmic scale.
Firstly team Uri has decided to explain the pH scale an how the concepts work in terms of logarithmic scale.
What is the pH scale?
The pH scale was introduced in 1909 by a Danish biochemist named S.P.L. Sorensen. "The letter p is derived from the German word potenz meaning power or exponent of, in this case, 10."
It is defined as:
"A scale from 0 to 14 reflecting the concentration of hydrogen ions in solution; the lower numbers denote acidic conditions and the upper numbers denote basic, or alkaline, conditions."
Or in mathematical terms, the negative logarithm value of the hydrogen ion concentration in the solution.
As shown below are examples on how the pH scale measures different solutions:
How Does it Work?
pH works on a logarithmic scale because in chemistry pH is defined as pH=-log[H3O+].To find pH in a solution the following logarithmic formula is used:A solution with [H3O+]= 1.0 x 10^-7 M (neutral) has pH of...
pH
= -log [H3O+]
= -log(1.0x10^-7)
= -(-7.00) = 7.00
In general at 25 degrees Celsius
pH < 7 is acidic
pH >7 is basic
pH = 7 neutral
Since pH scale is a logarithmic scale a change of one pH unit corresponds to a 10 fold change in [H3O+]concentration.
Example
A lime has a pH of 2.0 this is 10 times more acidic than plums with a pH of 3.0
Another example is using the pH formula to determine whether how acidic or alkaline the solution is. Say you are giving the information that the solution has a H+ concentration of 0.001 or ( 1*10^-4 Moles).
We would have to plug it into our pH equation:
pH= -log [H+]
pH= -log [0.001]
pH= -log [10^-3]
pH= 3
Its pH would be 3 and according to the pH scale the solution would be considered an acidic solution as the pH level is under 7.
Below is a table showing the different concentrations of Hydromium and pH levels:
Reference
Principles of Chemistry: A Molecular Approach by Nivaldo J. Tro