Logarithms

Open the file logs.xls.  You will use this file for both parts below.  Click on the worksheet tabs at the bottom to access the other files.

1. Richter scale (Click on the tab titled earthquakes.)

The Richter scale is used to measure the intensity of earthquakes.  It is a logarithmic relationship with the following formula:

 log I = R

I is the intensity of the earthquake and R is the number on the Richter scale. 

(Remember that if there is no base written with the log it is base 10).  Another way to write the same formula would be:

10^R = I

Which version you use depends on which variable you are given. 

Since the Richter scale is logarithmic, an increase of 1 on the Richter scale translates to 10 times increase in intensity.  Ie. R of 2 means an intensity of 100 while an R or 3 has an intensity of 1000 which is 10 times larger than the previous intensity.

a) Open the Richter worksheet in the Excel file.  For the first 9 earthquakes, calculate the Richter scale value and for the remaining calculate the intensity using the formulas above. Copy and paste the completed table into your Word document.

 

b) Which earthquake had the highest Richter scale value?

 

c)  If one earthquake had an intensity of 8,000,000 and another had an intensity of 80,000,000, how would their Richter values compare?

 

d) If one earthquake had an intensity of 1,500,000 and another had an intensity of 150,000,000, how would their Richter values compare?

e) If one earthquake had a Richter number of 5 and another had a Richter number of 6, how many times more intense would the second one be than the first?

 

f) If one earthquake had a Richter number of 3 and another had a Richter number of 5, how many times more intense would the second one be than the first?

2. pH scale (click on the tab titled pH)

The pH scale describes the relative acidity or basicity of a substance.  To the chemist, pH is a measure of the concentration of positive hydrogen ions, H+, in a solution.  The pH scale generally ranges from 1 to 14, but pH can be zero, negative, or greater than 14.  Pure distilled water at 25C (about room temperature) is said to be neutral and has a pH of 7.  Solutions with pH less than 7 are acidic and solutions with pH greater than 7 are basic.   The relationship between pH and the hydrogen ion concentration is a logarithmic function with the following formula:

 -log [H+] = pH

where [H+]  is the symbol for hydrogen ion concentration. 

a) What is the pH of water if it has a H+ concentration of 1.0 * 10^-7 M?

 

b)  What is the H+ concentration of a substance whose pH is 6?  (Hint: first divide by -1 to get rid of the negative sign on the right hand side of the formula, then convert to exponent form to solve for pH)

 

c) Borax, a cleaning agent, has a pH of 9.2.  Is it basic or acidic?  What is the H+ concentration?  (It is common to leave the [H+] concentration as a power of 10)

 

d) Open the pH worksheet.  Fill in the empty cells using the formula above with either the pH or the hydrogen ion concentration.  Round the pH values to one decimal place.  Copy and paste the completed table into your Word document. 

 

e) Find 2 substances whose pHs are exactly 1 apart from each other.  How do their Hydrogen ion concentrations relate to each other? 

 

f) In this case, does a substance with a larger pH have a larger H+ concentration?  Why or why not?