
Skip This! If words like pH and logarithm intimidate you, ignore this paragraph and explore the Playground below first. The pH is the negative logarithm of the [H^{+}] measured in moles per liter. A pH of 7.4 is equivalent to 40 nanoMols/liter [H^{+}] (hydrogen ion concentration). Many of us find that pH confuses us because we are not entirely comfortable with Logarithm. Moreover, as the acidity increases, the pH decreases. The Playground below takes the mystery out of pH.
pH = [H^{+}]= =  
Concentrate pH [H^{+}] −0.1 −0.3 −1.0 −3.0 
Dilute pH [H^{+}] +0.1 +0.3 +1.0 +3.0 
Introduction: This Playground uses approximate values to make it easy to visualize what pH really means – the concentration of Hydrogen Ions in a solution.
Buttons: Click on any of the Blue Multiply or Divide Buttons. For example, the number 2 buttons double or halve the [H^{+}] concentration and the number 10 buttons have a tenfold effect.
Watch the changes on the pH, the [H^{+}] and the Units. In particular look at how cumbersome it is to express dilute [H^{+}] concentrations in mol/L.
Clinical Range. The actual clinical range is between about 80 and 20 nanomol/L (pH 7.1 to pH 7.7). This range is comparable to other clinical variables. In medicine we really don't benefit from using pH.
We would probably have done better if we had been brought up to use concentration in nanomol/L. Too late now!
Number  Log  pH  Concentration 
1,000,000  6  6  1 megaMol/L 
1,000  3  3  1 kiloMol/L 
1  0  0  1 Mol/L 
0.001  3  3  1milliMol/L 
0.000,001  6  6  1 micMol/L 
0,000,000,001  9  9  1 nanoMol/L 
0,000,000,01  8  8  10 nanoMol/L 
0,000,000,1  7  7  100 nanoMol/L 
Make Yourself a pH Table. This is the way to really conquer the meaning of logarithm and pH.
1000 Steps. First step down in thousand fold jumps (See Table on Left). Of course it is impossible to make such concentrated solutions as a megaMol/L, but most of us can remember the logarithm of a thousand and a million.
Starting Numbers: Next, write a list of pH values starting at 8.0 and finishing at 6.8 (See Table below). Below these numbers, write in the the values for pH 8.0 and 7.0 from the table above. These numbers are starting points.
8.0  7.9  7.8  7.7  7.6  7.5  7.4  7.3  7.2  7.1  7.0  6.9  6.8 
10  12.5  16  20  25  32  40  50  64  80  100  128  160 
Now make use of: x 2 = + 0.3 i.e., a log jump of 0.3 corresponds almost exactly to doubling. Now, halve 100 (50, 25, 12.5) and double 10 (20, 40, 80, 160) to obtain the numbers in the table. When you get to 160, pH 6.8 is a tenfold jump away from pH 7.8 (16 followed by 32, 64, 128). Notice that the final number you insert (128 for pH = 6.9) also demonstrates the slight error of this method. Compare it to the value for pH = 7.9 (12.5). The correct values are 126 and 12.6  not errors which would be critical in medicine.
AcidBase Tutorial Alan W. Grogono 
Copyright Oct 2016. All Rights Reserved 