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Topic: pH Calculation  (Read 16582 times)

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pH Calculation
« on: August 26, 2004, 11:35:42 PM »
When calculating pH, such as pH=log 1/[H+].. do you have to calculate using the concentration of H+ in Moles/liter only, or can you use mM/L in  this formula?

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Re:pH Calculation
« Reply #1 on: August 27, 2004, 12:07:09 AM »
If you used mmol/L your answer would be off by 3 pH units.  If you look in a math book under log rules, you will find a relationships like these:

log [A*B] = log A + log B
log [A/B] = log A - log B
log [A^B] = B log A

I have usually seen the pH equation written as pH = -log [H+] which is just rearranged from the equation you wrote using the second rule above (by the way, log 1 = 0)

The two cases you described are related by a factor of 1000, right?  (1000 mmol/mol)  So using the first relationship above you could write the following equations:

-log A = -log A
A = B/1000

Where A is [H+] in mol/L and B is [H+] in mmol/L

Substitute B/1000 for A and divide through by -1:

-log A = -log (B/1000)
log A = log (B/1000)

Then apply the second log rule, listed above:

log A = log B - log 1000

evaluate the log and you get the answer:

log A [mol/L] = log B [mmol/L] - 3

Using the definition of pH = -log [H+] we can rewrite again to get:

pH = -log A [mol/L] = -log B [mmol/L] + 3

You can calculate pH from mmol, so long as you use mmol/mL, however.  It saves a lot of math too....

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