If the pH of a sample was 3 how many times more acidic is
it than a solution with a pH of 6?
pH is a logarithm (base 10) scale. It is defined in such a way that LOW
values of pH indicate an INCREASE in the hydrogen ion concentration (H+)
mols/liter. So pH = -log10(H+) = log10[1/(H+)].
So a change of pH from a value of 6 to a value of 3 means
that the (H+), or acidity is 1000 times more acidic. Neutral pH is a pH
value of 7, which means that the (H+) = 10^-7. To appreciate how small this
number is 10^-7 mols (H+) / liter = 1 mol (H+) / 10^+7 liters.
Now liter = 1000 cm^3, so this is 1 mol (H+) / 10^10 cm^3.
If you imagine a cube with a volume of 10^10 cm^3, it would have a side
equal to the cube root of 10^10 cm = 1642 cm or 16.42 meters on a side!!
Every step on the pH scale is a change by a factor of 10. Ie, pH 4 is 10
times stronger than pH 3.
pH = - log[concentration of H+ ions] OR this can be
pH = -log[H3O+]
So, if a solution has a pH of 3, the concentration of
H+ ions = .001
If a solution has a pH of 6, the concentration of H+
ions is .000001
How many times more acidic is the pH 3 solution?
.001/.000001 = 1000
Hope this helps.
At least two answers, Amber:
pH 3 means [H+] = 10^-3 molar.
pH 6 means [H+] = 10^-6 molar.
So the hydrogen ion concentration is 1000 times greater.
However, one might have a different measure of the quality "acidic".
After all, pH 7 means [H+] = 10^(-7) molar, and that's neutral water.
Is neutral water 10 times less acidic than pH 6? or is its acidity zero?
Because, at pH 7 the hydroxyl ion concentration [OH-] =10^-7 too,
and then the acidity might be considered [H+]-[OH-] = (1e-7)-(1e-7) = 0.
Using this definition, ((1e-3)-(1e-7)) / ((1e-6)-(1e-7)) is still
Maybe it's 1100.
A third idea of "acidity" is the "chemical potential" due to the high
concentration of H+ ions in the acid.
If one set up a kind of battery with two electrochemical half-cells,
one electrode being
H+ + e- <-> 1/2 H2 in the test acid (pH6 or pH3),
and the other electrode being
H+ + e- <-> 1/2 H2 in neutral water (pH7),
(same reaction on both sides, pushing against each other, but with higher
[H+] on one side than the other)
then the voltage it generates is proportional to the
logarithm of the [H+] concentration ratio.
For pH3, the concentration ratio between the two half-cells is
10^(-3) / 10^(-7) = 10^(+4)=10,000,
and the log10 of the ratio is 4.
At 60mV per decade, this cell might generate 0.240v.
For pH6, the concentration ratio between the two half-cells is
10^(-6) / 10^(-7) = 10^(+1) =10.
and the log10 of the ratio is 1.
At 60mV per decade, this cell might generate 0.060v
In this sense, pH3 is about 4 times more acidic than pH6.
It seems like an abstract and remote meaning,
but the tendency of many reactions to happen or not happen
often depends on the chemical potential that is pushing them.
PS- I think my "60mV per decade" might be wrong by a factor of two.
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Update: June 2012