
One of the ways that people show where the water equilibrium lies is by stating the pH of the water solution. pH is a shorthand description of the hydrogen ions concentration. It is defined as: pH =  log [H^{+}]
Some of you might never have seen a log function before, or so you think. Let's begin by reviewing a few math facts that should show you that you have indeed accomplished log problems before.
So this means log 1000 = log 10^{3} = 3 or that log 0.0000001 = log 10^{7}= 7 Log problems are just exponent problems involving powers of 10. So this means that some pH problems, the ones that are powers of 10 are vey easy. Let's look at some of these.
And so on.. Making a simplified chart.
This means that a pH of 3 has a [H^{+}] ten times greater than a pH of 4. A pH of 5 has 100 times as many hydrogen ions as a pH of 7. It also means that pH stand for the hydrogen ions concentration's power of 10. If the hydrogen concentration is not a power of ten, then a calculator comes in handy but we can still make a pretty good guess. Be certain to convert it to a number in scientific notation if it isn't one already when you see see it. By having a number in scientific notation, you can immediately interpret the power of 10, an approximate pH. [H^{+}] = 0.0000576 = 5.76
x 10^{5}M And you know that the pH for a [H^{+}] = 10^{4} M = 4 and the pH for a [H^{+} ] = 10 ^{5} M = 5, we can reason that he pH of a [H^{+}] = 5.76 x 10^{5} must be between 4 and 5. Actually calculating it... Using a calculator to find the pH:
To do just the opposite, given the pH to find the [H^{+}], if it is a whole number pH, it is another very easy problem. pH = 4 means the [H^{+}]= 10^{4}M for instance. Remember p stands for the power. Just put a negative sign in front of the exponent. [H^{+}] = 10^{pH}
p_ is just a short hand way of describing large concentration differences that exists for many other particles. pAg describes the concentration of silver ions. pCl describes the concentration of Cl ions. pOH descries the concentration of hydroxide ions. pOH is calculated in exactly the same way that pH is calculated. pOH =  log [OH^{}] Meaning that...Making a simplified chart....
To find the pOH of a solutions that does not have a [OH1] that is a power of 10, you can use a calculator and do the following. [OH^{}] = 0.00000000845 M Convert this first to a number in scientific notation. [OH^{}] = 8.45 x 10 ^{9} M (immediately you can see that the pOH should be close to 8 or 9) pOH =  log (8.45 x 10 ^{9}) = 8.07 = 8.07 See the calculator notes to see how you might use your calculator to solve pOH problems. To do just the opposite, given the pOH, to find the [OH^{}].... as before... [OH^{}] = 10^{pOH}

