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Today we are going to be talking about how to determine the concentration of a solution given its pH value.
This process involves the use of Logarithms, because pH is a Logarithmic Scale.
"What is a Logarithm?" you ask.
In its simplest terms, a Logarithm is something that will provide us with the answer to this question, "How many of one number do we multiply to get another number?"
Question: How many 10's do we multiply to get 1,000?
The answer is 3 because 10 x 10 x 10 = 1,000. Therefore, the Logarithm is 3.
If we changed the base of our logarithm from 10 to 2 we could ask a similar question: How many times do we multiple 2 by itself to get 8? The logarithm of log base 2 of 8 is 3. It is just the same. For this class, we will only be using Log base 10, which the pH scale is built around.
Let's look at how we write Logarithms.
Let's start with the Logarithm we just solved: 10 x 10 x 10 = 1,000.
We would write this in the following way: Log base 10 of 1,000 equals 3.
The equation for calculating pH is very similar as pH = -log[H+]
If we do not know the value of pH, but we are given the concentration of Acidic Protons in the solution, then we just take the log of that number, and multiply it by -1 as indicated in the equation. When we have the concentration of protons, we just plug in our value and solve it left-to-right. For instance, if we are given a solution that is known to have a proton concentration of 3.8 x 10^-4 M, we substitute that in for [H+] in our pH equation and solve accordingly. Taking the log of our concentration, we get -3.42, and then we multiply this by -1, because pH = -log[H+]. The pH for this solution is 3.42. It's an Acid!!
If we are given the pH, but we do not know the concentration, we can easily figure this out by taking the antilog of our pH value. This can confuse some students if they over-think this, but it is simple. Remember, a Logarithm is a way of expressing an exponential function. We can also move backwards like detectives investigating the scene of a crime. Let's take a look at an example where we are given a pH of 3.78, but do not know what molar concentration of protons in solution this represents. We start by plugging the given pH value into our equation: 3.78 = -log[H+]. There are 2 knowns in this problem and 1 unknown. Remember, we are working with log base 10--This is known. We also know that the pH is 3.78. What we do not know is the Molar Concentration of Protons in this solution. We multiply both sides of the equation by -1 so that our log[H+] is by itself. Therefore, 10 to the power of -3.78 equals 1.66 x 10^-4 M. This is the Molar Concentration of Protons we want. It is just that easy. You are now ready, willing, and able to solve any pH problem in the entire world!!