Parts Per Million (ppm) and Parts Per Billion (ppb) - Solution Concentration
INSTRUCTOR: In this video, we're going to work on solving problems associated with units of concentration, such as PPM and PPB. PPM stands for parts per million. PPB stands for parts per billion. In order to calculate the concentration in PPM, you need to take the mass of the solute in grams and divide it by the mass of the solution in grams. And then multiply that by ten to the sixth.
PPM is a special type of concentration. It is used for substances with a very low concentration in solution. Now, there are many different forms of concentration. Perhaps you heard of molarity, molality, normality, mass percent, volume percent. All of these you can use to represent the concentration of a solution.
But in this video, we're going to focus on PPM and PPB. Now, in this example problem, we have four milligrams of sodium chloride. We need to convert that to grams. One gram is equal to 1,000 milligrams. So to convert from milligrams to grams, divide by 1,000. So four divided by 1,000 is 0.04. So that's how much grams of solute we have in this solution.
And now we have eight kilograms of solution. To convert kilograms to grams, you need to multiply by 1,000. One kilogram is equal to 1,000 grams. So eight kilograms is 8,000 grams. And then we're going to multiply this by ten to the sixth. So 0.04 divided by 8,000, and then times one times ten to the sixth. This is 0.5. So this is the concentration of sodium chloride in the solution. It's 0.5 parts per million.
Now let's move on to the next problem. The concentration of potassium iodide is 150 parts per million in a solution with a mass of 7,500 grams. How many grams of KI is present in the solution? Now, it's helpful to represent the concentration in PPM in terms of the grams of solute relative to the grams of solution. So 150 PPM means that there's 150 grams of potassium for every ten to the sixth grams of solution. And expressing the PPM concentration in this way will make it easier for us to solve the problem using unit conversion.
So let's begin. Let's start with the mass that we're given, that is 7,500 grams of solution. And now let's convert this to the grams of KI. So using this concentration, we know that there's 150 grams of potassium iodide for every one million grams of solution. So in this example, we can see that the unit grams of solution cancels, so it's going to be 7,500 times 150 divided by one times ten to the sixth. So the answer is 1.125 grams of potassium iodide. So that's how you can calculate the mass of the solute given the solution concentration in PPM.
Now, let's confirm that this answer is correct. So let's recalculate our PPM concentration. So we know that it's the mass of solute in grams, divided by the mass of the solution in grams times ten to the sixth. The grams of solute is what we just got. That's 1.125 grams of KI. The grams of solution is 7,500 grams. And then we're going to multiply that by ten to the sixth. If our answer is correct, we should get 150. That is, we should get this number. So 1.125 divided by 7,500 times one times ten to sixth is indeed, 150 PPM. So this helps us to see that the answer that we have here is indeed correct.
Now, let's move on to the next problem. The concentration of sodium phosphate, Na3PO4, is 400 parts per billion in a 500 milliliter solution, with a density of 1.02 grams per milliliter. How many micrograms of sodium phosphate is present in the solution? Now, for those of you who want to try this problem, feel free to pause the video. And then when you're done, play it to see if you have the right answer.
So let's begin. Let's start with the mass of the solution. Now, notice that we're given the volume of the solution and the density. Combining these two things can give us the mass of the solution. So we have a volume of 500 millimeters. We're going to multiply that by the density of the solution. There's 1.02 grams of solution per one milliliter. That's what the density tells us. And so we could cancel the volume, that is the units of milliliters, and this will give us the grams of the solution.
Now, the solution concentration is 400 parts per billion. The formula for parts per billion is grams of solute divided by the grams of solution. But the only difference is, instead of multiplying it by a million, or ten to the sixth, we are going to multiply it by a billion, or ten to the ninth. So that's the formula for the parts per billion concentration.
Now, in this example, we have 400 parts per billion. We want to express this as the ratio of grams of solute to grams of solution. Now, this means that we have 400 grams of solute, the solute being Na3PO4, divided by a billion grams of solution, or one times ten to the ninth grams of solution. So since we're dealing with unit conversion, we want to express 400 parts per billion in this format. So that's what we're going to write in the next fraction.
So let's write 400 grams of Na3PO4 on the top of the fraction. And then one times ten to the ninth grams of solution on the bottom. So now, we can cross out the grams of solution. Now, the last thing we need to do is convert the grams of sodium phosphate to the grams-- I mean, to the micrograms of sodium phosphate.
So what's the conversion factor between grams and micrograms? Micro is ten to minus sixth. So one microgram is equal to ten to the minus sixth grams. So we're going to put ten to minus sixth grams on the bottom. And then we're going to put in one microgram on top, so that we can cross those units. So now, let's do the math. If we multiply 500 by 1.02, this will give us the grams of solution. So this is 510 grams of solution.
If we take that, multiply it by 400, and divide it by one times ten to the ninth, you'll get 2.04 times ten to the negative four. Take that number, divide it by one times ten to the minus sixth, and this will give us our answer, 204 micrograms. So that's the mass of sodium phosphate that is present in this solution.
Now, let's confirm our results. The PPB concentration, as mentioned before, is the grams of solute divided by the grams of solution, but times a billion, or ten to the ninth. So in this example, the grams of soolute is-- well, this is the micrograms. So the grams of solute is going to be 204 micrograms, or 204 times ten to the minus sixth grams.
The grams of solution is what we have here. It's 510 grams of solution. And then let's multiply that by ten to the ninth. If our answer is correct, we should get 400 parts per billion. So 204 times ten to minus sixth, divided by 510, times one times ten to the ninth is indeed 400 PPB. So it's always good to check your work to make sure that you indeed have the right answer.
Now, there's one more thing that I want to mention before concluding this video. And that is how to convert from PPM to PPB. So let's say we have a solution concentration of 0.25 PPM. What is the concentration in parts per billion? Well, it's important to know that one PPM is equal to 1,000 PPB. The only difference between the formulas of PPM and PPB is a million and a billion, ten to the sixth and ten to the ninth.
A billion is 1,000 more than a million. So one PPM is going to be 1,000 PPB. So to convert it, we're going to multiply it by 1,000 PPB per one PPM. So in order to convert from PPM to PPB, multiply by 1,000. If you need to go backwards from PPB to PPM, divide by 1,000. So 0.25 times 1,000 is 250 PPB. So now you know how to convert between PPM and PPB.