How To Find The Percent Abundance of Each Isotope - Chemistry

In this video we are going to talk about how to calculate the

percent

age

abundance

of

each

isotope

that makes up a certain element, so in our example we will use the element bromine. Now this element consists of two predominant

isotope

s of natural origin, there are others. but for the most part natural bromine is composed of those two isotopes. Now they give us the atomic mass of bromine 79 and bromine 81. The average atomic mass or weighted average is 79.9 with this information we want to calculate the

percent

age

abundance

of

each

isotope, which means on planet Earth, how much is bromine 79 and how much it grows at 81.

Did they let me write this? So, we have 40 percent bromine 79 and 60 bromine 81 or we have 30 percent bromine 79 and 70 bromine. 81. This is what we are trying to calculate what is the relative percentage abundance of each isotope. Now notice that 79.9 is almost in the middle of these two, which means it's almost 50 50. Now 79.9 is actually almost right in the middle. If it were closer to 79, we would have more bromine 79. If it were closer to bromine 81, we would have more of that isotope, but 79.9 is right between these two numbers, so it will be about 50 50. But let's go over the process of calculating the exact percentage abundance now let's use the letter a to represent the average atomic mass.

Now this is also a weighted average and to calculate the average atomic mass it will be equal to the mass of the isotope multiplied by the percentage of abundance and then it will be plus the mass of the second isotope multiplied by the percentage of abundance of that isotope and if there are more isotopes you can continue with this equation. There is no limit in terms of how many isotopes a specific element can have, so let's go to m1p1. to associate that with bromine 79. and m2p2 let's associate that with bromine 81 now this problem gave us the average atomic mass and that's 79.9 atomic mass units m1 is the mass of br79 it's not exactly 79 but it's close to that so m1 in this example is 78.918 p1 is the percentage abundance of bromine 79.

We don't know what that is, that's what we're looking for, so we'll call it x m2, which will be the mass of br81, which is 80.90. Now here's a I ask you what we're going to use for p2, the percent abundance of bromine 81. Now let's assume that bromine 79 has a percent abundance of 40 percent, which would mean that bromine 81 has a percent abundance of 60. We are assuming that this is not the real answer, but this is to help us understand what to do for p2 forty percent as a decimal is the point forty sixty percent is the point sixty now notice that the point sixty is one minus the point forty, so if point forty corresponds to x one minus point forty is one minus p2 we're going to write 1 minus x, so now we have an equation with one variable, which means we can solve the equation at this point, it's all algebra, let's go ahead and distribute 80,916 to one and negative x.

Now what we have to do is combine like terms and at the same time subtract both. sides times 80,916 so these two will cancel on the left we have 79.9 minus 80,916 and that is negative 1,016 if we combine these two it will be 78,918 minus 80,916 and that will be negative 1,998 times x to get x alone we need to divide both sides by negative 1,998, so negative 1.016 divided by negative 1.998 gives us the point five zero nine, so it's equal to x 1 minus x, which will be 1 minus 0.509, which is 0.491. Now let's clarify some things, there are many things. on the screen right now x was associated with bromine 79 so as a percentage this is fifty point nine percent and one minus so the percentage abundance of bromine 79 is equal to x or is 50.9 percent and the percentage abundance of bromine 81 is 1 minus x, so it will be 49.1 percent and as we could see these two numbers are approximately equal, is close to 50 because as mentioned before, 79.9 is almost in the middle of these two numbers, now we have a little more bromine 79 than bromine 81. because it makes sense, 79.9 is a little closer to 79 than 81. is a little bit closer to this number and then that number, that's how you can

find

the percentage abundance of the isotopes that make up a specific element.

Now, if you want, you can also check your work to make sure you have the right answer to do it. that replaces the numbers in this formula and make sure you get the average atomic mass, so m1 is this number 78.918 and we're going to multiply it by the decimal value of the percentage abundance of br79 which is 0.509 and then plus m2 the mass of bromine 82 , which is 80.916 times the percentage abundance of bromine 81 and that's 0.491, so go ahead and plug these values ​​into your calculator, so the answer I got was 70, wow, 79.899, which is about 79.9, so this tells us that the answers that we have are correct, so this is the percentage abundance of bromine 79 and that is the percentage abundance of bromine 81.

That's basically it for this video, now you know how to

find

the percentage abundance of an element that consists mainly of two isotopes. By the way, for those of you who want more

chemistry

videos, feel free to check out my

chemistry

video playlist. You can find it on my channel or on my website www.thevideodashtutor.net. I also have playlists on other topics like physics, algebra, trigonometry, pre-calculus calculus 1 and 2 and a few other things too, so feel free to check it out for those of you who may need help in those other areas as well. That's all for this video, if you like it, don't forget to like it. comment on this video and even subscribe to this channel, so thanks again for watching.