In this video you're finally gonna understand what an isotope is and how to calculate percent abundance. All right let's do this. Hello hello Melissa Maribel here and I help students like you understand what you just learned in class so you stress less and you graduate faster. Before we get started let's take a deep breath. It's gonna be a lot easier than you think. Starting with our first example let's just talk about the concept of isotopes. So back in 2009 I weighed a hundred and twenty pounds. Then in 2012 I weighed a hundred and thirty pounds and then in 2015 when I discovered my love for sushi I weighed a hundred and forty pounds. So even though there were different weights or different versions of myself, I am still the same person. Isotopes are different versions of the same element. So how does this relate back to chemistry. Let's talk about gold. The chemical symbol for gold is Au. Take this gold bar, it weighs 196 amu. Our second gold bar weighs 197 amu and our third gold bar weighs 198 amu. All of these gold bars have different weights but are made out of the same element which is gold. These are three different types of isotopes of gold. If we were to look at the periodic table and look for where Au is or Gold, we'd see it has a bottom number, right? That atomic mass. That atomic mass is actually the average of all the different types of isotopes of that element. Isotopes have the same atomic number, the same protons and electrons. However, they do not have the same masses. So they have different masses and a different number of neutrons. Let's go into our first example talking about percent abundance. A certain element X has four isotopes 0.5600% of X has a mass of 83.91343 amu. Second isotope, 9.860% of X has a mass of 85.90927 amu. our third isotope, 7.000% of X has a mass of 86.90890 amu and our last isotope 82.58% of X has a mass of 87.90562 amu. Find the average atomic mass of element X. You have four different isotopes, those are our givens. That 0.5600% of our certain amount of mass. So this is what we refer to as percent abundance, where we have a certain amount of percent of our first isotope of a mass. So you see it changes for every single isotope, however, if we were to add up all the percentages, it's always out of a hundred percent. In this example, you are finding your average atomic mass. Step one is to convert all percentages to decimals by dividing by 100. Your first given 0.5600. We'll divide that by 100. And you get 0.005600 There's a trick for this. What we can instead do is move the decimal place over twice to the left for every single percentage to get our decimal form and we'll see we keep doing this and it gives us our answer. Moving on we'll jump to our actual percent abundance formula where our atomic mass is equal to the percentage converted to a decimal, times, the mass of that specific isotope and we'll keep adding every different type of isotope. Since we have four isotopes, I went ahead and added our first decimal form of that percentage multiplied by the mass of that first isotope and kept doing that for every single isotope since we have four. Looking at this first portion we'll multiply 0.005600, times the mass of 83.91343 and that gives us 0.469915. We would then do this for every single isotope and you'll get this. We'll add them all together, that'll give us 87.616626 amu. The reason why we're going to round to only four sig figs is because going back to our given we actually only had four significant figures, 82.58 is four sig figs, same with 7.000 and you'll see that every single one actually has four sig figs. So we'll round up and our final atomic mass is 87.62 amu. In the second example we are solving for percent composition or percent abundance we're no longer solving for the average atomic mass. Naturally occurring copper consists of Cu at 63, this is just the isotope notation, where our mass is equal to 62.9296 amu and our second isotope, copper at 65, which our mass is 64.9278 amu, quick note, they're just rounding here. This is the mass number but they do give us the exact mass amount. Continuing with this question, with an average atomic mass of 63.546 amu. What is the percent abundance of copper in terms of these two isotopes? You're given, are the two different types of isotopes so we're really just focusing on our masses that are exact in this case. This is just the proper notation that they typically have it, but as mentioned we're just focusing on these masses. We're also given the average atomic mass of 63.546 amu and we're asked to find the percent composition of copper. What they're actually referring to here is, they're saying how much of this isotope, what percentage, is within our atomic mass? So we're really looking for two different percentages for our two different isotopes. Using our percent abundance formula once more, our atomic mass is equal to that percentage however we don't know what the percentage is of our first isotope. So in that case we're actually just going to refer to this as X. I also went ahead and placed what we do know which was that atomic mass. So referring to this percentage as X, it's just a way to be able to figure out what X is towards the end. Our mass of our first isotope was this. And next we once again do not know what the second percentage of our isotope is. So what we'll do is we'll subtract it from 1. What 1 refers to is really saying, it's out of a hundred percent so if we don't know what X is, we'll then subtract it from 1 or a hundred percent and that would then give us our second percentage of our isotope. We'll multiply this by our mass of our second isotope. Next, going back to math, let's go ahead and actually distribute this mass to both the one and that negative X. When we do this we end up getting this, and you want to group your X's together so we'll combine these two X values. We're actually subtracting since this is a negative 64.9278. When we do that we end up getting negative 1.9982x. From there we want to isolate our x value. So we'll subtract over that 64.9278 to both sides. These would then cancel and subtracting these two we get a negative 1.3818. And we want to isolate that X by itself, so we'll get rid of that negative 1.9982 by dividing it for both sides. Those would then cancel and our x value gives us a positive value of 0.6915. That was just for our first isotope which was that copper at 63. For our second isotope what we'll do is, taking that 1 minus X, we're actually going to subtract this x value from the 1 and that would then give us 0.30847. The next step is to multiply both of these decimals by 100. The reason is because we want this to be a percentage, so multiplying this by 100 turns it into our percentages. We'll see that our first isotope, that copper 63, has a percentage of 69.15%. Our second isotope, where copper 65, has a percentage of 30.85%. These are our percent compositions of our isotopes. Now that we've worked on two possible exam questions, hint hint, it's your turn to see if you're ready for your exam. Musica maestro! So are you ready for your exam? As a tutor, I always tell my students to do these practice problems, to get them down, because I do see them on exams over and over again. Teachers like to reuse their exam questions, so if you feel like you're not ready, you need some more help, check the description box below and you can find my available times for tutoring. And make sure to LIKE, subscribe and I'll see you guys next time.