Hi guys, in this episode of Shree series we're going to be talking about calculating percentage abundance from two isotopes whereby their average relative atomic mass is given. Alright, so if you look at this question here, I'll read it out for you. Copper exists as two isotopes Cu 63 and Cu 65. Given that the average relative atomic mass of copper is 63.55, determine the percentage of each isotope present.
All right. Now, if you look at my previous video, what we had was we had the individual isotopes with their respective percentages and we had to eventually work out the average relative atomic mass. All right.
In this question, though, we've been given the average relative atomic mass and we need to work out the percentage abundance of Cu 63 and Cu 65. All right. So what I've done here is I've got my information. We've got the two isotopes Cu 63, Cu 65 and we also have our average which is 63.55.
All right. Now in a situation like this, we don't know what the actual percentages are. However, we know that when you've got two isotopes, both their percentage abundance need to add up to 100. All right.
So we can go by that assumption and work. through this in a step-by-step process. So let us make some assumptions here.
So let x be the percentage abundance of Cu 63. So let x be the percentage abundance of Cu 63 and let 100 minus x be the percentage abundance of Cu65, all right. So the logic behind that is if one percentage is x then the other percentage will be 100 minus x because you know very well when you've got two isotopes their relative percentage abundance should add up to 100%, all right. So now that we've put this bit here I'll now write it in short form so in that way we have more working space okay so if you look at this question here the percentage abundance will be x and then this one here will be 100 minus x okay so this is the framework that we're going to be using to solve this question okay now that we've we've got that cu corresponds to x in terms of percentage and cu 65 corresponds to 100 minus x and the average relative atomic mass is 63.55 that's given there.
So let's now work through this problem. You will notice that as you work through the process, it ends up becoming more of a mathematics problem than a chemistry problem. Because if you look at the processes of working out, anybody looking at the working would automatically assume this is a maths question, alright? So let's work through the process. So we know that the abundance of 63 is x.
So you go x over 100 times 63 plus 100 minus x over 100 multiplied by 65 is equal to 63.55. All right. So this is the expression that you start off with. OK, so we know that the atomic mass of copper 63. has a percentage abundance of x, the atomic mass of copper 65 will have a percentage abundance of 100 minus x, you divide it by 100 and that average is 63.55, all right. Now from here onwards this becomes a maths lesson.
So what do we do in a situation where we now need to work out the value of x? So what I would do is I would get rid of my denominator, the beauty about this part is the denominators are the same which is 100, I'm going to multiply everything by 100. Alright, I'm going to multiply my left-hand side by 100 and I'm going to multiply my right-hand side by 100. What do we get from there? So that's going to be 63x plus 65. 100 minus x is equal to 6355. So what I've done is I've made a fractional expression into a linear expression.
Alright, so I've gotten rid of my hundreds which are denominators on my left-hand side. and I've multiplied the 100 by 63.55 and I've got that. All right.
So now from here onwards, this is literally expanding. All right. So what we do there is we go 63 times X, 65 times 100, 65 times negative X. All right. So what does that become?
63X plus 6,500 minus 65X equals 6,355. All right. So now we group like terms, we put the X's on one side, put the numbers on the other side. So that 63X minus 65X equals 6355 minus 6500. We end up getting negative 2X is equal to negative 145 and X is equal to 72.5%. All right, so we know very well that the isotope of Cu 63 will have a percentage abundance as 72.5% and then the Cu 65 will be 100 minus 72.5 which is 27.5 percent Alright, so that ends up being the answer for the percentages of Cu63, 72.5 and Cu65, 27.5.
When you add 27.5 and 72.5, you get exactly 100. So you can see from here onwards and you work down methodically from top to bottom, this eventually becomes a maps problem, alright? The chemistry part comes in by making the assumption that 63 will have a percentage abundance as x. And Cu65 will have a percentage abundance as 100 minus X and then you work your way down here. Alright, thanks for listening guys. Bye now.