How to Calculate Atomic Mass Practice Problems

Gallium has two stable isotopes, and the

mass

es of gallium 69, which is 60.11 percent abundant, and gallium 71 (39.89 percent abundant), are 68.926 amu and 70.925 amu, respectively. Do you know what it means respectively? It means we have two

mass

es here and two atoms here. So, respectively, it means that the first of these masses goes with the first mentioned atom and then the second of these masses goes with the second mentioned atom, so don't let that term confuse you. So that's what it means respectively. Anyway,

calculate

that average

atomic

mass of gallium. So to do this, we'll take the mass of the first isotope, multiply it by its percentage expressed as a decimal, and then we'll take the mass of the second isotope, multiply it by its percentage abundance expressed. as a decimal and we will add them.

So we'll start with gallium 69. So what is its mass? It's the first one here, so we'll respectively use the first mass, it's 68.926 and now we want to multiply this by gallium with an abundance of 69 percent, but expressed as a decimal. So we'll move the decimal place two points to the left multiplied by 0.6011, that's the first part. Now we're going to want to do the same thing with gallium 71. So its mass is the second one here, 70.925 and multiply it by its percentage abundance expressed as a decimal. Move this place two to the left to get 0.3989, multiply both and then add them together, what you get is 69.72 amu for the average

atomic

mass of gallium.

If you wanted to just check your work, you could look up gallium on the periodic table, here's what it would look like, and under the element name is the average atomic mass which matches what we just

calculate

d. Now, very quickly, look at this. We have two isotopes of gallium, one weighs about 69 and the other weighs about 71 and the mass is closer to 69 than 71. And that makes sense because there is more gallium 69 (60 percent) compared to gallium 71 which is only about 40 percent abundant. So it makes sense that our weighted average would be closer to this one that's more plentiful than this one that we don't have as much of.

Rubidium has two isotopes: rubidium 85 which has an atomic mass of 84.911 amu and rubidium 87 with an atomic mass of 86.909 amu. The atomic weight of rubidium reported in the periodic table is 85.47 and in this question when they say atomic weight they are referring to atomic mass, relative atomic mass, any of these terms can be used interchangeably. Based on this information, which of the rubidium isotopes is most abundant? We are talking about whether it is Rubidium 85 or Rubidium 87 and how do you know which is more abundant? This is a thought question, we don't really have to do any calculations and it revolves around the idea of ​​relative atomic mass, atomic weight.

So how is this related to these two isotopes? We have Rubidium 85 which weighs pretty close to 85 amu and then we have Rubidium 87 which weighs pretty close to 87 amu. So for these two things, the regular average, if we had exactly the same amount of both, would be right in the middle, it would be 86 amu, but instead we can say from here and from the periodic table that the atomic mass of Rubidium 85, The weighted average is not 86 but 85.47 uma. This means it is closer to the mass of Rubidium 85. It is not in the middle or close to 87, which means that the weighted average tells us that we have more Rubidium 85 because this weighted average number is closer to this.

So there is more of this that is reducing the weighted average number, so Rubidium 85 is more abundant because the weighted average atomic mass is closer to that than this. Magnesium has three stable isotopes. Calculate its average atomic mass, using the information in the following table. We've already done this with two isotopes, but you can do it with as many isotopes as you need, it's the same process every time. So let's start with magnesium 24. We'll take its mass, which is 23.985, and multiply it by its abundance expressed in decimal, 0.7899. That was magnesium 24, now let's move on to magnesium 25, take its mass of 24.9586, multiply it by its abundance as a decimal, that is, 0.1000.

Well and finally Magnesium 26 with 25.983 times 0.110. Ah, I fit it all into one line. So we're going to do these calculations and we're going to end up with 24.31 amu, which is the average atomic mass. You can check this for yourself by looking it up in the periodic table and you will find that the reported atomic mass is the same. like what we calculate here.