 # 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 respectively means? It means that we've got two

## mass

es here and two atoms here. So respectively means the first of these

## mass

es goes with the first atom mentioned and then the second one of these

## mass

es goes with the second atom mentioned, so don't let that term throw you off. So that's what respectively means. Anyway,

that average

## mass

of Gallium. So to do this, we're going to want to 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 percent abundance expressed as a decimal and we'll add the two of them together. So we will start with Gallium 69. So what's its

## mass

? It's the first one here so respectively we will use the first

## mass

, it is 68.926 and now we want to multiply this by Gallium 69 percent abundance but expressed as a decimal. So we'll be moving the decimal place two spots to the left times 0.6011, that's the first part. Now we're going to want to do the same thing for Gallium 71. So its

## mass

is the second one here, 70.925 and multiply it by its percent abundance as expressed as a decimal. Move this place two to the left so we get 0.3989, multiply both of these together and then add them up, what... you're going to get is 69.72 amu for that average

## mass

for Gallium. If you wanted to just check your work, you could look Gallium up on the periodic table, here's what it would look like, and underneath the element name is the average

## mass

which matches what we just

### calculate

d. Now very quickly, check this out. We have two isotopes of Gallium, one weighs about 69 and the other weighs about 71 and the

## mass

is closer to 69 than it is to 71. And that makes sense because there is more Gallium 69 (60 percent) as compared to Gallium 71 which is only about 40 percent abundant. So it makes sense that our weighted average should be closer to this one that's more abundant than into this one which we don't have as much of. Rubidium has two isotopes: Rubidium 85 which has an

## mass

of 84.911 amu and Rubidium 87 with an

## mass

of 86.909 amu. The

#### atomic

weight of Rubidium reported on the periodic table is 85.47 and in this question when they say

weight they mean

, relative

## mass

, any of these terms you can use interchangeably. Based on this information, which of the isotopes of Rubidium is more abundant? We're talking about is it Rubidium 85 or Rubidium 87 and how do you know which one is more abundant? This is a thought question, we don't really have to any calculation and it revolves around the idea of relative

## mass

,

#### atomic

weight. So how does this relate to these two isotopes? We have Rubidium 85 which weighs... pretty close to 85 amu and then we have Rubidium 87 that weighs pretty close to 87 amu. So for these two things, the regular average if we had the exact same amount of both would be right in the middle, it would be 86 amu but instead we can tell from here and from the periodic table that the

## mass

of Rubidium 85, the weighted average isn't 86 but it is 85.47 amu. This means that it's closer to the

## mass

of Rubidium 85. It's not in the middle and it's not close to 87, so that means that the weighted average is telling us that we have more Rubidium 85 because this weighted average number is closer to this. So there's more of this that is pulling the weighted average number down so Rubidium 85 is more abundant because the

## mass

weighted average is closer to that than it is to this. Magnesium has three stable isotopes.

its average

## mass

, using information in the chart below. We've already done this with two isotopes but you can do this with as many isotopes as you need, it's the same process throughout. So let's start with Magnesium 24. We're going to want to take its

## mass

which is 23.985 and multiply it by its abundance expressed as a decimal, 0.7899. That was Magnesium 24, now we're going to go on to Magnesium 25, take its

## mass

of 24.9586, multiply that by its abundance as a decimal so 0.1000. Okay and then finally Magnesium 26 with 25.983 times 0.110. Ah, I fit it all on one line. So we're going to do this... math and we're going to end up with 24.31 amu which is the average

## mass

and you can check yourself by looking it up on the periodic table and you find that the reported

## mass

is the same as what we

d here.