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 twomass
es here and two atoms here. So respectively means the first of thesemass
es goes with the first atom mentioned and then the second one of thesemass
es goes with the second atom mentioned, so don't let that term throw you off. So that's whatrespectively means. Anyway,
calculate
that averageatomic
mass
of Gallium. So to do this, we're going to want to take themass
of the first isotope, multiply it by its percentage expressed as a decimal, and then we'll take themass
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 itsmass
? It's the first one here so respectively we will use the firstmass
, itis 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, whatyou're going to get
is 69.72 amu for that average
atomic
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 averageatomic
mass
which matches what we justcalculate
d. Now very quickly, check this out. We have two isotopes of Gallium, one weighs about 69 and the other weighs about 71 and themass
is closer to 69 than it is to 71. And that makes sense because thereis 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
atomic
mass
of 84.911 amu and Rubidium 87 with anatomic
mass
of 86.909 amu. Theatomic
weight of Rubidium reported on the periodic table is 85.47 and in this question when they sayatomic
weightthey mean
atomic
mass
, relativeatomic
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 relativeatomic
mass
,atomic
weight. So how does this relate to these two isotopes? We have Rubidium 85 which weighspretty 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
atomic
mass
of Rubidium 85, the weighted average isn't 86 but it is 85.47 amu. This means that it's closer to themass
of Rubidium 85. It's not in the middle and it's not close to 87, so thatmeans 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
atomic
mass
weighted average is closer to that than it is to this. Magnesium has three stable isotopes.Calculate
its averageatomic
mass
, using information in the chart below. We've already done this with two isotopes but you can do this withas 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 itsmass
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 thismath and we're going
to end up with 24.31 amu which is the average