Calculating Average Atomic Mass
Summary
TLDRThis tutorial explains how to calculate the average atomic mass of an element using magnesium as an example. It clarifies that the average atomic mass is a weighted average of all natural isotopes' masses by their abundance. The video demonstrates the calculation process by multiplying each isotope's mass with its fractional abundance and summing these products to find the average. It also highlights that the most abundant isotope corresponds to the rounded average atomic mass listed on the periodic table.
Takeaways
- 🔍 The average atomic mass of an element represents the weighted average of the masses of all its natural isotopes by their abundance.
- 📊 The relative atomic mass is also known as the average atomic mass and is found at the bottom of the periodic table entry for each element.
- 🌏 When calculating the average atomic mass, isotopes are not simply averaged; instead, their abundance in nature is taken into account.
- 🧲 Magnesium, with an atomic number of 12, has isotopes with mass numbers 24, 25, and 26, each with different natural abundances.
- 📉 The most abundant isotope of magnesium is magnesium-24, which makes up 78.9% of naturally occurring magnesium.
- 🔢 The mass numbers of isotopes are not whole numbers because atomic mass units are rounded off values based on the masses of protons and neutrons.
- 🧮 To calculate the average atomic mass, multiply the fractional abundance of each isotope by its mass and sum these products.
- 📐 The mass of magnesium-24 is approximately 23.98504, which is very close to its rounded off mass number of 24.
- 📝 The calculated average atomic mass of magnesium (24.3052986), when rounded to two decimal places, matches the value on the periodic table (24.31).
- 🔎 The periodic table's listed average atomic mass can be used to identify the most abundant isotope of an element.
Q & A
What is the average atomic mass of magnesium?
-The average atomic mass of magnesium is 24.31, as indicated on the periodic table.
What is the difference between atomic number and atomic mass number?
-The atomic number of an element is the number of protons in the nucleus, which for magnesium is 12. The atomic mass number is the sum of protons and neutrons, and for magnesium's isotopes, they are 24, 25, and 26 respectively.
What is a weighted average in the context of atomic mass?
-A weighted average in the context of atomic mass refers to the average atomic mass of an element calculated by taking into account the relative abundance of each isotope and their respective masses.
Why is the average atomic mass not a whole number for magnesium?
-The average atomic mass is not a whole number because it is based on the actual masses of the isotopes, which are not whole numbers. These actual masses are rounded off to the nearest whole number for simplicity.
How is the abundance of an isotope determined?
-The abundance of an isotope is determined by its natural occurrence in a sample of the element. For example, magnesium-24 is the most abundant isotope, making up 78.9% of naturally occurring magnesium.
What is the mass of magnesium-24 in atomic mass units?
-The mass of magnesium-24 is approximately 23.98 atomic mass units.
How are the masses of isotopes used to calculate the average atomic mass?
-The masses of isotopes are used to calculate the average atomic mass by multiplying the mass of each isotope by its fractional abundance and then summing these products for all isotopes.
What is the significance of the number 24.31 in the context of magnesium?
-The number 24.31 represents the average atomic mass of magnesium, which is a weighted average that takes into account the natural abundance of its isotopes.
How can you find the most abundant isotope of an element without a table?
-You can find the most abundant isotope of an element without a table by calculating the average atomic mass and rounding it to the nearest whole number, which usually corresponds to the most abundant isotope.
Why is it important to use the fractional form of percent abundance in calculations?
-It is important to use the fractional form of percent abundance in calculations to accurately reflect the proportion of each isotope in the average atomic mass calculation.
What is the relationship between the average atomic mass and the most abundant isotope?
-The most abundant isotope often corresponds to the whole number part of the average atomic mass, as it contributes the greatest portion to the weighted average.
Outlines
🔍 Understanding Average Atomic Mass
This paragraph explains the concept of average atomic mass using magnesium as an example. The speaker begins by pointing out the average atomic mass of magnesium, which is 24.31 on the periodic table. This value represents a weighted average of the masses of all natural isotopes of magnesium, taking into account their relative abundance. The speaker clarifies that the average atomic mass is not a simple average but a weighted one, reflecting the varying proportions of each isotope found in nature. Magnesium, for instance, is not found as a single isotope but as a mixture with different isotopes present in different quantities. The calculation involves multiplying the mass of each isotope by its fractional abundance and then summing these products to get the average atomic mass. The most abundant isotope of magnesium is Magnesium-24, which makes up 78.9% of naturally occurring magnesium, with isotopes Magnesium-25 and Magnesium-26 present in lesser amounts. The actual masses of these isotopes are not whole numbers because atomic mass units are approximate masses of protons and neutrons. The speaker demonstrates the calculation process, multiplying the abundance and mass of each isotope and adding them up to arrive at the average atomic mass of 24.31, which matches the value on the periodic table.
📊 Calculating and Interpreting Average Atomic Mass
The second paragraph continues the discussion on calculating average atomic mass, emphasizing that it is derived by summing the product of the percent abundance and the mass of each isotope for all natural isotopes of an element. The speaker stresses the importance of using the fractional form of percent abundance in the calculation. The paragraph also explains how to identify the most abundant isotope using the average atomic mass. If the periodic table is not available, one can round the calculated average atomic mass to the nearest whole number, which typically corresponds to the most abundant isotope. The speaker uses magnesium as an example again, showing that Magnesium-24 is the most abundant isotope because it contributes the greatest portion to the average. The paragraph concludes by reinforcing that the value listed below an element on the periodic table is the average atomic mass of all isotopes and can be used to determine the most common isotope when rounded to the nearest whole number.
Mindmap
Keywords
💡Average Atomic Mass
💡Periodic Table
💡Isotopes
💡Abundance
💡Atomic Number
💡Mass Number
💡Weighted Average
💡Atomic Mass Units (amu)
💡Percent Abundance
💡Natural Isotopes
💡Significant Figures
Highlights
Introduction to calculating average atomic mass
Explanation of average atomic mass as a weighted average
Importance of considering natural isotope abundance
Mention of magnesium's atomic number and isotopes
Description of isotopes in magnesium ore
How to calculate average atomic mass using weighted average
Explanation of percent abundance and its role in calculation
Detailed calculation of magnesium's average atomic mass
Use of atomic mass units and their approximation to actual mass
Calculation of the mass contribution from each isotope
Summation of mass contributions to find average atomic mass
Rounding the calculated average to match periodic table value
General formula for calculating average atomic mass
How to find the most abundant isotope using average atomic mass
Practical application of the calculation in determining the most common isotope
Conclusion and summary of the tutorial's key points
Transcripts
welcome to the ukm tutorial on
calculating average atomic
mass what we're going to do is look at a
periodic table entry and here is the
periodic table entry for magnesium and
what I'm going to do is look at that
number down at the there at the bottom
that 24.31 which is the average atomic
mass and I'm going to show you how
that's calculated so you understand what
that is and then also how to determine
that if you're given the information
that you would need for this calculation
so let's take a look at magnesium um it
has an atomic number of 12 and that
thing down there at the bottom those
numbers down there below it
are an average but a special type of
average that gives us the average atomic
mass this is also known as the relative
atomic
mass so what this is is a weighted
average of masses of all the natural
isotopes of element by their abundance
so if I were to go into the ground and I
were to pull out some magnesium ore all
right and I were to look at that
magnesium what I would find is that that
magnesium metal contains not just one
isotope of magnesium it actually
contains several isotopes of magnesium
and they aren't all found in the same
abundance or that sample will have
different percentages of different
isotopes of magnesium so what we need to
do is determine an average mass because
every time I pull some magnesium out of
the ground I'm not going to just pull
one isotope I'm going to pull this
selection and that's going to have an
average mass so let's look at that um
this average atomic mass is found by
looking at this weighted average and a
weighted average isn't just an average
of each um isotope so in order to
determine
24.31 um I don't just take 24 + 25 + 26
and I don't divide that by three what I
need to do is I need to look at how much
of isotope 24 there is naturally how
much there is of isotope 25 naturally
and how much there is of 26 naturally in
a particular sample and then I'm going
to determine the abundance of each and
then what I'm going to do is proportion
my average so that I'm looking at an
overall sample and I'm saying okay
there's so much of that that's 24 so
much that's 25 so much that's 26 to give
me an average that's weighted so that
the average takes into account the fact
that there might be more of one isotope
in a sample than the others so let's
take a look at the percent abundance so
most of the Magnesium that I would find
if I dug it up out of the ground would
be
78.9% magnesium 24 so in magnesium 24 I
have um the atomic number 12 all right
and the mass number 24 which means means
that that particular isotope of
magnesium would have 12 protons 12
neutrons and 12 electrons and that's the
most common form the most abundant form
however there are those other forms down
there 25 and 26 that have a couple more
neutrons and so those are also found in
natural abundances of 10% and 11% in any
sample that I might find naturally so
I'm going to look at the mass of each
and the reason why these masses are not
whole numbers is because we look at
atomic mass units as being the mass in
quotation marks of a proton or a neutron
it's really a rounded off Mass they're
roughly equal and so these are the
actual masses one atomic mass unit for a
proton is not a very accurate
determination of its actual mass it's
just a little bit more um and the
neutrons are just a little bit different
than the protons so if we really add up
the mass for magnesium 24 we get the
mass of 23.98 501 417 so it's really
really close to 2 4 and if we look for
magnesium 25 and 26 we'll see that
there're decimals that are really really
close to their rounded off values all
right so let's take a look at those the
mass and that's the abundance what I'm
going to do is I'm going to get the
portion of the average and I'm going to
get the portion of the average
contributed by each isotope and I do
that by multiplying the abundance all
right the fractional abundance so
7899 times the
mass and I get 18
94576 269 for the portion that comes
from magnesium 24 do the same for 25 and
I'll do the same for
26 okay and then what I do is I just add
those and I get
24.305
2986 and if I look at that long number
what I'll find is I'll see that if I
round that number to two decimal places
which takes account the significant
figures in the abundance there what I'll
find is 24.31 and lo and behold I have
calculated the average atomic mass and
it agrees with that that I got from my
periodic
table so in general calculation of the
average atomic mass
occurs when you take the sum of the
percent abundance of each isotope times
the mass of the isotope for all natural
isotopes of an element so what I mean by
per abundance you do need to take the
percent like
79.2% and remember that you're going to
use it in its fractional form not
multiplying the mass of the isotope by
75 but multiplying it by
7529 okay and you're just going to take
that for every single isotope and once
you found the fraction of the um the
whole that comes from each isotope you
add them up and that'll give you that
average atomic mass so one thing to
remember is remember on the periodic
table that mass that comes below each
element is the average atomic mass of
all
Isotopes if you want to find the most
common isotope okay what you need to do
is go back and take a look so let's go
back and take a look
at that table that I had and the most
abundant isotope is that of magnesium 24
and if I would like to find the most
abundant isotope I look okay for the
isotope
that in my average atomic mass whatever
that rounds to that is usually my most
abundant isotope because it is the
greatest portion of my average all right
so if you're looking for the most
abundant isotope and in this case that
would
be my magnesium
24 and I would find the most abundant
all right if I didn't have this
table I would find that
rounding the average atomic
mass gives you the
most
abundant isotope
okay so this calculation can be done to
determine the overall Mass I can also
look at the result of this to find the
most abundant isotope if I don't have
that whole table
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