Calculating Average Atomic Mass

Summary

This 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

00:00

🔍 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.

05:01

📊 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.

Keywords

💡Average Atomic Mass

Average Atomic Mass refers to the weighted average mass of all the natural isotopes of an element, taking into account their abundance. In the context of the video, it is used to explain the number 24.31 found at the bottom of the periodic table entry for magnesium. This number represents the average atomic mass of magnesium, which is calculated by considering the mass and abundance of each of its isotopes.

💡Periodic Table

The Periodic Table is a tabular arrangement of chemical elements organized by atomic number, electron configuration, and recurring chemical properties. In the video, the periodic table is used as a reference to find the average atomic mass of magnesium, which is listed as 24.31. It serves as a quick lookup for the average atomic mass of elements.

💡Isotopes

Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. The video discusses magnesium's isotopes, such as magnesium-24, magnesium-25, and magnesium-26, emphasizing that these isotopes have different numbers of neutrons and slightly different masses, contributing to the overall average atomic mass.

💡Abundance

Abundance, in the context of chemistry, refers to the occurrence of a particular isotope in nature relative to the total amount of the element. The video explains that the average atomic mass of magnesium is calculated by considering the abundance of each isotope, such as 78.9% for magnesium-24, 10% for magnesium-25, and 11% for magnesium-26.

💡Atomic Number

The Atomic Number is the number of protons found in the nucleus of an atom, which determines the chemical properties of an element. The video mentions that magnesium has an atomic number of 12, which means that all isotopes of magnesium have 12 protons, contributing to their chemical identity.

💡Mass Number

The Mass Number is the total number of protons and neutrons in the nucleus of an atom. The video uses the mass numbers of magnesium isotopes (24, 25, and 26) to illustrate how the number of neutrons varies among isotopes, affecting their individual masses.

💡Weighted Average

A Weighted Average is an average in which each value is multiplied by a weight or factor before summing up the values. In the video, the calculation of the average atomic mass of magnesium is described as a weighted average, where the mass of each isotope is multiplied by its fractional abundance to reflect the isotope's contribution to the overall average.

💡Atomic Mass Units (amu)

Atomic Mass Units (amu) are units of mass defined as 1/12th the mass of a carbon-12 atom and are used to express the mass of all other atoms. The video explains that the masses of isotopes are given in amu, which are roughly equal to the mass of a proton or neutron, and these values are used to calculate the average atomic mass.

💡Percent Abundance

Percent Abundance is the percentage of a particular isotope relative to the total amount of all isotopes of an element. The video script uses percent abundance to calculate the weighted average atomic mass of magnesium, multiplying the mass of each isotope by its percent abundance to find the contribution of each isotope to the average.

💡Natural Isotopes

Natural Isotopes are isotopes of an element that occur in nature and can be found in various proportions. The video discusses how magnesium's natural isotopes—magnesium-24, magnesium-25, and magnesium-26—are found in different abundances, which are considered in the calculation of the average atomic mass.

💡Significant Figures

Significant Figures are digits in a number that carry meaning contributing to its precision. The video mentions rounding the calculated average atomic mass to two decimal places, which corresponds to the significant figures in the percent abundance values, ensuring the result is precise and meaningful.

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