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Avogadro's Number, The Mole, Grams, Atoms, Molar Mass Calculations - Introduction

so what exactly is the mole what is that

represent in chemistry doesn't represent

the animal it represents a number to

illustrate it think of a dozen when you

hear the word dozen

what do you think of a dozen equates to

12 a dozen eggs mean you have 12 eggs a

dozen calculators is 12 calculators a

mole is similar to a dozen a dozen is

equal to 12 but a mole represents a much

larger number a mole represents 6.02

times 10 to the 23 so if you have a mole

of pens you have 6 times 10 to the 23

pens if you have a mole of pennies you

have 6 times 10 to the 23 panels but

typically the mole is associated with a

very small particle like an atom a

molecule a formula unit within an ionic

compound things like that now this

number of 6 times 10 to the 23 that is

also known as Avogadro's number so what

do we use this for typically you would

use this for a conversion problem let's

say a female the number of moles of

carbon atoms you can calculate the

number of carbon atoms so let's say if

we have four moles of carbon atoms how

can we convert it to the number of atoms

so let's start with what we have four

moles of carbon over one now based on

the conversion that we wrote before one

mole is equal to abogados number which

instead of writing 6.02 I'm just going

to round it to 6 times 10 to the 23 and

this is atoms of carbon so what's 4

times 6 times 10 to 23 4 times 6 is

equal to 24 so we have 24 times 10 to

the 23

now if we move the decimal point one

unit to left

this becomes 2.4 times 10 to the 24 if

you want your answer in scientific

notation this number must be between 1

and 10 it can be equal to or greater

than 1 but less than 10 another way you

can see it is you can view 24 as 2.4

times 10 and we still have the 10 to the

23rd so if you multiply 10 to the 1 by

10 to the 23rd you need to add the

exponents and that's why I change to 24

so whenever you move the decimal point

in wanting it to the left the exponent

will increase by 1 so that's how many

carbon atoms we have in this particular

problem now you need to know want to use

words like atoms molecules or formula

units if you have carbon zinc neon these

are composed of atoms if you have h 2 h

2o c 6 h 6 these are composed of

molecules a molecule is a particle that

has multiple atoms now if you see

something like sodium chloride magnesium

oxide even though it has multiple atoms

it's made up of ions whenever you have a

metal and a nonmetal it's an ionic

compound and so therefore you would use

the term formula units when dealing with

molar conversions so let's say if we

have five moles of methane convert it

into molecules of methane because ch4 is

a molecule it's a particle that has

multiple atoms molecules are usually

made up of nonmetals carbon and hydrogen

are nonmetals if we had a metal and a

nonmetal it will be ionic and we will

use the term formula units so convert

this into molecules of ch4 and also

atoms of hydrogen so let's start with

the first part so we have five moles of

ch4 over one and using Avogadro's number

one mole is equal to six times ten to

twenty three so we have six times ten to

twenty three molecules now you want to

set it in such a way that these units

they cancel so now we can multiply 5

times 6 5 times 6 is 30 so we have 30

times 10 to the 23 and if we move the

decimal one unit to the left

the answer is 3.0 times 10 to the 24

molecules of ch4 now how can we answer

this second part of the question

how can we convert molecules of ch4 into

atoms of hydrogen one molecule of ch4

contains four atoms of hydrogen so we

got to take our answer and multiply by

four so five times four is twenty 20

times six is 120

so we have 120 times 10 to the 23 so if

we take the decimal point move two units

to the left this is the same as 1.2

times 10 to the 25 atoms of hydrogen so

sometimes you may need to take in

another step if you want to go from

molecules to atoms

now let's try another example let's say

if we have four moles of aluminum

chloride

how many formula units of aluminum

chloride are there and also how many

chloride ions are in this sample so

let's start with the first part so four

moles of alcl3 over one so let's convert

it to formula units 1 mole of alcl3 is

equal to 6 times 10 to the 23 for

millions and the reason why we use the

term formula units for this compound is

because aluminum chloride is composed of

ions it's an ionic compound aluminum is

a metal chlorine is nominal whenever you

have them it's represented in formula so

this is going to give us the first

answer notice that the unit moles of

alcl3 cancel so 6 times 4 is 24

so 24 times 10 to the 23 is the same as

2.4 times 10 to the 23 formula units now

to find the next answer the number of

chloride ions we can say that there are

three chloride ions per one formula unit

of alcl3

so 2.4 times 3 that's going to be 7

point 2 so we have 7 point 2 times 10 to

the 23 chloride ions and so sometimes

you just need to take it and extra step

further now what about working backwards

so if we have 5 times 10 to the 24

actually let's say

three times 10 to the 24 atoms of

hydrogen how can we convert it into

moles of hydrogen so if you want to go

from atoms or molecules or formula units

to moles here's what you need to do

start with the number that you have over

one and then use Avogadro's number but

this time instead of being on top it's

going to be on the bottom on top we're

going to have the unit 1 mole of

hydrogen so notice that the unit atoms

cancel and so we just got to divide by

Avogadro's number if you want to go from

atoms molecules or formal units back to

moles so 6 divided by 3 is 2 and 3 over

6 is 1/2 so we have 1 over 2 times 10 to

the 1 power to notice that we have 10 to

the 24 divided by 10 to the 23 when you

divide a common basis you need to

subtract 24 minus 23 is 1 so this is 1/2

times 10 half of 10 is 5 so we have 5

moles of hydrogen now the next thing you

need to be able to do is you need to be

able to calculate the molar mass of a

compound let's say if you want to find

the molar mass of c2h6

to do so you need to use the periodic

table in a periodic table the atomic

mass for carbon is 12 but there's two of

them and for hydrogen is 1 and are 6 so

you get 24 plus 6 which is 30 you can

say 30 atomic units or more commonly 30

grams per mole go ahead and find the

molar mass for the following compounds

feel free to pause the video as you work

out these examples sodium has an atomic

mass of 23 and for oxygen is 16 for

hydrogen is 1 so if we add these numbers

we're going to get 40 grams per mole now

what about glucose c6h12o6 so we have 6

carbon atoms each with an atomic mass of

12 12 hydrogen atoms and 6 oxygen atoms

each with an atomic mass of 16 6 times

12 is 72 and 6 times 16 is 96 72 plus 12

that's 84 84 96 that's 180 so the molar

mass is 180 grams per mole now you can

use the molar mass to convert from grams

to moles so let's say if we have 34

grams of ammonia go ahead and convert

that into moles so the first thing you

need to do is you need to find the molar

mass of nh3 nitrogen is 14 and plus 3

for the three hydrogen atoms so the

molar mass is 17 so start with what you

have 34 grams of nh3 now the molar mass

is 17 grams per mole so what that means

is that one mole of NH Dream has a mass

of 17 grams so you want to set it in

such a way that grams cancel and you get

moles on top so 34 divided by 17 is 2 so

it's 2 moles of nh3

that's how you can convert from grams to

moles you simply have to take the mass

and divide it by the molar mass now

let's try working backwards how can you

use the molar mass to convert back to

grams so let's say if we have 3 moles of

neon convert it to grams

of neon so let's start with what we're

given three moles of any over one now

the atomic mass of neon is simply it's

about twenty so what that means is that

twenty grams of neon is equal to 1 mole

of neon so the unit's cancel and since

we have two numbers on top we need to

multiply so it's 3 times 20 which equals

60 grams of neon now let's make sense of

it let's understand what the molar mass

really is the molar mass is the ratio

between grams and moles so the molar

mass of neon is 20 so as we said one

mole of neon is equal to 20 grams of

neon that means two moles of neon is

equal to 40 grams of neon and so

therefore three moles of neon is equal

to sixty grams of neon which is the

answer to the question so that's another

way you can solve that problem so how

can we convert from grams to atoms so

let's say if we have 12 grams of helium

gas

how many helium atoms do we have so if

you want to go from grams to atoms you

need to convert grams to moles most

atoms if you think you know how to do

this feel free to pause the video and

work out this example and then unpause

it when you're ready to see the solution

so let's start with twelve grams of

helium and let's convert it to moles the

molar mass of helium in the periodic

table is about 4 so there's 4 grams of

helium per 1 mole and the way we set it

up is we set up in such a way that grams

cancel so now let's convert moles to

atoms we know that one mole is equal to

6 times 10 to the 23 the same way as a

dozen represents 12 so the unit moles

cancel

so now let's do the math 12 divided by 4

is string and 3 times 6 is 18 so it's 18

times 10 to the 23 so if we move the

decimal one unit to left this is the

same as 1.8 times 10 to the 24 atoms of

helium so now you know how to convert

from grams to atoms now what about going

backwards atoms to grams so let's say if

we have 9 times 10 to the 24 atoms of

let's choose argon convert that to the

grams of argon so let's start with what

we're given nine times 29 times 10 to 24

atoms over 1 so if you want to go from

atoms to moles you need to put a

Vogler's number on the bottom so that

the atoms will cancel and so we're going

to have 1 mole of argon on top so the

atoms will disappear now the last thing

you need to do is convert moles to grams

so the molar mass of argon is like 39.95

but we're going to round it to 40 so

there's 40 grams of argon for every mole

of argon so these units will cancel so

now we can do the math so it's let's

break down 9 into 3 times 3 and 40 let's

make it 20 times 2 and we have a 6 on

the bottom a 10 to the 23 on the bottom

and on top we have 10 to the 24 now

notice that 3 times 2 is equal to 6 so

we can cancel these numbers so on top

what we have left over is

three times 20 which is 60 and now we

can divide ten to the 24 by 10 to the 23

which is 10 to the first power 24 minus

twenty-three is 1 so we have 10 to the 1

so we can leave the answer as 600 grams

or we can move the decimal one unit to

the left and say it's 6 times 10 to the

2 grams but 600 grams is a nice number

so we'll go with that so we have 600

grams of argon so now you know how to

convert from atoms to grams so that is

it for this video thanks for watching

and have a great day