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in today's video we're going to be

focusing on this equation

which links the volume of a gas in

decimeters cubed

to how many moles of that gas we have

it's actually a really simple equation

because it doesn't matter which type of

gas you have

like whether you have chlorine or water

vapor or oxygen

all you have to do is multiply the

number of moles that you have

by the number 24

and that will give you the volume that

the gas takes up

measured in decimeters cubed

for example if we had 3.5 moles of

chlorine gas

then we would just do 3.5

times 24

to find that it took up 84 decimeters

cubed

we can also use the equation the other

way around

for example if we had 60 decimeters

cubed of oxygen

and we wanted to know how many moles

that was

we'd just rearrange the equation

to volume over 24 equals moles

and then do 60 divided by 24

which gives us 2.5 moles of oxygen

it can get a bit trickier if we're not

given the moles

for example if we had 27 grams of water

vapor

how would we find its volume

well we can see from our equation that

to find the volume we first need to find

the moles

so we're going to have to use this other

equation first

which links mass

moles and relative formula mass

already know that the mass is 27 grams

so we just need the mr

which for water which is h2o

would be 16 for the oxygen

plus 2 times 1 for the hydrogens

so eighteen

then we can divide the mass of 27 grams

by the mr of 18

to find that we must have 1.5 moles of

water vapor

then lastly all we need to do is go back

to our original equation

take our 1.5 moles

and multiply it by 24

to find that the water vapor would have

a volume of 36 decimeters cubed

another thing you might be asked to do

in the exam

is to find the volume of a product when

you're given the volume of a reactant

for example in this equation here

what volume of ammonia would be produced

if we reacted 18 decimeters cubed of

nitrogen with excess hydrogen

the first thing to notice is that the

hydrogen is in excess

which means that the nitrogen must be

the limiting reagent

and so the quantity of ammonia produced

is going to depend entirely on how much

nitrogen we have

next the normal thing to do in this sort

of question would be to find out how

many moles of nitrogen we have

so we take our volume of 18 decimeters

cubed

and divide it by 24

which tells us that we have

0.75 moles of nitrogen

and then we can use the molar ratio to

find out how many moles of ammonia that

will form

remember we find the molar ratio by

comparing these big numbers in front of

the chemical symbols

so an imaginary one for nitrogen because

when there's no number it just means

there's an unwritten one

and a two for ammonia

so the ratio is one to two

which tells us that for every mole of

nitrogen we have

we're going to make two moles of ammonia

so as we have 0.75 moles of nitrogen

we must have 0.75 times 2 moles of

ammonia

so 1.5 moles of ammonia

then finally we just go back to our

original equation

and multiply the 1.5 moles of ammonia by

24

to find that we'll make 36 decimeters

cubed of ammonia

now this whole idea of finding the moles

and then using molar ratios

is what you would normally have to do in

a question like this

however if you're only converting

between gas volumes like we are here

then you don't actually have to do any

of this stuff

all you need to do is look at the modal

ratio

which is one to two

and so you can multiply the original

volume of nitrogen which is 18

decimeters cubed

by two

to find that you'd make 36 decimeters

cubed of ammonia

and the reason we can do this is because

if we have twice as many moles of a gas

it's going to take up twice the volume

to see the zim practice let's change the

question a bit

if we start with four decimeters cubed

of nitrogen

how much hydrogen would it react with

because we're only converting gas

volumes we can just look at the molar

ratio between nitrogen and hydrogen

which is one two three

so then we just take the nitrogen's

volume of four decimeters cubed

and multiply it by 3

to find that it would react with 12

decimeters cubed of hydrogen

the very last thing i want to mention

is that this equation with the number 24

only works for gases at room temperature

and pressure

if we change the temperature or the

pressure

then it would change the number

as gases occupy different volumes at

different temperatures or pressures

but in the exams this equation with the

number 24 is the only one that you'll

need to use

anyway that's everything for this video

so hope you found it useful and we'll

see you again soon