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calculate the molarity of a solution

prepared by dissolving 9.8 moles of

solid NaOH the sodium hydroxide in

enough water to make three point six two

liters of solution define molarity you

take moles of solute and divide it by

liters of solution so to set our

equation up here we have molarity equals

moles of solute sodium hydroxide is the

solute here because it's getting

dissolved in water and we have nine

point eight moles of that divided by

liters of solution which is three point

six two liters right here so find

molarity nine point eight divided by

three point six two round the answer to

two significant figures because I have

nine point eight up here and I get two

point seven one should the units be four

this when you find molarity the final

answer is in units of molar capital M so

this two point seven molar

but what two point seven molar really

means is that there are two point seven

moles of NaOH of the solute for every

one litre of the solution so two point

seven molar

but don't forget that that means two

point seven moles for each one liter of

this solution up here you dissolve 152

point five grams of cucl two that's

copper chloride in water to make a

solution with a final volume of 2.25

liters what is its molarity so for

molarity as you know we want to take

moles of solute divided by liters of

solution cucl two copper chloride is our

solute in this case because it's getting

dissolved in the water but the problem

doesn't tell us how many moles of copper

chloride we have it tells us how many

grams of copper chloride we have so 150

two point five we can't use that number

instead we have to convert this

two moles and then we can plug it into

the molarity equation so to convert this

amount in grams into moles the first

thing that we got to start with is the

molar mass of copper chloride and so to

find the molar mass of copper chloride

we've got to find copper and chlorine on

the periodic table and take a look at

their atomic masses so copper there is

one copper atom in copper chloride so

I'll take the molar mass of copper 63

point five five and then there are two

of these chlorines and copper chloride

so I want to take two times the molar

mass of chlorine which is thirty five

point four four when I add these

together I get one thirty four point

four five grams per one mole okay that's

like the molar mass of it now we're

gonna have to use this as a conversion

factor to go between grams and moles so

remember that when we have conversion

factors like this we can always write

them in two ways we can write it like

this or we can flip it and so we can say

one mole for every one hundred and

thirty-four point four five grams both

of these are ways to express the

relationship between grams and moles for

copper chloride now that I know how to

go between grams and moles with this

conversion factor I can take one fifty

two point five grams and I can multiply

it by one of these two conversion

factors I want to use the one that gets

rid of grams from the top of the

equation up here since grams on the top

I'm going to choose this conversion

factor with grams down here so now grams

cancels out grams cancels out I'm left

with moles and I'm gonna do 150 two

point five times one divided by one

thirty four point four five and that is

gonna give me one point one three four

moles

I'm rounding to four significant figures

here because I have one two three four

significant figures and I don't worry

about the one because it's part of a

definition so now I know that I have one

point one three four moles of C UCL two

now I can go ahead and calculate the

molarity so molarity is going to be

moles of solute one point one three four

moles divided by liters of solution

equals two point two five liters and

want to crank through that rounding it

to three significant figures because I

have three sig figs there it's going to

be zero point five zero four molar and

as I said before don't forget that what

that means is that there are one zero

point five zero four moles of C UCL two

for every one liter of this solution

that we're making here a solution has a

volume of 375 milliliters and contains

42 point five grams of NaCl sodium

chloride what is its molarity this is

kind of a challenging question because

there are two things we need to

calculate molarity moles of solute and

liters of solution we aren't given

either of these two things in the

problem okay instead of moles of solute

we're given grams of solute sodium

chloride is a solute so we can't use

that right away we'll have to convert

grams to moles and then instead of

getting liters of solution we get

milliliters of solution so before we can

run this equation we're gonna have to

convert milliliters of solution into

liters of solution so let's go step by

step to show how we do these conversions

and then how we can do the molarity at

the end the first thing that I'm going

to do is I'm going to take this forty

two point five grams of sodium chloride

and turn it into moles of sodium

chloride so I'm gonna need to start with

a molar mass of sodium chloride look at

sodium and chlorine on the periodic

table to get their masses and I'm gonna

do 20 2.99 for sodium I only have one

sodium and I only only have one chlorine

here so I'm just gonna do 35 0.44 here

add those together

and I'll get the molar mass which I'm

going to be using as a conversion factor

okay so I'm gonna write this as 58.4 for

grams over one mole that's one way to

write it or I can flip the conversion

factor and I can write one mole divided

by eighty eight fifty eight point four

four grams now I have the two conversion

factors that I'll use for taking forty

two point five grams of sodium chloride

multiplying up by one of these it's

going to be this one because I have

grams up here grams down there so these

cancel out forty two point five divided

by fifty eight point four four and that

is going to I'll put the answer down

here and that is going to give me zero

point seven two seven moles sodium

chloride now I know how many moles of

sodium chloride I have so I'm halfway

there the next thing that I have to do

is I have to take the volume which is

375 milliliters and multiply that by a

conversion factor so I can change it

from milliliters into liters so there

are 100 1000 milliliters in 1 liter

which means that we can write these two

conversion factors I want to use a

conversion factor that's going to turn

milliliters into liters so since it's on

the top here I will use a version of

this conversion factor that puts

milliliters on the bottom here so I'll

cancel this out cancel this out I'll be

left with liters and when I do that 375

divided by a thousand I'm left with

0.375 liters now I know my leaders so

now my moles of sodium chloride and my

liters of solution and I can finish this

by saying molarity equals zero point

seven two seven moles divided by zero

point three seven five liters and I mean

yeah one point nine four that's

- one two three significant figures for

a my molarity 1.94 are the units and as

before

don't forget what this really means it

means that for every litre of this

solution there are one point nine four

moles one point nine four moles per one

liter of solution so sometimes you won't

always be given moles you won't always

be given liters and you'll probably have

to convert from grams to moles or from

milliliters into liters so just make

sure you got your conversion factors set

up straight now in the next video

instead of having moles and leaders in

calculating molarity you'll be given

molarity and then you'll have to use

that as a conversion factor to move

between moles in a solution and liters

of a solution