The Ideal Gas equation | A level Chemistry
Summary
TLDRThis chemistry video tutorial delves into the ideal gas equation, a fundamental concept in A-Level chemistry. It explains the equation's derivation through everyday examples like party balloons, illustrating how gas behavior relates to temperature (Charles's Law), pressure (Boyle's Law), and the number of gas molecules. The video meticulously covers unit conversions crucial for using the equation correctly, such as converting Pascals, cubic meters, and Kelvin. It also guides through solving practical problems using the ideal gas equation, including calculating moles of gas and applying it to chemical reactions, ensuring a comprehensive understanding of this essential chemistry topic.
Takeaways
- 🎈 The ideal gas equation, PV=nRT, is derived from observing how gases behave under different conditions, such as temperature and pressure changes.
- 🔍 Charles's Law states that the volume of a gas is directly proportional to its temperature (V∝T).
- 📉 Boyle's Law indicates that the pressure of a gas is inversely proportional to its volume (P∝1/V) when temperature is constant.
- 🌡️ The number of moles of a gas is directly proportional to the volume it occupies, which is a fundamental concept in the ideal gas law.
- 📐 The ideal gas equation is applicable to all gases under ideal conditions, regardless of the type of gas.
- ⚖️ The units for the ideal gas equation are crucial: pressure (Pascals), volume (cubic meters), moles (moles), temperature (Kelvin), and the gas constant (8.31 J/K/mol).
- 🔄 Understanding unit conversions is vital for correctly applying the ideal gas equation, especially between Kelvin and Celsius, and cubic meters with other volume units.
- 🔢 The ideal gas equation can be rearranged to solve for different variables, such as pressure, volume, or the number of moles.
- 🧪 Practical applications of the ideal gas equation include calculating moles of gases in reactions, determining temperatures in chemical processes, and finding the molar mass of volatile liquids.
- 🔄 The ideal gas equation can be combined with chemical equations to perform stoichiometric calculations and find the amounts of reactants or products in chemical reactions.
Q & A
What is the ideal gas equation?
-The ideal gas equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
What is Charles's law as mentioned in the script?
-Charles's law states that the volume of a gas is proportional to its temperature, when the pressure is held constant.
What is Boyle's law and how does it relate to the volume of a gas?
-Boyle's law states that the pressure of a gas is inversely proportional to its volume, provided the temperature and the amount of gas remain constant.
How does the number of moles of gas affect its volume according to the script?
-The volume of a gas is directly proportional to the number of moles of gas it contains, assuming the temperature and pressure are constant.
What does the ideal gas equation assume about the behavior of gases?
-The ideal gas equation assumes that all gases behave in the same ideal way, regardless of their composition, obeying the rules of direct or inverse proportionality with volume, pressure, and temperature.
What is the value of the gas constant R in the ideal gas equation?
-The gas constant R in the ideal gas equation is 8.31 joules per Kelvin per mole.
How can you convert pressure from kilopascals to pascals?
-To convert pressure from kilopascals to pascals, you multiply by 1,000 (since 1 kilopascal is equal to 1,000 pascals).
What is the Kelvin temperature scale and how does it relate to the Celsius scale?
-The Kelvin scale is a temperature scale that starts at absolute zero (0 K) and increases by the same amount as the Celsius scale. To convert Celsius to Kelvin, you add 273.15.
How do you convert cubic centimeters to cubic meters?
-To convert cubic centimeters to cubic meters, you divide by one million, because one cubic meter is equal to one million cubic centimeters.
What is the significance of the units used in the ideal gas equation?
-The units used in the ideal gas equation (Pascals for pressure, cubic meters for volume, Kelvin for temperature) are significant because they ensure the equation's balance and allow for accurate calculations of gas properties.
How can the ideal gas equation be rearranged to solve for different variables?
-The ideal gas equation can be rearranged algebraically to solve for different variables such as pressure (P = nRT/V), volume (V = nRT/P), temperature (T = PV/nR), and the number of moles (n = PV/RT).
Outlines
🎈 Introduction to the Ideal Gas Equation
This paragraph introduces the Ideal Gas Equation, a fundamental concept in A-Level Chemistry, specifically in the chapter on the amount of substance. The origin of the equation is explained through a relatable example involving party balloons and their behavior under different conditions. The script discusses how balloons expand in warm environments due to increased temperature (Charles's Law), contract when cooled (inversely related to volume), and increase in volume when more gas is added (directly related to the number of moles). These observations lead to the formulation of the Ideal Gas Equation: PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin. The importance of memorizing this equation for exams is emphasized, along with understanding the units for each variable.
🔍 Understanding Units in the Ideal Gas Equation
This section delves into the units used in the Ideal Gas Equation, focusing on pressure in Pascals (Pa), volume in cubic meters (m³), and temperature in Kelvin (K). The script clarifies common unit conversions, such as kiloPascals to Pascals and the conversion between Celsius and Kelvin scales. It also addresses the less familiar unit of volume, cubic meters, and provides conversions to more commonly used units like cubic centimeters and cubic decimeters. The goal is to ensure that students can comfortably work with the units required for the Ideal Gas Equation in various exam scenarios.
🧪 Manipulating the Ideal Gas Equation
The script explains how to manipulate the Ideal Gas Equation to solve for different variables, such as pressure, volume, or the number of moles. It emphasizes the importance of rearranging the equation to isolate the desired variable and then substituting the known values. The process involves converting all quantities to their SI units before solving. An example calculation for the number of moles of oxygen gas is provided, demonstrating the step-by-step approach, including unit conversions and the final calculation.
🔬 Applications of the Ideal Gas Equation
This part of the script explores practical applications of the Ideal Gas Equation, such as determining the molar mass (M R) of a volatile liquid. The process involves measuring the volume of gas produced when a liquid evaporates and the mass loss of the liquid container. The Ideal Gas Equation is used to calculate the number of moles of the gas, which then allows for the calculation of the M R. The script also discusses how the Ideal Gas Equation can be combined with chemical equations to perform stoichiometric calculations, such as determining the number of moles of reactants or products based on the gas laws.
📚 Advanced Problems Using the Ideal Gas Equation
The final paragraph presents more complex problems that involve using the Ideal Gas Equation to find the volume of gases produced in chemical reactions. It covers scenarios where the reaction conditions (temperature and pressure) are given, and the task is to calculate the volume of gas produced from a known mass of a reactant. The script demonstrates how to use the Ideal Gas Equation to find the number of moles of a gas, and then how to use stoichiometry to find the volume of another gas in the reaction. This section showcases the application of the Ideal Gas Equation in solving multi-step chemical problems.
Mindmap
Keywords
💡Ideal Gas Equation
💡Charles's Law
💡Boyle's Law
💡Moles
💡Pascal
💡Kelvin
💡Gas Constant (R)
💡Unit Conversions
💡Volume
💡Molar Mass
💡Chemical Reactions
Highlights
Introduction to the ideal gas equation in A-Level Chemistry
Explaining the origin of the ideal gas equation using party balloons
Charles's law: Volume of a gas is proportional to temperature
Boyle's law: Pressure is inversely proportional to volume
Volume is proportional to the number of moles of gas
Combining relationships to form the ideal gas equation PV=NRT
Importance of remembering the ideal gas equation for exams
Units for each quantity in the ideal gas equation
Conversion of pressure units from kilopascals to pascals
Understanding Kelvin scale and its conversion from Celsius
Volume units in cubic meters and their conversions
Rearrange the ideal gas equation to solve for different variables
Calculating the number of moles of oxygen gas using the ideal gas equation
Determining the temperature in degrees Celsius using the ideal gas equation
Using the ideal gas equation to find the molar mass of a volatile liquid
Combining the ideal gas equation with chemical equations for combustion reactions
Calculating the total volume of gas produced from a cracking reaction
Transcripts
hello everybody and welcome to this a
level chemistry video about the ideal
gas equation this is one of these sub
topics in the amount of substance
chapter 4 a level chemistry and in this
video we'll look briefly at the origin
of the ideal gas equation we'll look in
depth at how you use the ideal gas
equation including unit conversions and
then we'll finish by looking at how we
can work with gases in equations
including a couple of questions to that
effect the origin of the ideal gas
equation can be explained using a simple
example of party balloons if we take a
number of identical party balloons with
an identical number of molecules of air
inside them we can subject these
balloons to different conditions and see
how they behave and their behavior
allows us to come up with some
scientific rules that form the ideal gas
equation first of all if we place a
party balloon in a warm environment say
a boiler cupboard then the party
balloons will expand and then they might
pop you can see this same effect if
people have put party balloons outside
their house for somebody's birthday and
it's a hot day and the balloons will pop
in the same way but the opposite way
around if you took a party balloon and
put it inside a freezer that party
balloon would shrivel up maybe not go
shrivel down to nothing but it would
definitely get smaller and what this
allows us to realize is that the volume
of space a gas occupies the gas inside
the balloon is proportional to the
temperature of those gasses so the
volume V is proportional to the
temperature T and this is actually known
as Charles's law after one of the
scientists who did a lot of work in this
area if we took another party balloon
and we just simply squeezed it as we've
all done probably when we were younger
we can say that that party balloon
assuming that we're squeezing it and
stopping it moving out from between our
fingers
that party balloons actually going to
get smaller and what that means is that
the pressure that we exert on gases is
influencing the volume and the pressure
is inversely proportional to the volume
what that means is if we increase the
pressure the volume gets smaller and so
this is Boyle's law pressure is
inversely proportional to the volume and
then last of all if we were to carefully
undo the knot in the balloon and breathe
out more air into that balloon we would
find that the balloon of course would
get larger the volume would increase and
what that means is we've put more
molecules of gas into the balloon more
moles and so the volume of that balloon
is increasing because volume is
proportional to the number of moles of
gas inside the balloon and this these
three relationships that we've got here
on the slide that combine together to
give us the ideal gas equation and it's
called the ideal gas equation because
all gases are assumed to behave in this
same ideal way regardless of whether
they're carbon dioxide or oxygen or
nitrogen they all obey these rules where
their volume is proportional to a number
of different factors so this is the
ideal gas equation PV equals NRT it's
got quite a nice rhythm to it when you
say it like that you need to remember
this so you can use it in exam questions
because it won't be given to you and
you'll get a mark for remembering it not
only do you need to remember it you need
to be able to understand it and use it
including understanding the units for
each of these quantities so P is
pressure and that's measured in Pascal's
and Pascal's is the international symbol
international unit for pressure V is
volume measured in cubic meters n stands
the number of moles T is the temperature
measured in Kelvin which has got a
symbol K and last of all R is the gas
constant and it's got a number 8.31
joules per Kelvin per mole and you need
to remember those numbers 8.31 because
that is a constant which means that
whatever the gas is it will always have
that many joules of energy per Kelvin
per mole that means if you've got one
mole of a substance at 20 Kelvin it will
have 8.31 times by 20 that's how much
energy that gas will have let's move
back to the units Pascal's cubic meters
and kelvins probably not units that we
use frequently so let's have a look at
each of those now let's start with our
units by looking at pressure in Pascal's
in exam questions they like to try and
trip you up by giving you the units in
something that is not the SI form not
the standard way of giving it to you so
they might give it to you in kiloPascals
and if that's the case well that's
really lovely because they might give
you a pressure of 3 kilo Pascal's which
to convert into Pascal's you simply
multiply by a thousand in the same way
that three thousand grams is three
kilograms or three kilograms is three
thousand grams so that's nice
atmospheric pressure is taken to be 101
kiloPascals so they might talk to you
about atmospheric pressure that would be
a bit mean expecting you to remember 101
kiloPascals but that is atmospheric
pressure sometimes approximated to 100
kilo Pascal's so to convert killer
Pascal's into Pascal's you just simply
multiply by 1,000 now temperature
temperature is in Kelvin and that is an
entirely new temperature scale named
after a scientist Lord Kelvin who
all sorts of crazy experiments in his
country house but essentially the Kelvin
scale is a recalibrated degrees Celsius
scale that starts at zero you might have
wondered why we have a temperature scale
that goes negative wouldn't it be easier
if we have one that starts at zero and
that's what the Kelvin scale does it
starts at zero and that is referred to
as absolute zero that is as cold as it
is theoretically possible to get we've
got below 1 Kelvin
I believe but never down to zero it's a
theoretical temperature now the good
news for you and your exams is it's not
a really tricky conversion to work
between degrees Celsius and Kelvin zero
degrees Kelvin is minus 273 degrees
Celsius 20 Kelvin is minus 253 degrees
Celsius so you can see that what we're
doing is we're adding 273 on to the
degree Celsius scale to get us into our
kelvin scale so zero degrees Celsius is
273 Kelvin 50 Celsius is 323 Kelvin and
so the scale is nice that's plus 273 or
minus 273 depending on which way you're
converting most likely you'll be adding
273 to convert into Kelvin but what's
really nice is that that increase of one
degree Celsius from say 50 to 51 is the
same as one Kelvin from three to three
to three to four so these first two
conversions aren't too bad let's take a
look at volume volume is usually taken
to be the trickiest one now the units of
volume for the ideal gas equation are in
meters cubed and a cubic metre is
actually really quite big and the reason
that we have these big volumes is
because gases occupy a lot of space now
you can just accept that the volume is
in cubic meters and you can also accept
the conversions so I'll start with the
conversions to convert to be centimeters
which is quite common through given a
volume in cubic centimeters into cubic
meters you divide by a million and
that's because a cubic centimeter is
tiny compared to a cubic meter so a
beaker that holds 500 cubic centimeters
of volume would actually only be 5 times
10 to the minus 4 cubic meters with the
volume so centimeters cubed 2 meters
cubed you divide by a million and then
centimeters cubed to decimeters cubed
you divide by 1,000 the origin of that
can be explained using cubes here we've
got a cube which I will take to be one
meter by one meter by one meter so that
is one cubic meter now a decimeter is
1/10 of a meter so this 1 meter
dimension here is actually 10 decimeters
and so is this one and so it's this one
so the volume is 10 by 10 by 10 which is
1,000 cubic decimeters so one cubic
meter is 1000 cubic decimeters but we
also know that one meter is 100
centimeters so this dimension could also
be referred to as 100 centimeters and
this one 100 centimeters of this one 100
centimeters as well so the volume in
cubic centimeters we is 100 times 100
times 100 so a million and that's the
origin of these conversions cm cubed 2
meters cubed we multiply by 10 to the
minus 6 or divide by a million DM cubed
into meters cubed we divide by a
thousand and it's the opposite going the
other way
so those are the really important
conversions to remember let's get back
to the ideal gas equation itself PV
equals NRT and let's explore the
different forms of this equation because
you might be asked to work out P and
then you need to have an equation where
P equals something so you might prefer
to write that equation and then
substitute numbers into it and then
rearrange numbers people often find that
easier and so that would be possibly
what I recommend remember what the units
are
then alternatively you could use algebra
as your method so PV equals NRT if I've
been asked to work out what P is I need
to divide both sides of this equation by
V and then the V's on the left hand side
cancel out and we're left with NRT
divided by V and making V the subjects
of the equation works in the exact same
way however if we wanted to work out a
number of moles we would need to divide
both sides of the equation by RT and
then the RT would cancel on the right
hand side and would be left with PV
divided by RT equals N and so that's the
rearranging of the ideal gas equation
either by subbing the numbers in at the
beginning or by doing the algebraic
method so let's take a look at a couple
of questions here how many moles are
there in 0.050 cubic meters of oxygen
gas at a temperature of 450 Kelvin and
60,000 Pascal's so the first thing that
I recommend you do is you write the
ideal gas equation out PV equals NRT you
rearrange it to make n the subject N
equals PV over RT and then you write the
quantities V equals T equals P equals
and then you do the conversions because
getting into this routine like this
encourages you to remember to do the
conversions and if you make a slip-up
you're more likely to get method marks
when you say use the wrong volume later
that you've shown that you think it's
the volume whereas if you just use the
wrong volume later without saying what
it is that you're doing you're less
likely to get method marks so convert
each of those quantities like this now
on this occasion no conversions are
necessary because all of the units are
in the correct form but it's a really
good habit to force yourself into then
plug those numbers into the equation you
get your answer and don't forget to put
the unit's in and in this second
question
what was the temperature in degree C of
a gas that has got a pressure of 110,000
Pascal's 0.4 moles of gas occupying a
volume of 1600 cubic centimeters so
again my suggestion is that you write
the ideal gas equation this time with T
as a subject so T equals PV divided by n
R we write down our quantities and then
we take a moment to look at the units
and this time we find out that the
volume is not in the SI units that we
need it's in cubic centimeters so we
need to divide that by a million and get
the correct number of meters cubed so
dividing 1600 by a million we get one
point six times ten to the minus three
cubic meters and so we plug those
numbers into the equation and we get a
temperature now we should note I said
before don't forget to put the unit's
the temperature units are in Kelvin but
this question asked for the temperature
in degrees Celsius so our value in
Kelvin remember is 273 bigger than our
value in degree C would be so we need to
subtract 273 off this to get our
temperature in degrees C so this is our
answer here another application of the
ideal gas equation is that you can use
it to find the M R of a volatile liquid
and to do this what you have is you have
a canister that contains the volatile
liquid and you inject some of it through
a syringe into a second chamber and the
second chamber is inside an oven and
volatile means it turns into a gas
easily and so once the liquid has moved
into the oven it will evaporate and
become a gas and so we can measure the
volume of gas that is produced in this
chamber and we can take a look at what
the mass has dropped by from this
canister
so if the canister lost a certain mass
we will know that that canisters mass
loss is all to do with the fact that the
liquid left through the syringe and into
the oven and then it became a gas whose
volume we measured so let's say that we
collected 1,000 cubic centimeters of gas
inside the oven and that the mass of the
canister began at 30 point-0 grams but
then it dropped and it dropped down to
twenty-five point four two grams and so
we can work out what mass has been
injected and that mass is four point
five eight grams and that four point
five eight grams of the liquid has got a
volume once vaporized of one thousand
cubic centimeters so the first thing
that we need to do to work out what the
M R is is to work out how we're going to
calculate the M R at the end
and since moles equals mass over M R
that means that M R is mass over moles
and so the final calculation that we're
going to do is mass divided by moles to
work out what the mr is and so that
means that the previous step must be to
work out what the moles is because we
know what mass has been lost four point
five eight grams but we don't know the
moles and so we need to use the ideal
gas equation to work out the moles so
that's in the form n equals PV divided
by RT we've got our volume of one
thousand centimeters cubed we need to
convert that into meters cubed by
dividing by a million and we need to
take the temperature of the oven and
that is at only forty four degrees C and
so 44 degrees C we need to convert that
into Kelvin by adding 273 on to it and
then the pressure is 101 kiloPascals
which we then multiply by a thousand to
get one hundred and one thousand
Pascal's we plug those numbers into the
equation
remembering the value for R is eight
point three
and we get a value for our moles we then
take this value of moles and we put it
into the equation down here and we
divide our 4.5 eight grams by the moles
we've just calculated and we get our M R
value you don't normally need to use the
units of M R grams per mole but I like
to put it in because I think it helps
give em our more meaning we're going to
finish this video by taking a look at
how we can combine the ideal gas
equation with other calculations and
with other chemical equations so we've
got a situation here where octane a
hydrocarbon with a molecular formula
c8h18 burns completely in air to give
water and carbon dioxide
there's the chemical equation for it
here we can see the numbers in the
equation nine eight one and one and then
we've been given some data a sample of
octane burns completely in air the
carbon dioxide produced occupies a
volume of twenty thousand cubic
centimeters and has a temperature of 55
degrees C and 101 kiloPascals of
pressure we have to calculate the number
of moles of carbon dioxide present to do
this we need to use the ideal gas
equation PV equals NRT we're going to
rearrange it in the form n equals PV
divided by RT in our data volume is
twenty thousand cubic centimeters which
we need to divide by a million to get
into cubic meters so 0.020
cubic meters the temperature is 55
degrees Celsius which we need to add on
to 73 to get 328 Kelvin and last of all
the pressure is 101 kiloPascals and we
just simply need to multiply that by
1,000 to get one hundred and one
thousand Pascal's of pressure and then
we need to substitute these values into
the calculation and this
final answer of 0.074 1 moles of carbon
dioxide and then there's a follow-up
question asks us to calculate a number
of moles of octane burnt and if we look
at the chemical equation the ratio of
octane to carbon dioxide is 1 octane for
8 carbon dioxide and so to convert the
moles of carbon dioxide into moles of
octane which is what we need to do we
need to divide it by 8 so our answer
from the previous question needs to be
divided by 8 and when we do that we get
9 point 2 6 times 10 to the minus 3
moles of octane and so you can use the
coefficients in the equation those
multipliers to work with moles without
having to use moles mass and M are you
just simply use their proportions from
the multiples in the equation okay we'll
take a look at one last question now a
sample of decane is cracked to produce
butane and ethene as shown in the
equation below and we've got decane on
the left and we've got butane on the
right and three moles of ethene and
that's really important that the decane
produces one mole of butane and three
moles of ici now the reaction is carried
out it's 550 degrees Celsius that's T
and 200 kilo Pascal's so there is P and
our command is if eleven point six grams
of butane are produced what is the total
volume of gas in cubic centimeters
that's so important let's highlight that
now what we need to do first is we need
to go PV equals NRT our final answer
needs to be for the volume so V equals
NRT divided by P which means that we
need to know n RT and P so n is the
number of moles we actually don't have
that yet so that's going to be something
we're going to need to calculate using
the mass R we know is eight point three
one might give it to you
they might not temperature is 550
degrees Celsius which is
823 Kelvin remember we need to add 273 P
is 200 kilo Pascal's which is 200,000
Pascal's now n is the moles of gas and
this is the tricky bit here we've got
two gases we've got ething and we've got
butane and so what we're going to need
to do here is we're going to need to
work out the total moles of gas before
we need to then work out the total
volume of gas and so we've got the mass
of butane 11.6 so mass divided by M R is
moles of butane and the moles of butane
is therefore eleven point six divided by
58 which is the M R of butane which
gives us an answer of not 0.2 moles so
this is how many moles of butane we've
got then we need to look up at the
equation and the ratio is one to three
so we forgot to not point to moles of
butane we will have naught point six
moles of ethene because it needs to be
three times as big and so therefore the
total moles is 0.8 and so this now can
be plugged in for our value of N and so
to finish off we need to calculate not
0.8 times by 8.3 1 times by 8 - 3
divided by 200,000 which comes out at
0.027 for cubic meters and that's not
quite our final answer because they
asked for it in cubic centimeters so now
we need to multiply that by a million
and we've got 27,400
cubic centimeters and so that's the end
of this question we've got our final
answer there this would probably be a
four or five mark question at the very
least ok that's the end of this ideal
gas equation run through hope it was
useful I'll see you next time
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