Ideal Gases and the Ideal Gas Law

8/9/2019 Ideal Gases and the Ideal Gas Law

1/7

IDEAL GASES AND THE IDEAL GAS LAW

This p age looks a t the assumptions w hich are made in the KineticTheory a bout ideal gases, and takes a n introductory look a t theIdeal Gas Law: pV = nRT. This i s intended only a s a n introductionsuitable for chemistry s tudents a t about UK A level standard (for 16- 18 year olds), and so there is n o attempt to derive the ideal gaslaw using physics-style calculations.

Kinetic Theory assumptions a bout ideal gases

There is n o such thing a s a n ideal gas, of course, but many g asesbehave approximately a s i f they were ideal at ordinary w orkingtemperatures a nd pressures. Real gases a re dealt with in moredetail on another page.

The assumptions a re:

• Gases ar e made u p o f molecules w hich a re in constantrandom motion in straight lines.

• The molecules behave a s r igid spheres.

• Pressure is d ue t o collisions b etween the molecules a nd thewalls o f the container.

• All collisions, both between the molecules themselves, andbetween the molecules a nd the walls o f the container, are

perfectly elastic. (That means that there is no loss of kineticenergy during the collision.)

• The temperature of the gas i s p roportional to the averagekinetic e nergy o f the molecules.

And then two absolutely key assumptions, because these are the


2/7

two most important ways in which real gases d iffer from idealgases:

• There are no (or entirely n egligible) intermolecular forcesbetween the gas m olecules.

• The volume o ccupied by the molecules t hemselves i sentirely negligible relative to the volume of the container.

The Ideal Gas E quation

The ideal gas e quation is:

pV = nRT

On the w hole, this is an easy eq uation to remember and u se. Theproblems l ie almost entirely in the units. I am assuming below thatyou are working in strict SI units ( as y ou will be if you are doing aUK-based e xam, for example).

Exploring the va rious t erms

Pressure, p

Pressure is m easured in pascals, Pa - sometimes exp ressed a snewtons pe r square m etre, N m -2 . These m ean exact ly the samething.

Be careful if you are given pressures i n kPa (kilopascals). Forexample, 150 kP a is 15 0,000 P a. You must make that conversionbefore you use the ideal gas e quation.

Should you want to co nvert from other pressure m easurements:


3/7

• 1 atmosphere = 101,325 Pa

• 1 bar = 100 kPa = 1 00,000 Pa

Volume, V

This i s t he most likely p lace for you to go wrong when you use thisequation. That's because the SI unit of volume is the cubic m etre,m3 - not cm 3 or dm 3.

1 m 3 = 1000 dm 3 = 1 ,000,000 cm 3

So if you are inserting values of volume into the equation, you rsthave to convert them into cubic m etres.

You would have t o divide a vo lume in dm 3 by 1 000, or in cm 3 by amillion.

Similarly, if you are working out a volume using the equation,remember to covert the answer in c ubic m etres into dm 3 or cm 3 ifyou need to - this t ime by m ultiplying by a 1000 or a million.

If you get this w rong, you are going to end up with a silly a nswer,out by a factor of a thousand or a million. So it is usually fairlyobvious if you have d one so mething wrong, and you ca n ch eckback ag ain.

Number of moles, n

This i s e asy, of course - it is j ust a number. You already k now thatyou work it out by dividing the mass i n grams b y the mass of onemole in grams.

You will most often use the ideal gas e quation by rst making thesubstitution to give:


4/7

I don't recommend that you remember the ideal gas e quation in thisform, but you must be condent that you can convert it into thisform.

The g as constant, R

A value for R will be given you if you need it, or you can look i t up ina data source. The SI value for R is 8 .31441 J K -1 mol -1 .

Note: You may come across o ther values f or this w ith different units.A commonly used o ne in the p ast was 82 .053 cm 3 atm K -1 mol -1 . Theunits t ell you that the v olume would be in c ubic ce ntimetres a nd thepressure in atmospheres. Unfortunately t he units i n the SI versionaren't so obviously helpful.

The temperature, T

The temperature has t o be in kelvin. Don't forget to add 273 if youare given a temperature in degrees C elsius.

Using the ideal gas equation

Calculations u sing the ideal gas e quation are included in mycalculations b ook ( see the link a t the very b ottom of the page), and

I can't repeat them here. There are, however, a couple ofcalculations t hat I haven't done in the book which give a reasonableidea of how the ideal gas e quation works.

The m olar volume at stp

If you have done simple calculations f rom equations, you have


5/7


6/7

The molar volume of an ideal gas i s t herefore 22.4 dm 3 a t stp.

And, of course, you could redo this c alculation to nd the volume of1 mole of an ideal gas a t room temperature and pressure - or anyother temperature a nd pressure.

Finding the relative formula mass of a gas from its density

This i s a bout as t ricky a s i t gets u sing the ideal gas e quation.

The density o f ethane is 1 .264 g dm -3 a t 20°C and 1 atmosphere.Calculate the relative formula mass o f ethane.

The d ensity value m eans that 1 dm 3 of ethane weighs 1. 264 g .

Again, before we do a nything e lse, get the awkward units so rtedout.

A pressure o f 1 a tmosphere is 10 1325 Pa.

The volume o f 1 dm 3 has t o be converted to cubic m etres, by

dividing by 1000. We h ave a volume o f 0.001 m3

.

The temperature is 29 3 K.

Now put all the numbers i nto the form of the ideal gas e quationwhich lets yo u work with m asses, and rearrange i t to work out themass of 1 mole.


7/7

The mass o f 1 mole of anything is si mply the relative formula massin grams.

So the relative formula mass o f ethane is 3 0.4, to 3 sig gs.

Now, if you add up the relative formula mass o f ethane, C 2H6 us ingaccurate va lues o f relative a tomic m asses, you g et an a nswer of30.07 to 4 signicant gures. Which is d ifferent from our answer -so w hat's w rong?

There are two possibilities.

• The density va lue I have used may not be correct. I did thesum again using a slightly different value quoted at adifferent temperature from another source. This t ime I got ananswer of 30.3. So the density va lues m ay not be entirelyaccurate, but they are b oth giving much the same sort ofanswer.

• Ethane isn't an ideal gas. Well, of course it isn't an ideal gas- there's n o such thing! However, assuming that the densityvalues are close to correct, the error is within 1% of what youwould expect. So although ethane isn't exactly b ehaving likean ideal gas, it isn't far off.

If you need to know about real gases, now is a good time to readabout them.

Documents

Ideal Gases and the Ideal Gas Law