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Prepared by Lawrence Kok
IB Chemistry Kinetic Theory, Ideal Gas Equation and RMM determination of gases.
Kinetic Theory of Gases
Maxwell Boltzmann Distribution Curve- Molecular speed/energies at constant temp
- Molecule at low, most probable, root mean square speed- Higher temp –greater spread of energy to right
(total area under curve the same)
Straight line Curve lineVol gas – negligible IMF - (negligible)
Low temp
High temp
Kinetic Theory simulation
2
21 mvKE
Kinetic Theory of Gas 5 assumption- Continuous random motion, in straight lines - Perfect elastic collision- Ave kinetic energy directly proportional to abs temp ( E α T )- Vol gas is negligible - Intermolecular forces attraction doesn’t exist
Kinetic Theory of Gases
Distribution of molecular speed, Xe, Ar, Ne, He at same temp
At same temp•Xe, Ar, Ne and He have same Ave KE
•Mass He lowest – speed fastest •Mass Xe highest – speed slowest
He ArNe Xe
Why kinetic energy same for small and large particles?He – mass low ↓ - speed v high ↑ 2.21 vmKE
Xe – mass high ↑ - speed v low ↓ 2.21 vmKE
Kinetic energy SAME
Maxwell Boltzman Distribution Curve•Molecular speed/energy at constant Temp •Molecule at low, most probable and high speed•Higher temp –greater spread of energy to right• Area under curve proportional to number of molecules• Wide range of molecules with diff KE at particular temp• Y axis – fraction molecules having a given KE• X axis – kinetic energy/speed for molecule
2
21 mvKE
Pressure Law
Ideal Gas Equation
PV = nRT PV = constant
V = constant/P V ∝ 1/p
Charles’s Law
PV = nRT 4 diff variables → P, V, n, T
Avogadro’s Law
PV = nRT V = constant x
T V = constant T
V ∝ T
P1V1 = P2V2 V1 = V2
T1 T2
V1 = V2
n1 n2
R = gas constantUnit - 8.314 Jmol-1K-1
V = Vol gasUnit – m3
PV = nRT Fix 2 variables↓
change to diff gas Laws
Boyle’s Law
n, T fix n, P fix n, V fix
PV = nRT V = constant x n
V ∝ n
P, T fix
P = PressureUnit – Nm-2/Pa/kPa
n = number of moles
T = Abs Temp in K
VolPressure
TempVol Temp
Pressure Vol
n
PV = nRT P = constant
x T P ∝ T
P1 = P2
T1 T2
Ideal Gas Equation
PV = nRT (n, T fix)PV = constant
V = constant/P V ∝ 1/p
PV = nRT 4 diff variables → P, V, n, T
P1V1 = P2V2
R = gas constantUnit - 8.314 Jmol-1K-1
V = Vol gasUnit – m3
PV = nRT
Boyle’s Law
n, T fix
P = PressureUnit – Nm-2/Pa/kPa
n = number of moles
T = Abs Temp in K
Pressure
Vol
Boyle’s Law Lab Simulator
Video on Boyle’s Law
Ideal Gas Equation
Charles’s Law
PV = nRT 4 diff variables → P, V, n, T
PV = nRT V = constant x
T V = constant T
V ∝ T
V1 = V2
T1 T2
R = gas constantUnit - 8.314 Jmol-1K-1
V = Vol gasUnit – m3
PV = nRT
n, P fix
P = PressureUnit – Nm-2/Pa/kPa
n = number of moles
T = Abs Temp in K
Vol
Temp
Charles’s Law Lab Simulator
Video on Charles’s Law
Ideal Gas Equation
PV = nRT 4 diff variables → P, V, n, T
R = gas constantUnit - 8.314 Jmol-1K-1
V = Vol gasUnit – m3
PV = nRT
n, V fix
P = PressureUnit – Nm-2/Pa/kPa
n = number of moles
T = Abs Temp in K
Pressure
Temp
Pressure Law
PV = nRT (n, V fix) P = constant x T
P ∝ T
P1 = P2
T1 T2
Pressure Law Lab Simulator
Video on Pressure Law
Ideal Gas Equation
PV = nRT 4 diff variables → P, V, n, T
R = gas constantUnit - 8.314 Jmol-1K-1
V = Vol gasUnit – m3
PV = nRT
P, V fix
P = PressureUnit – Nm-2/Pa/kPa
n = number of moles
T = Abs Temp in K
Vol
n
Video on Pressure Law
Avogadro’s Law
PV = nRT V = constant x n
V ∝ n
V1 = V2
n1 n2
Avogadro Law Lab Simulator
Video on Avogadro Law
Avogadro’s Law
Gas Helium Nitrogen Oxygen
Mole/mol 1 1 1Mass/g 4.0 28.0 32.0
Press /atm 1 1 1 Temp/K 273 273 273
Vol/L 22.7L 22.7L 22.7LParticles 6.02 x
1023 6.02 x
1023 6.02 x
1023
22.7L
“ equal vol of gases at same temp/press contain equal numbers of molecules”
T – 0C (273.15 K)
Unit conversion
1 m3 = 103 dm3 = 106 cm3
1 dm3 = 1 litre
Standard Molar Volume
“molar vol of all gases same at given T and P” ↓ 22.7L
22.7L
Video on Avogadro’s Law
1 mole gas
• 1 mole of any gas at STP (Std Temp/Press)• occupy a vol of 22.7 dm3/22 700 cm3
P - 1 atm = 760 mmHg = 100 000 Pa (Nm-
2) = 100 kPa
22.7L
Unit conversion
1 atm ↔ 760 mmHg ↔ 100 000 Pa ↔ 100 kPa1m3 ↔ 103 dm3 ↔ 106 cm3
1 dm3 ↔ 1000 cm3 ↔ 1000 ml ↔ 1 litre x 103 x 103
cm3 dm3 m3
x 10-3 x 10-3
Pressure Law
Ideal Gas Equation
PV = nRT PV = constant
V = constant/P V ∝ 1/p
Charles’s Law Avogadro’s Law
PV = nRT V = constant x
T V = constant T
V ∝ T
P1V1 = P2V2V1 = V2
T1 T2
V1 = V2
n1 n2
PV = nRT
Boyle’s Lawn, T fix n, P fix n, V fix
PV = nRT V = constant x n
V ∝ n
P, T fix
PV = nRT P = constant
x T P ∝ T
P1 = P2
T1 T2
Combined Boyle + Charles + Avogadro
2
22
1
11
TVP
TVP
Combined Boyle + Charles
nRTPV
PnTV
Find R at molar vol
n = 1 molT = 273K
P = 100 000 PaV = 22.7 x 10-3 m3
R = ?R = 8.31 JK-1 mol-1
nTPVR
T = 273K
V = 22.7 x 10-3 m3
P = 100 000 Pa
Volatile Liquid (Propanone)
Volatile Gas (Butane)
Syringe MethodDirect WeighingDirect Weighing
Heated – convert to gas
RMM calculated - m, T, P, V, ρ are known
n = mass M
PRTM
PRT
VmM
RTMmPV
nRTPV
Density ρ = m (mass) V (vol)
PVmRTM
RTMmPV
nRTPV
Molar mass
RMM using Ideal Gas Eqn
PV = nRT
Direct Weighing
PV = nRT PV = mass x R x T MM = m x R x T PV= 0.52 x 8.314 x 373 101325 x 2.84 x 10-4
= 56.33
1. Cover top with aluminium foil.
2. Make a hole on aluminium foil
3. Record mass flask + foil
4. Pour 2 ml volatile liq to flask
5. Place flask in water, heat to boiling Temp and record press
6. Vapour fill flask when heat
7. Cool flask in ice bath –allow vapour to condense to liquid
8. Take mass flask + foil + liquid
Mass flask + foil 115.15 gMass flask + foil + condensed vapour
115.67 g
Mass condensed vapour
0.52 g
Pressure 101325 Pa
Temp of boiling water
100 0C 373K
Vol of flask 284 cm3 2.84 x 10-4 m3
Data Processing
Vol gas =Vol water in flask = Mass waterAssume density water = 1 g/ml
Click here for lab procedure
Video on RMM determination
RMM (LIQUID) using Ideal Gas Eqn
Procedure
Data Collection
Direct Weighing1. Fill flask with water and invert it .
2. Record press + temp of water
3. Mass of butane + lighter (ini)
4. Release gas into flask
6. Measure vol gas
7. Mass of butane + lighter (final)
Total Press (atm) = partial P(butane) + partial P(H2O) P butane = P(atm) – P(H2O) = (760 – 19.32) mmHg P butane = 743.911 mmHg → 99.17Pa
Dalton’s Law of Partial Press:Total press of mix of gas = sum of partial press of all
individual gas
5. Adjust water level in flask until the same as atm pressure
RMM butane RMM butane Collection gas
RMM (GAS) using Ideal Gas Eqn
Procedure Data CollectionMass butane +
lighter 87.63 g
Mass butane + lighter(final)
86.98 g
Mass butane 0.65 g
Pressure 99.17 Pa
Temp of boiling water
21.7 0C 294 K
Vol of flask 276 cm3 2.76 x 10-4 m3
Data Processing
PV = nRT PV = mass x R x T MM = m x R x T PV = 0.65 x 8.314 x 294 99.17 x 2.76 x 10-4
= 58.17
Syringe Method1. Set temp furnace to 98C.
2.Put 0.2ml liq into a syringe3. Record mass syringe + liq
5. Inject liq into syringe
6. Liq will vaporise , Record vol of heat vapour + air
4. Record vol of heated air.
Mass syringe + liqbef injection
15.39 g
Mass syringe + liqafter injection
15.27 g
Mass of vapour 0.12 gPressure 100792Pa
Temp of vapour 371 KVol heated air 7 cm3
Vol heated air + vapour
79 cm3
Vol of vapour 72 – 7 = 72 cm3
7.2 x 10-5 m3
Video on RMM determination
RMM (LIQUID) using Ideal Gas Eqn
Data CollectionProcedure
Data Processing
PV = nRT PV = mass x R x T MM = m x R x T PV = 0.12 x 8.314 x 371 100792 x 7.2 x 10-5
= 51.1
P = 101 kNm-2 = 101 x 103
Nm-2
Calculate RMM of gas Mass empty flask = 25.385 gMass flask fill gas = 26.017
gMass flask fill water =
231.985 gTemp = 32C, P = 101 kPa
Find molar mass gas by direct weighing, T-23C , P- 97.7 kPaMass empty flask = 183.257 gMass flask + gas = 187.942 gMass flask + water = 987.560 gMass gas = (187.942 – 183.257) = 4.685 gVol gas = Vol water = Mass water = (987.560 – 183.257) = 804.303 cm3
RMM determination
PV = nRTPV = mass x R x T MM = mass x R x T PV = 4.685 x 8.314 x 296 97700 x 804.303 x 10-6
= 146.7
Vol gas = 804.303 cm3 = 804.303 x 10-6 m3
P = 97.7 kPa = 97700 Pa
Density water = 1g/cm3
M = m x RT PV = 0.632 x 8.314 x 305 101 x 103 x 206 x 10-6 = 76.8
m gas = (26.017 – 25.385) = 0.632 g
vol gas = (231.985 – 25.385) = 206 x 10-6
m3
X contain C, H and O. 0.06234 g of X combusted,
0.1755 g of CO2 and 0.07187 g of H2O produced.
Find EF of X
Element C H O
Step 1 Mass/g 0.0479 0.00805 0.006384
RAM/RMM 12 1 16
Step 2 Number moles/mol
0.0479/1 2= 0.00393
0.00805/1=
0.00797
0.006384/16 = 0.000393
Step 3 Simplest ratio
0.003930.000393
= 10
0.007970.00039
3= 20
0.0003930.000393
= 1
Conservation of massMass C atom before = Mass C atom afterMass H atom before = Mass C atom after
CHO + O2 CO2 + H2O
Mol C atom in CO2= 0.1755 = 0.00393 mol 44
Mass C = mol x RAM C = 0.00393 x 12 = 0.0479 g
Mol H atom in H2O= 0.07187 = 0.0039 x 2 = 0.00797 mol 18
Mass H = mol x RAM H = 0.00797 x 1.01 = 0.00805 g
Mass of O = (Mass CHO – Mass C – Mass H) = 0.06234 – 0.0479 - 0.00805 = 0.006384 g
0.06234 g 0.1755 g 0.07187 g
Empirical formula – C10H20O1
Find EF for X with composition by mass. S 23.7 %, O 23.7 %, CI 52.6 %
Given, T- 70 C, P- 98 kNm-2 density - 4.67g/dm3 What molecular formula?
Empirical formula - SO2CI2
Density ρ = m (mass) V (vol)
Ideal Gas Equation
Element S O CI
Composition 23.7 23.7 52.6
Moles 23.732.1
= 0.738
23.716.0
= 1.48
52.635.5
= 1.48
Mole ratio 0.738 0.738
1
1.48 0.738
2
1.48 0.738
2PRTM
PRT
VmM
RTMmPV
nRTPV
Density = 4.67 gdm-3
= 4.67 x 10-3 gm-3
M = (4.67 x 10-3) x 8.31 x (273 +70) 9.8 x 104
M = 135.8135.8 = n [ 32 + (2 x 16)+(2 x 35.5) ]135.8 = n [ 135.8]n = 1MF = SO2CI2
P = 98 kN-2
= 9.8 x 104 Nm-2
3.376 g gas occupies 2.368 dm3 at T- 17.6C, P - 96.73 kPa.
Find molar massPV = nRTPV = mass x RT MM = mass x R x T PV = 3.376 x 8.314 x 290.6 96730 x 2.368 x 10-3 = 35.61
Vol = 2.368 dm3
= 2.368 x 10-3 m3
P – 96.73 kPa → 96730Pa
T – 290.6K
6.32 g gas occupy 2200 cm3, T- 100C , P -101 kPa.
Calculate RMM of gas
PV = nRT n = PV RT n = (101 x 103) (2200 x 10-6) 8.31 x ( 373 )
n = 7.17 x 10-2 mol
Vol = 2200 cm3
= 2200 x 10-6 m3 RMM = mass
nRMM = 6.32 7.17 x 10-2
= 88.15
Sodium azide, undergoes decomposition rxn to produce N2 used in air bag
2NaN3(s) → 2Na(s) + 3N2(g)Temp, mass and pressure was collected in table below
i. State number of sig figures for Temp, Mass, and Pressure
i. Temp – 4 sig fig Mass – 3 sig fig Pressure – 3 sig fig
Temp/C Mass NaN3/kg Pressure/atm
25.00 0.0650 1.08
ii. Find amt, mol of NaN3 present
ii.
iii. Find vol of N2, dm3 produced in these condition
RMM NaN3 – 65.02
molMol
RMMmassMol
00.102.600.65
PnRTV
nRTPV
n = 1.50 mol
P – 1.08 x 101000 Pa = 109080 Pa
2NaN3(s) → 2Na(s) + 3N2(g)
T – 25.00 + 273.15 = 298.15K
2 mol – 3 mol N2
1 mol – 1.5 mol N2
33 1.340341.0109080
15.29831.850.1
dmmV
V
PnRTV
Density gas is 2.6 gdm-3 , T- 25C , P – 101 kPaFind RMM of gas
PRTM
PRT
VmM
RTMmPV
nRTPV
Density ρ = m (mass) V (vol)
M = (2.6 x 103) x 8.31 x (298) 101 x 103
M = 63.7
Sodium azide, undergoes decomposition rxn to produce N2 used in air bag
2NaN3(s) → 2Na(s) + 3N2(g)Temp, mass and pressure was collected in table below
Temp/C Volume N2/L Pressure/atm
26.0 36 1.15
Find mass of NaN3 needed to produce 36L of N2
RMM NaN3 – 65.02
RTPVn
nRTPV
1.1 x 65.02 = 72 g NaN3
P – 1.15 x 101000 Pa = 116150 Pa
2NaN3(s) → 2Na(s) + 3N2(g)
T – 26.0 + 273.15 = 299.15K
3 mol N2 – 2 mol NaN3
1.7 mol N2 – 1.1 mol NaN3
moln
n
7.115.29931.81036116150 3
Vol = 36 dm3
= 36 x 10-3 m3
Convert mole NaN3 → Mass /g
Density gas is 1.25g dm-3 at T- 25C ,P- 101 kPa. Find RMM of gas
PRTM
PRT
VmM
RTMmPV
nRTPV
Density ρ = m (mass) V (vol)
M = (1.25 x 103) x 8.31 x (298) 101 x 103
M = 30.6
PVmRTM
RTMmPV
nRTPV
Copper carbonate, CuCO3, undergo decomposition to produce a gas.
Determine molar mass for gas X
CuCO3(s) → CuO(s) + X (g)Temp, mass, vol and pressure was collected in table below
Temp/K Vol gas/ cm3
Pressure/kPa
Mass gas/g
293 38.1 101.3 0.088 Find Molar mass for gas X
P – 101300 Pa
T – 293 K
Vol = 38.1 cm3
= 38.1 x 10-6 m3 5.55
101.3810130029331.8088.0
6
M
M
Potassium chlorate, KCIO3, undergo decomposition to produce a O2.
Find amt O2 collected and mass of KCIO3 decomposed
KCIO3
Temp/K Vol gas/ dm3
Pressure/kPa
299 0.250 101.32KCIO3(s) → 2KCI(s) + 3O2 (g)
RTPVn
nRTPV
2
3
.010.029931.8
10250.0101300
Omoln
n
Vol = 0.250 dm3
= 0.250 x 10-3 m3
P – 101300 Pa
Convert mole KCIO3 → Mass
2KCIO3 → 2KCI + 3O2
2 mol – 3 mol O2
0.0066 mol – 0.01 mol O2
0.0066 x 122.6 = 0.81 g KCIO3
RMM KCIO3 – 122.6
Gas occupy at (constant P)
V – 125 cm3 , T - 27 CFind its vol at 35 C
V1 = V2 (constant P) T1 T2
↓ 125 = V2
(27+273) (35 + 273)
↓V2 = 128 cm3
Find final vol, V2, at (constant T) compressed to P2 = 250
kPaV1 - 100 cm3 , P1 – 100 kPa V2 - ? P2 – 250 kPa
p1V1 = p2V2 (constant T)↓
100 x 100 = 250 x V2
↓V2 = 40 cm3
What vol (dm3) of 1 mol gas at
P - 101325 Pa, T - 25C pV = nRT V = nRT P
V = 1 x 8.31 x (273 + 25) 101325 = 0.0244m3 = 24.4dm3
Find vol (m3) of 1 mol of gas at
T - 298K, P - 101 325PaPV = nRT V = nRT P
V = 1 x 8.314 x 298 101325 = 0.0244 m3
Find vol (dm3) of 2.00g CO at
T → 20C, P → 6250Nm-2
PV = nRT V = nRT P
= 0.0714 x 8.314 x 293 6250
= 0.0278 m3 = 27.8dm3
IB Questions on Ideal Gas
T → 293K
3.0 dm3 of SO2 react with 2.0 dm3 of O2
2SO2(g) + O2(g) → 2SO3(g)Find vol of SO2 , dm3 at stp
PV = nRT (at constant P,T)V ∝ n
2SO2(g) + 1 O2(g) → 2SO3(g)
2 mol 1 mol 2 mol
2 vol 1 vol 2 vol
3dm3 2dm3 ?
↓SO2 is limiting
2dm3 SO2 → 2dm3 SO3
3dm3 SO2 → 3dm3 SO3
Boyle, Charles, Avogadro Law
no need to convert to SI units
cancel off at both sides2 variables involved
n → 2.00/28= 0.0714 mol
A syringe contains gas atV1 – 50 cm3 , P1 – 1 atm, T1 -
293KWhat vol , V2, if gas heat toV2 ? T2 - 373 K, P2 - 5 atm
Find vol of gas when its press and temp are
double ?
Volume no change
Which change in conditions would increase
vol by x4 of a fix mass of gas?
Pressure /kPa Temperature /KA. Doubled DoubledB. Halved HalvedC. Doubled HalvedD. Halved Doubled
Initial P1 → Final P2 = 1/2P1
Initial T1 → Final T2 = 2T1Initial V1 → Final V2 = ?
Vol increase by x4
Fix mass ideal gas has a V1 = 800cm3 , P1, T1
Find vol, V2 when P and T doubled.P2 = 2P1
T2 = 2T1Initial P1 → Final P2 = 2P1
Initial T1 → Final T2 = 2T1
Initial V1 800 → Final V2 = ?
A. 200 cm3
B. 800 cm3
C. 1600 cm3
D. 3200 cm3
32
2
2
22
1
11
13373
5293
501
cmV
VTVP
TVP
12
1
21
1
11
2
22
1
11
22
VVTVP
TVP
TVP
TVP
12
1
21
1
11
2
22
1
11
422
VVTVP
TVP
TVP
TVP
3
2
1
21
1
1
2
22
1
11
800
22800
cmV
TVP
TP
TVP
TVP
Fix mass ideal gas has a V1 = 1dm3, P1, T1
Find V2 ,when T doubled (x2), P tripled (x3)
V2 = ?, P2 = 3P1, T2 = 2T1Initial P1 → Final P2 = 3P1
Initial T1 → Final T2 = 2T1
Initial V1 = 1 dm3 → Final V2 =?
Fix mass ideal gas has a V1 = 2 dm3 , P1, T1
Find V2 ,when T double (x2), P quadruple (x4)
V2 = ?, P2 = 4P1, T2 = 2T1Initial P1 → Final P2 = 4P1
Initial T1 → Final T2 = 2T1
Initial V1 2dm3 → Final V2 = ?
Fix mass ideal gas has a P1 = 40 kPa , V1, T1
Find P2 of gas when V and T doubled.P2 = ?, V2 = 2V1, T2 = 2T1
Initial V1 → Final V2 = 2V1
Initial T1 → Final T2 = 2T1
Initial P1 =40 → Final P2 = ?
3/22
31
2
1
21
1
1
2
22
1
11
VTVP
TP
TVP
TVP
32
1
21
1
1
2
22
1
11
1
242
dmV
TVP
TP
TVP
TVP
402
240
2
1
12
1
1
2
22
1
11
PTVP
TVTVP
TVP
What conditions would one mole
CH4, occupy the smallest vol?A. 273 K and 1.01×105 PaB. 273 K and 2.02×105 PaC. 546 K and 1.01×105 PaD. 546 K and 2.02×105 Pa
PV = nRT V = nRT P = low T, high P
Find total vol and composition of remaining gas
10cm3 ethyne react with 50cm3 hydrogen C2H2(g) + 2H2 (g) → C2H6 (g) at stp
PV = nRT (at constant P,T) V ∝ nC2H2 (g) + 2H2(g) → C2H6 (g)
1 mol 2 mol 1 mol1 vol 2 vol 1 vol10cm3 20cm3 10cm3
C2H6 = 10cm3 producedH2 = 50-20 =30 cm3 remain (excess)
Which conditions does a fix mass
of an ideal gas have greatest vol?
Temperature PressureA. low lowB. low highC. high highD. high low
PV = nRT V = nRT P = high T, low P
Find vol of 6 g of chlorine at 27oC and 101 kPa.
pV = nRTT = 300K,n = 6/71 = 0.08451 mol CI2, Mr(Cl2)= 71p = 101000 Pa.
3002087.0101000
30031.808451.0
mV
V
PnRTV
5 litre container contain 0.5 kg butane gas (C4H10).
Cal press at 25oC.Mr(C4H10)= 58, 0.5kg = 500gmoles n = 500/58 = 8.621, T = 298K5 litre = 5 dm3 = 5 x 10-3 m3
kPaP
P
VnRTP
4272105
29831.8621.83
P = 202600 Pan = 0.050 mol T = 400KV = ? m3
What vol need to store 0.050 moles
of helium, P= 202.6 kPa , T= 400 K V = 7.5 x 10-3 m3
molar mass (H2) =2.016 g mol-1 n = 20.16 ÷ 2.016 = 10 mol T = 293 K
What press exerted by 20.16 g hydrogen
in 7.5 L cylinder at 20oC?
300082.0202600
40031.8050.0
mV
V
PnRTV
nRTPV
kPaP
P
VnRTP
nRTPV
3248105.7
29331.8103
50 L fill with argon to a press of 101 kPa at 30oC.
How many moles of argon ?P = 101000PaV = 50 x 10-3 m3
n = ? mol T = 303 K
moln
n
RTPVn
nRTPV
230331.8
1050101000 3
What temp does a 250 mL cylinder containing
0.40 g helium need to be cool to a press of 253.25 kPa?P = 253250 Pa
V = 0.250 x 10-3 m3
mass = 0.40 g , molar mass (He) = 4.003 n = 0.40 ÷ 4.003 = 0.1 mol
KT
T
nRPVT
nRTPV
15.7631.81.0
10250.0253250 3
Acknowledgements
Thanks to source of pictures and video used in this presentation
Thanks to Creative Commons for excellent contribution on licenseshttp://creativecommons.org/licenses/http://kwokthechemteacher.blogspot.hk/2011/07/ideal-gas-assumptions.html
Prepared by Lawrence Kok
Check out more video tutorials from my site and hope you enjoy this tutorialhttp://lawrencekok.blogspot.com