ib chemistry on deviation from ideal gas and ideal gas equation
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IB Chemistry on Deviation from Ideal Gas and Ideal Gas Equation.TRANSCRIPT
Kinetic Theory of Gases
Kinetic Theory of Gases5 assumptions • Continuous random motion, in straight lines • Perfectly elastic collision• Average kinetic energy directly proportional to absolute temp ( E α T )• Gas consists of tiny negligible volume• Intermolecular forces attraction does not exist bet gases
Maxwell Boltzman Distribution Curve• Molecular speed/energies at constant temperature • Molecule at low, most probable, root mean square speed• Higher temperature –greater spread of energies to the right
(total area under curve the same)
Straight line Curve line
Volume gas – small (negligible)
Intermolecular forces - (negligible)
Low temp
High temp
Kinetic Theory simulation
Kinetic Theory of Gases
Maxwell Boltzman Distribution Curve• Molecular speed/energies at constant Temp • Molecule at low, most probable and high speed• Higher temperature –greater spread of energies to the right
(total area under curve the same) • Area under curve proportional to number of molecules• Wide range of molecules with diff kinetic energy at particular temp• Y axis – fraction molecules having a given kinetic energy• X axis – kinetic energy/speed for molecule
Distribution of molecular speed, Xe, Ar, Ne, He at same temp At same temperature• Xe, Ar, Ne and He have same average kinetic energy • 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.
2
1vmKE
Xe – mass high ↑ - speed v low ↓ 2.
2
1vmKE
Kinetic energy SAME
Real Gas vs Ideal Gas
Deviation from ideal increase as
Ideal Gas• No volume• No intermolecular forces attraction
Real Gas• Volume• Intermolecular forces attraction
• Molecule close together • Forces of attraction exist
• Kinetic energy low• Molecule closer together – condense• Intermolecular forces stronger
Deviation of Real gas from Ideal behaviour
No forces attractionForces attraction
1RT
PVconstant1
RT
PV1
RT
PVor
Pressure increase ↑
Pressure exerton wall less ↓
1RT
PV
Temp decrease ↓
Temp ↓
At Low temperature• Molecules close together – condense• Presence of intermolecular attraction• Molecule will exert lower pressure at wall
Positive deviation• Volume of molecules
1RT
PV
Negative deviation• Presence of intermolecular attraction
Deviation of Real gas from Ideal behaviour
At High Pressure• Molecule close together • Forces of attraction exist
At Very High Pressure• Volume gas is significant
Vol available for molecule to move abt is less than observed volbecause molecule occupy space. As pressure increase, free space formolecule to move become smaller.
Volume gas
significant at
high pressure
1RT
PV
Vol used for
calculation
Actual vol is less
for gas to move
1RT
PVVol used in calculation is vol of container (too large)
Click here for notes from chemguide
At low temp- greater deviation
Boiling point CO2 = - 57oCCH4 = - 1640CN2 = - 195oCH2 = 252oC
Deviation greatest forCO2 > CH4 > N2 > H2
Ideal gas equation
At Low pressure + High Temp
Real gas/Van Der Waals equation
Ideal Gas vs Real Gas
Ideal gas Real gas
Ideal gas equation
At High pressure + Low Temp
Real gas/Van Der Waals equation
Correction for pressure due to
intermolecular forces bet molecules
Correction for volume due to
vol occupied by gas molecule
Deviation of real gases
Temperature decrease ↓
Higher boiling point
Easier to condense
Intermolecular forces increase
Negative deviation
Ideal Gas Equation
PV = nRT (n, T fix)PV = constant
V = constant/P
V ∝ 1/p
Charles’s Law
PV = nRT
4 different variables → P, V, n, T
Avogadro’s Law
T = Absolute Temperature in K
PV = nRT (n ,P fix)V = constant x T V = constantT
V ∝ T
P1V1 = P2V2V1 = V2
T1 T2
PV = nRT (n, V fix)P = constant x T
P ∝ T
V1 = V2
n1 n2
R = universal gas constantUnit - 8.314Jmol-1K-1 or 0.0821 atm L mol-1 K-1
n = number of moles
V = Volume gasUnit – dm3 or m3
P = PressureUnit – Nm-2/Pa/kPa/atm
PV = nRT Fix 2 variables → change to different gas Laws
Boyle’s Law Pressure Law
P1 = P2
T1 T2
PV = nRT (P, T fix)V = constant x n
V ∝ n
PV = nRT (n, T fix)PV = constant
V = constant/P
V ∝ 1/p
Charles’s Law Avogadro’s Law
PV = nRT (n ,P fix)V = constant x T V = constant
T V ∝ T
P1V1 = P2V2V1 = V2
T1 T2
PV = nRT (n, V fix)P = constant x T
P ∝ T
V1 = V2
n1 n2
PV = nRT Fix 2 variables → change to different gas Laws
Pressure Law
P1 = P2
T1 T2
PV = nRT (P, T fix)V = constant x n
V ∝ n
Boyle’s LawPV = nRT (n, T fix)PV = constant
V = constantP
• V inversely proportional to P
V ∝ 1P
P1V1 = P2V2
Boyle’s Law Lab Simulator
Video on Boyle’s Law
Boyle’s Law
PV = nRT (n, T fix)PV = constant
V = constant/P
V ∝ 1/p
Charles’s Law Avogadro’s Law
PV = nRT (n ,P fix)V = constant x T V = constant
T V ∝ T
P1V1 = P2V2V1 = V2
T1 T2
PV = nRT (n, V fix)P = constant x T
P ∝ T
V1 = V2
n1 n2
PV = nRT Fix 2 variables → change to different gas Laws
Pressure Law
P1 = P2
T1 T2
PV = nRT (P, T fix)V = constant x n
V∝ n
Charles’s Law Lab Simulator
Video on Charles’s Law
Boyle’s Law
Charles’s LawPV = nRT (n, P fix)
V = constant x T• V directly proportional to T
V ∝ TV1 = V2
T1 T2
Temp increase ↑ → kinetic energy increase ↑ → collision bet particles with container increase ↑ → volume increase ↑
PV = nRT (n, T fix)PV = constant
V = constant/P
V ∝ 1/p
Charles’s Law Avogadro’s Law
PV = nRT (n ,P fix)V = constant x T V = constant
T V ∝ T
P1V1 = P2V2V1 = V2
T1 T2
PV = nRT (n, V fix)P = constant x T
P ∝ T
V1 = V2
n1 n2
PV = nRT Fix 2 variables → change to different gas Laws
Pressure Law
P1 = P2
T1 T2
PV = nRT (P, T fix)V = constant x n
V∝ n
Pressure Law Lab Simulator
Video on Pressure Law
Boyle’s Law
Pressure LawPV = nRT (n, V fix)
P = constant x TP directly proportional to T
P ∝ TP1 = P2
T1 T2
Temp increase ↑ → kinetic energy increase ↑ → collision bet particles with container increase ↑ → pressure increase ↑
PV = nRT (n, T fix)PV = constant
V = constant/P
V ∝ 1/p
Charles’s Law Avogadro’s Law
PV = nRT (n ,P fix)V = constant x T V = constant
T V ∝ T
P1V1 = P2V2V1 = V2
T1 T2
PV = nRT (n, V fix)P = constant x T
P ∝ T
V1 = V2
n1 n2
PV = nRT Fix 2 variables → change to different gas Laws
Pressure Law
P1 = P2
T1 T2
PV = nRT (P, T fix)V = constant x n
V ∝ n
Avogadro Law Lab Simulator
Video on Avogadro Law
Boyle’s Law
Avogadro LawPV = nRT (P, T fix)
V = constant x nV directly proportional to n
V ∝ nV1 = V2
n1 n2
• 1 mole of any gas at fix STP (Std Temp/Pressure)occupies a volume of 22.7dm3/22700cm3
Avogadro’s Law
http://leifchemistry.blogspot.kr/2011/01/molar-volume-at-stp.html
Gas Helium Nitrogen Oxygen
Mole/mol 1 1 1
Mass/g 4.0 28.0 32.0
Pressure/atm 1 1 1
Temp/K 273 273 273
Vol/L 22.7L 22.7L 22.7L
Particles 6.02 x 1023 6.02 x 1023 6.02 x 1023
22.7L
“ equal vol of gases at same temperature/pressure
contain equal numbers of molecules”
T – 0C (273.15K)Unit conversion
1 atm = 760 mmHg/Torr = 101 325Pa(Nm-2) =101.325kPa1m3 = 103 dm3 = 106cm3
1dm3 = 1 litre
P - 1 atm = 760 mmHg = 101 325Pa (Nm-2) = 101.325kPa
Standard Molar VolumeStandard Temp/Pressure
“molar volume of all gases the same at given T and P”
↓
22.7L
22.7L 22.7L
Video on Avogadro’s Law
1 mole gas
PV = nRT (n, T fix)PV = constant
V = constant/P
V ∝ 1/p
Charles’s Law Avogadro’s Law
PV = nRT (n ,P fix)V = constant x T V = constant
T V ∝ T
PV = nRT (n, V fix)P = constant x T
P ∝ T
PV = nRT Fix 2 variables → change different gas Laws
Pressure Law
PV = nRT (P, T fix)V = constant x n
V∝ n
Boyle’s Law
Combined Gas Law
Boyle’s Law Charles’s Law
V ∝ 1P
V ∝ T
CombinedBoyle + Charles Law
PV = constantT
PV = R T
Gas constant, R
V ∝ TP
P1V 1 = P2V2
T1 T23 different variables
Charles’s Law Boyle’s Law Pressure Law Avogadro’s Law
Combined Boyle Law + Charles Law Combined Gas Law
2 different variables
2 different variables 3 different variables
PV = nRT (n, T fix)PV = constant
V = constant/P
V ∝ 1/p
Charles’s Law Avogadro’s Law
PV = nRT (n ,P fix)V = constant x T V = constant
T V ∝ T
PV = nRT (n, V fix)P = constant x T
P ∝ T
PV = nRT Fix 2 variables → change different gas Laws
Pressure Law
PV = nRT (P, T fix)V = constant x n
V∝ n
Boyle’s Law
Boyle’s Law Charles’s Law
V ∝ 1P
V ∝ n
Boyle + Charles + Avogadro Law
Proportionality constantGas constant, R
V ∝ n TP
4 different variables
Charles’s Law Boyle’s Law Pressure Law Avogadro’s Law
Boyle + Charles + Avogadro Law Ideal Gas Equation
2 different variables
PV = nRT
Ideal Gas Equation
Avogadro’s Law
V ∝ T
PV = n R T
Charles’s Law Pressure Law
PV = nRT
Avogadro’s LawBoyle’s Law
V ∝ 1P
V ∝ T P ∝ TV ∝ n
When n = 1 mol – Gas constant, R is 8.31 JK-1mol-1or NmK-1
For 1 mole – PV = RTFor n mole – PV = nRTP1V 1 = P2V2
T1 T2
PV = nRT
Ideal Gas EquationCombined Gas Law
+
+
2 different variables
3 different variables
4 different variables
PV = nRT
R = P Vn T
n 1 mol
Temp/T oC → 273K
Pressure/P 101 325 Pa(Nm-2)
Volume/V22.7dm3 → 22.7 x 10-3 m3
R = 101325 x 22.7 x 10-3
1 x 273
R = 8.31 JK-1mol-1or NmK-1
Find R (Universal Gas Constant)
at molar volume
n = 1 mol
T = 273K
P = 101325Pa/Nm-2
V = 22.7 x 10-3m3
R = ?
Value of gas constant, R (Universal Gas Constant) at molar volume
DifferentUnits Used
Volume/V22.7dm3 → 22.7 x 10-3 m3
PV = nRTPressure/P
101 325 Pa(Nm-2)
Temp/T oC → 273K
n 1 mol R = P V
n T
R = 101325 x 22.7 x 10-3
1 x 273R = 8.31 JK-1mol-1 or NmK-1
PV = nRT
R = P Vn T
n 1 mol
Temp/T 0C → 273K
Volume/V22.7L
Pressure/P 1 atm
R = 1 x 22.7 1 x 273
R = 0.0821 atmLmol-1K-1
1 atm ↔ 760 mmHg/Torr ↔ 101325Pa/Nm-2↔ 101.325kPa1m3 ↔ 103 dm3 ↔ 106cm3
1dm3 ↔ 1000cm3 ↔ 1000ml ↔ 1 litrex 103 x 103
cm3 dm3 m3
x 10-3 x 10-3
Unit conversion
DifferentUnits Used
A gas occupy at (constant P)• V - 125cm3
• T - 27CCalculate its volume at 35C
Answer: (Charles Law)V1 = V2 (constant P)T1 T2
125 = V2
(27+273) (35 + 273)V2 = 128cm3
Find final vol, V2, gas at (constant T) compressed to P2 = 250kPaV1 - 100cm3
P1 - 100kPa V2 - ?P2 – 250kPa
Answer: (Boyle Law)p1V1 = p2V2 (constant T)100 x 100 = 250 x V2
V2 = 40cm3
What volume (dm3) of 1 mol gas at P - 101325Nm-2
T - 25C
Answer: (Ideal gas eqn)pV = nRT
V = nRTP
V = 1 x 8.31 x (273 + 25)101325
= 0.0244m3 = 24.4dm3
Find volume (m3) of 1 mol of gas at• T - 298K• P - 101 325Pa
Answer: (Ideal gas eqn)PV = nRT
V = nRTP
V = 1 x 8.314 x 298101325
= 0.0244m3
Find volume (dm3) of 2.00g CO at• T → 20C• P → 6250Nm-2
Answer: (Ideal Gas Eqn)PV = nRT
V = nRTP
= 0.0714 x 8.314 x 2936250
=0.0278m3 = 27.8dm3
IB Questions on Ideal Gas
T → (20 + 273) = 293Kn → 2.00/28 = 0.0714 mol
Using PV = nRT (Ideal gas eqn)• Need to convert to SI units• 4 variables involved
3.0 dm3 of SO2 reacted with 2.0 dm3 of O2
2SO2(g) + O2(g) → 2SO3(g)Find volume of SO2 in dm3 at stp
Answer: (Avogadro Law)PV = nRT (at constant P,T)V ∝ n2SO2(g) + 1O2(g) → 2SO3(g)2 mol 1 mol 2 mol2 vol 1 vol 2 vol3dm3 2dm3 ?
SO2 is limiting2dm3 SO2 → 2dm3 SO3
3dm3 SO2 → 3dm3 SO3
Boyle, Charles, Avogadro Law
• no need to convert to SI units
• cancel off at both sides
• 2 variables involved
1 2 3
4 5 6
IB Questions on Ideal Gas
Combined gas Law
• no need to convert to SI units
• cancel off at both sides
• 3 variables involved
7 8 3
9 10
A syringe contains gas atV1 - 50cm3
P1 – 1atmT1 - 20C → 293KWhat volume , V2, if gas heated toV2 - ?T2 - 100C → 373KP2 - 5 atm
Answer: (Combine Gas Law)P1V1 = P2V2
T1 T2
1 x 50 = 5 x V2293 373V2 = 13cm3
Find volume fixed mass gas when its pressure and temp are double ?
Answer: (Combine Gas Law)Initial P1 → Final P2 = 2P1
Initial T1 → Final T2 = 2T1
Initial V1 → Final V2 = ?
P1V1 = P2V2T1 T2
P1V1 = 2P1V2T1 2T1
V2 = V1
Volume no change
P and T double
Which change in conditions would increase the volume by x4 of a fix mass of gas?
Pressure /kPa Temperature /K
A. Doubled Doubled
B. Halved Halved
C. Doubled Halved
D. Halved Doubled
Answer: (Combine Gas Law)Initial P1 → Final P2 = 1/2P1
Initial T1 → Final T2 = 2T1
Initial V1 → Final V2 = ?
P1V1 = P2V2T1 T2
P1V1 = P1V2T1 2 x 2T1
V2 = 4V1
Volume increase by x4
Fix mass ideal gas has a V1 = 800cm3 , P1, T1
Find vol, V2 when P and T doubled.V2 = ?P2 = 2P1
T2 = 2T1
Answer: (Combine Gas Law)Initial P1 → Final P2 = 2P1
Initial T1 → Final T2 = 2T1
Initial V1 800 → Final V2 = ?P1V1 = P2V2T1 T2
P1 x 800 = 2P1V2T1 2T1
V2 = 800
A. 200 cm3
B. 800 cm3
C. 1600 cm3
D. 3200 cm3
P halvedT double
A. 1 dm3
B. 2 dm3
C. 3 dm3
D. 4 dm3
IB Questions on Ideal Gas
Fix mass ideal gas has a V1 = 1dm3
P1
T1
Find V2 ,when T doubled (x2), P tripled (x3)V2 = ?P2 = 3P1
T2 = 2T1
Answer: (Combine Gas Law)Initial P1 → Final P2 = 3P1
Initial T1 → Final T2 = 2T1
Initial V1 = 1dm3 → Final V2 =?P1V1 = P2V2T1 T2
P1 x 1 = 3P1 x V2T1 2T1
V2 = 2/3
A. 1/3
B. 2/3
C. 3/2
D. 1/6
11 Fix mass ideal gas has a V1 = 2dm3
P1
T1
Find V2 ,when T double (x2), P quadruple (x4)V2 = ?P2 = 4P1
T2 = 2T1
Answer: (Combine Gas Law)Initial P1 → Final P2 = 4P1
Initial T1 → Final T2 = 2T1
Initial V1 2dm3 → Final V2 = ?P1V1 = P2V2T1 T2
P1 x 2 = 4P1V2T1 2T1
V2 = 1 dm3
12
Fix mass ideal gas has a P1 = 40kPa V1
T1
Find P2 of gas when V and T doubled.P2 = ?V2 = 2V1
T2 = 2T1
Answer: (Combine Gas Law)Initial V1 → Final V2 = 2V1
Initial T1 → Final T2 = 2T1
Initial P1 =40 → Final P2 = ?P1V1 = P2V2T1 T2
40 x V1 = P2 x 2V1T1 2T1
P2 = 40
A. 10kPa
B. 20kPa
C. 40kPa
D. 480kPa
13
Combined gas Law
• no need to convert to SI units
• cancel off at both sides
• 3 variables involved
IB Questions on Ideal Gas
Calculate total volume and composition of remaining gas10cm3 ethyne react with 50cm3 hydrogen to produce ethaneC2H2(g) + 2H2(g) → C2H6(g) at stp
Answer: (Avogadro Law)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 = 30cm3 remains (excess)
Which conditions does a fix mass of an ideal gas have greatest volume?
Temperature Pressure
A. low low
B. low high
C. high high
D. high low
Answer: (Ideal Gas Eqn)PV = nRT
V = nRTP
= high T, low P
What conditions would one mole of, CH4, occupy the smallest volume?
Answer: (Ideal Gas Eqn)PV = nRT
V = nRTP
= low T, high P
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
14 15
16
IB Questions on Ideal Gas
AnswerpV = nRTT = 273 + 27 = 300K,n = 6/71 = 0.08451 mol chlorine, Mr(Cl2) = 2 x 35.5 = 71p = 101 x 1000 = 101000 Pa.V = nRT/pV = 0.08451 x 8.314 x 300/101000 = 0.002087 m3
AnswerMr(C4H10) = (4 x 12) + 10 = 58, 0.5kg = 500gmoles n = 500/58 = 8.621, T = 273 + 25 = 298KPV = nRT, P = nRT/V, 5 litre = 5 dm3 = 5 x 10-3 m3
P = 8.621 x 8.314 x 298/(5 x 10-3)P = 4271830 Pa = 4272 kPa
Find vol of 6g of chlorine at 27oC and 101 kPa. 5 litre container contain 0.5kg butane gas (C4H10). Cal pressure at 25oC.
17 18
AnswerPV = nRTP = 202.6 kPa - 202600 Pan = 0.050 molT = 400KV = ? LR = 8.314 J K-1 mol-1
202600 x V = 0.050 x 8.314 x 400202600 x V = 166.28V = 166.28 ÷ 202600V = 0.00082 m3
What vol needed to store 0.050 moles of helium at 202.6 kPa and 400 K?
19
AnswerPV = nRTV = 7.5 L → 7.5 x 10-3 m3
molar mass (H2) = 2 x 1.008 = 2.016 g mol-1
n = 20.16 ÷ 2.016 = 10 molT = 20 + 273 = 293 KPV = nRTP x 7.5 x 10-3 = 10 x 8.314 x 293P x 7.5 x 10-3 = 24360.02P = 3248 kPa
What pressure exerted by 20.16 g hydrogen in a 7.5L cylinder at 20oC?
20
AnswerP = 101 kPa → 101000PaV = 50 L → 50 x 10-3m3
n = ? molT = 30 + 273 = 303 KPV = nRT101000 x 50 x 10-3 = n x 8.314 x 3035050 = n x 2519.142n = 5050 ÷ 2519.142 = 2.00 mol
50 L cylinder fill with argon to a pressure of 101 kPa at 30oC. How many moles of argon ?
IB Questions on Ideal Gas
21
AnswerP = 253.25 kPa → 253250PaV = 250 mL → 250 ÷ 1000 = 0.250 L → 0.250 x 10-3 m3
Mass = 0.40 gMolar mass (He) = 4.003 gmol-1
n = 0.40 ÷ 4.003 = 0.10 molT = ? KPV = nRT253250 x 0.250 x 10-3 = 0.10 x 8.314 x T63.3125 = 0.8314 x TT = 63.3125 ÷ 0.8314 = 76.15 K
To what temperature does a 250 mL cylinder containing 0.40 g helium need to be cooled to a pressure of 253.25 kPa?
22
Ideal Gas Law Lab simulation
Ideal Gas Law Videos