Understanding Combined Gas Law and Ideal Gas Law for Final Exam Preparation

Read Chapter 8 (Combined Gas Law and Ideal Gas Law)
Final Exam Tuesday 12 Dec 12:30 (This room)
 
The `Combined’ Gas Law (page 281, equation 8.2):
when gas moles (n) are constant
P
1
V
1
 
   = 
P
2
V
2
  T
1
  
   T
2
 
P in atm
V in liters (L)
T in K
 
httsp://www.youtube.com/watch?v=N5xft2fIqQU
Where the Combined Gas comes from
 
(see pages 285-290)
 
1) 
Boyle’s Law
:  hold n and T constant and let P and V vary
 
Boyle’s law in  words:
 
Boyle’s law 
in math-speak:
If 
P
 increases, 
V
 decreases
P = a/V
 
Boyle’s Law 
Observed
=> P
1
V
1
=P
2
V
2
Where the Combined Gas comes from (continued)
 
 
2) 
Charle’s Law
:  hold n and P constant and let T and V vary
 
Charle’s law in  words:
If 
T
 increases, 
V
 increases
 
Charle’s law 
in math-speak:
V =  bT
=> 
V
1
 =  
V
2
      T
1
      T
2
 
Charle’s Law 
Observed: can crush
Where the Combined Gas comes from (continued)
 
 
3) 
Gay-Lussac’s Law
:  hold n and V constant and let T and P vary
 
Gay-Lussac’s law in  words:
If 
T
 increases, 
P
 increases
 
Gay-Lussac’s law 
in math-speak:
P =  cT
 
egg     https://www.youtube.com/watch?v=xceBXe5YHj0
 
Gay-Lussac’s Law 
Observed: egg in a bottle
 
P vs T     https://www.youtube.com/watch?v=1pVVZGOBIVg
 
P
1      
=   
P
2
     T
1
 
  
 
T
2
H
o
w
 
B
o
y
l
e
,
 
G
a
y
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u
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s
a
c
 
a
n
d
 
C
h
a
r
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e
s
 
L
a
w
s
 
a
r
e
 
r
e
f
l
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c
t
e
d
 
i
n
 
t
h
e
C
o
m
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i
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e
d
 
G
a
s
 
L
a
w
 
(
w
h
e
n
 
n
 
i
s
 
c
o
n
s
t
a
n
t
)
P
1
V
1
 
    = 
 
   P
2 
V
2
   
T
1
  
      T
2
 
constant
n,P
 
P
1
V
1
 
    = 
 
   P
2 
V
2
   
T
1
  
      T
2
Charles’ Law
(P
1
=P
2
)
constant
n, T
Boyle’s Law
(T
1
=T
2
)
constant
n, V
Gay-Lussac’s Law
(V
1
=V
2
)
 
Combined Gas Law
constant
 n
 
P
1
V
1
 
    = 
 
   
P
2 
V
2
   
T
1
  
      T
2
 
P
1
V
1
    
    = 
 
   
P
2 
V
2
   
T
1
  
      T
2
 
C
o
n
d
i
t
i
o
n
s
 
N
a
m
e
 
o
f
G
a
s
 
L
a
w
 
G
a
s
 
L
a
w
E
q
u
a
t
i
o
n
In-class practice on board working
combined gas law problems
A
n
 
i
d
e
a
l
 
g
a
s
 
a
t
 
c
o
n
s
t
a
n
t
 
V
 
a
n
d
 
P
=
2
 
a
t
m
 
i
s
 
h
e
a
t
e
d
f
r
o
m
 
3
0
0
 
t
o
 
6
0
0
 
K
.
 
W
h
a
t
 
i
s
 
t
h
e
 
f
i
n
a
l
 
P
 
?
A.
1 atm
B.
2 atm
C.
3 atm
D.
4 atm
1.
A sample of oxygen gas is expanded from 20 to 50
       liters at constant temperature. The final pressure is 4
atm. What was the initial pressure ?
 
P
1
=10 atm
COMBINED GAS LAW PROBLEMS…BOARD WORK
A sample of ideal gas arrives at 300K when expanded
from 3 to 9 L at constant P. What was the original
temperature ?
A.
900 K
B.
100 K
C.
600 K
D.
150 K
 
  
2. A  child’s balloon originally occupies 5 liters at sea level 
        (P=1 atm)
 
and room temperature  (300 K) . It is released 
        
and is allowed to rise
   
to an altitude where the pressure 
 
     
is 0.25 atm and the temperature
   
is 150 K. 
        
What is the balloon’s new volume 
?
10 L
COMBINED GAS LAW PROBLEMS…BOARD WORK (CONT.)
An ideal gas in a fixed volume and an initial pressure of
10 atm and initial T of 177 C has a final pressure of 3.33
atm. What is the final T(K)
(K=C+273)
A.
150 K
B.
59 K
C.
450 K
D.
531 K
 
3.
The volume of a piston at fixed pressure changes as it is
 
     
 cooled from 500 
o
C to 250
o
C.  If the final volume is 6.76 L,
        
what is the initial volume ?
V
1
=10 L
COMBINED GAS LAW PROBLEMS…BOARD WORK (CONT.)
 
 
4.
 
    Autoclaves are essentially pressure cookers. At 1 atm,
       s
team has a temperature of 100
o 
C. Would you expect the
     
 pressure 
 
to double if the autoclave to attains a steam
      
temperature of 200
o
C ?
a
) NO…must convert C
 K…ratio is not 200/100
 
What pressure do you actually expect to reach at 200 
o
C?
473.15
 =1.73 atm
373.15
COMBINED GAS LAW PROBLEMS…BOARD WORK (CONT.)
Need more practice with Combined Gas Law ????
What happens if we
let n vary too ??
P  (piston head)
n
V
(varies
T
Heating
/
cooling
coils
piston
walls
Hypothetical Gas
Property 
testing
apparatus
Ideal Gas Law: letting
T,P,V, n and gas ID all
vary. P 277-8
G
A
S
GAS
VALVE
insulation
        0
o
  
 1                     1         
  
  
22.414
        0
o
  
 1       
  
  1          
 
 
22.414
        0
o
  
 1                     1         
  
  
22.414
        0
o
  
 1                     1          
 
 
22.414
Vary gas and fix three out of four gas variables…
Gas varied
H
2
(2)
He(4)
N
2
(28)
CO
2
(44)
SF
6 
(146)
      T(
O
C)   P(atm)    n(moles)
V(obs)
 
Variables fixed at constant values (`
STP
’)
 
STP =S
tandard
 T
emperature & 
P
ressure ( and n=1)
..see what happens
Gas ID (and size) not important
Ideal Gas derived: Why gas identity not important
        0
o
  
 1                     1         
  
  
22.414
What happens if we hold different sets of three variables
constant
 and  watch the 
fourth
 for a given gas ?
P(atm)
 
   V(L)       T(K)
 
n(moles)
2
  
400
  
1
1
   300
  
   1
  5
 
       2                    300
 5               5
3
 
16.43
 
24.65
 
0.406
 
 
101
 
PV/nT
Anything constant ??
0.08206
0.08206
0.08206
0.08206
Ideal Gas Law derived (cont.): origin of R
 
PV
 
 = 
0.08205746
nT
 
=
R
  (
atm L)
  
(
mol K )
PV   =n
R
T
 
Or…
 
The ideal gas law leads to :
 
molecular masses
 verification of stoichiometries
 
1.
 
An 11 gram sample of a gas occupies 2.0
liters at 2.0538 atm and 200 K. What is
the molecular mass  of the gas ?
(R=0.08206)
 
44 g/mol
2.
 
What volume is occupied by 0.09 g
of gas phase H
2
O (MW=18 g/mol) at
300 K and 0.123 atm ?
 
1.00 L
3.    A 1.5 liter can of gas reaches a
 
pressure of 45.45 atm at 500 K.
 
How many molecules of gas are in
 
the can ? (R=0.08206 atm L/K mol)
1.0*10
24
1 mol count =6.02*10
23
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Explore the concepts of Combined Gas Law, Boyle's Law, Charles's Law, Gay-Lussac's Law, and their reflection in the Ideal Gas Law. Learn how to solve problems using these laws, prepare for your final exam scheduled for Tuesday, December 12 at 12:30 in the specified room. Dive into in-class practice to enhance your understanding.


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  1. Read Chapter 8 (Combined Gas Law and Ideal Gas Law) Final Exam Tuesday 12 Dec 12:30 (This room)

  2. The `Combined Gas Law (page 281, equation 8.2): when gas moles (n) are constant P1V1 T1 = P2V2 T2 P in atm V in liters (L) T in K

  3. Where the Combined Gas comes from (see pages 285-290) 1) Boyle s Law: hold n and T constant and let P and V vary Boyle s law in words: If P increases, V decreases Boyle s law in math-speak: P = a/V => P1V1=P2V2 Boyle s Law Observed httsp://www.youtube.com/watch?v=N5xft2fIqQU

  4. Where the Combined Gas comes from (continued) 2) Charle s Law: hold n and P constant and let T and V vary Charle s law in words: If T increases, V increases Charle s law in math-speak: V = bT => V1 = V2 T1 T2 Charle s Law Observed: can crush

  5. Where the Combined Gas comes from (continued) 3) Gay-Lussac s Law: hold n and V constant and let T and P vary Gay-Lussac s law in words: If T increases, P increases Gay-Lussac s law in math-speak: P = cT P1 = P2 T1 T2 Gay-Lussac s Law Observed: egg in a bottle egg https://www.youtube.com/watch?v=xceBXe5YHj0 P vs T https://www.youtube.com/watch?v=1pVVZGOBIVg

  6. How Boyle, Gay How Boyle, Gay- -Lussac and Charles Laws are reflected in the Lussac and Charles Laws are reflected in the Combined Gas Law Combined Gas Law (when n is constant) (when n is constant) Gas Law Gas Law Equation Equation Conditions Conditions Name of Name of Gas Law Gas Law constant n P1V1 = T1 P2 V2 T2 Combined Gas Law constant n,P Charles Law (P1=P2) P1V1 = T1 P1V1 = T1 P2 V2 T2 P2 V2 T2 constant n, T Boyle s Law (T1=T2) Gay-Lussac s Law (V1=V2) P1V1 T1 = P2 V2 T2 constant n, V

  7. In-class practice on board working combined gas law problems

  8. An ideal gas at constant V and P=2 atm is heated An ideal gas at constant V and P=2 atm is heated from 300 to 600 K. What is the final P ? from 300 to 600 K. What is the final P ? A. 1 atm B. 2 atm C. 3 atm D. 4 atm 25% 25% 25% 25% 1 atm 2 atm 3 atm 4 atm

  9. COMBINED GAS LAW PROBLEMSBOARD WORK 1. A sample of oxygen gas is expanded from 20 to 50 liters at constant temperature. The final pressure is 4 atm. What was the initial pressure ? P1=10 atm

  10. A sample of ideal gas arrives at 300K when expanded from 3 to 9 L at constant P. What was the original temperature ? 25% 25% 25% 25% A. 900 K B. 100 K C. 600 K D. 150 K 900 K 100 K 600 K 150 K

  11. COMBINED GAS LAW PROBLEMSBOARD WORK (CONT.) 2. A child s balloon originally occupies 5 liters at sea level (P=1 atm) and room temperature (300 K) . It is released and is allowed to rise to an altitude where the pressure is 0.25 atm and the temperature is 150 K. What is the balloon s new volume ? 10 L

  12. An ideal gas in a fixed volume and an initial pressure of 10 atm and initial T of 177 C has a final pressure of 3.33 atm. What is the final T(K) (K=C+273) 25% 25% 25% 25% A. 150 K B. 59 K C. 450 K D. 531 K 59 K 150 K 450 K 531 K

  13. COMBINED GAS LAW PROBLEMSBOARD WORK (CONT.) 3. The volume of a piston at fixed pressure changes as it is cooled from 500 oC to 250oC. If the final volume is 6.76 L, what is the initial volume ? V1=10 L

  14. COMBINED GAS LAW PROBLEMSBOARD WORK (CONT.) 4. Autoclaves are essentially pressure cookers. At 1 atm, steam has a temperature of 100o C. Would you expect the pressure to double if the autoclave to attains a steam temperature of 200oC ? K ratio is not 200/100 a) NO must convert C What pressure do you actually expect to reach at 200 oC? 473.15 =1.73 atm 373.15

  15. Need more practice with Combined Gas Law ????

  16. What happens if we let n vary too ??

  17. Ideal Gas Law: letting T,P,V, n and gas ID all vary. P 277-8 P (piston head) Hypothetical Gas Property testing apparatus piston walls insulation T n V (varies G A S GAS VALVE Heating/cooling

  18. Ideal Gas derived: Why gas identity not important ..see what happens Vary gas and fix three out of four gas variables Gas ID (and size) not important Variables fixed at constant values (`STP ) Gas varied H2(2) He(4) T(OC) P(atm) n(moles) V(obs) 22.414 22.414 22.414 22.414 22.414 0o 1 1 0o 1 1 N2(28) CO2(44) SF6 (146) 0o 1 1 0o 1 1 0o 1 1 STP =Standard Temperature & Pressure ( and n=1)

  19. Ideal Gas Law derived (cont.): origin of R What happens if we hold different sets of three variables constant and watch the fourth for a given gas ? Anything constant ?? P(atm) V(L) T(K) n(moles) PV/nT 0.08206 2 400 1 16.43 1 24.65 0.08206 0.08206 0.08206 300 1 5 2 300 0.406 3 101 5 5

  20. PV = 0.08205746 nT =R (atm L) (mol K ) PV =nRT Or

  21. The ideal gas law leads to : molecular masses verification of stoichiometries

  22. 1. An 11 gram sample of a gas occupies 2.0 liters at 2.0538 atm and 200 K. What is the molecular mass of the gas ? (R=0.08206) 44 g/mol 2. What volume is occupied by 0.09 g of gas phase H2O (MW=18 g/mol) at 300 K and 0.123 atm ? 1.00 L

  23. 3. A 1.5 liter can of gas reaches a pressure of 45.45 atm at 500 K. How many molecules of gas are in the can ? (R=0.08206 atm L/K mol) 1 mol count =6.02*1023 1.0*1024

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