Charles Law

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Charles Law
Mr. Shields Regents Chemistry U05 L06
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Charles Law
V/T k (constant P and n)

• Jacques Charles (1746 1823)
• Charles Law (1787)
• Volume vs. Temp relationship of a gas

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Charles Law
In 1787 Charles law was published This law
looked at the variables of Volume (V)
and Temperature (T) V/T k V, T
variables P, n Constants
Charless law states that the volume of a gas
at constant p,n varies DIRECTLY with
its absolute Temperature (in Kelvin!)
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Developing Charles Law
Since velocity will increases with increasing
temp then The number of collisions with the
containers wall per unit time must be
increasing And increasing the rate of collisions
with the containers Walls increases
pressure BUT Charles law assumes constant P
with increasing temp. So how does P stay
constant if T increases ?
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Developing Charles Law
Remember Boyles law? Boyles law says we can
reduce the pressure if we Increase the
volume PVk As V P In other
words, if there is a driving force that
increases pressure we can decrease the pressure
by increasing the container volume.
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Developing Charles Law
So if T increases we can hold pressure constant
if we Increase volume at the same time T
increases This is just what Charles Law
says V/T k A direct relationship (p,n
const) Or in a more useful form for
calculations V1/T1 V2/T2 (why is this
true?) So what does the relationship V/T look
like?
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Charles Law
Below is a data table relating temperature to
volume
Trial T (C) V (mL)
1 -124.00 50.00
2 -100.00 58.05
3 -75.00 66.44
4 0.00 91.61
5 25.00 100.00
6 30.00 101.68
7 45.00 106.71
8 100.00 125.17
9 225.00 167.11
10 323.00 200.00
Note that all V/T equals the same k (try trial
2,4,8) A graph of this data looks like this
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Why Kelvin for Calculations?
T and V are related such that for each doubling
(or Halving) of the temperature (in Kelvin)
Volume Doubles (or halves) i.e a direct
relationship NOTE WELL This relationship is
only true for Deg. Kelvin NOT degrees Celsius.
But Why? What would happen if the temp were 0
deg. Celsius Division by zero is undefined
2x
1x
100k 200k
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Why Kelvin?
And What would happen if Temperature was
NEAGATIVE? Predicted Volume would be negative
Lets try it If V11 L and T1 25 deg C and T2
equals 50 deg C what does V2 equal? V1/T1V2/T2
1/25 V2/-50 Then V2 -2 L (????)
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Decreasing Temperatures

• What happens when a gas drops to VERY LOW TEMP
• (assuming the gas does not condense to a liquid)?
• Charles law would predict the following
• The direct relationship of V/T remains a straight
  line
• (2) Extending the line to zero volume shows there
• is a lower limit to temperature (i.e. Avg
  KE)
• The lower limit for temperature is 0 deg. Kelvin.
  
• This is called ABSOLUTE ZERO

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There is a direct relationship between T(kelvin),
V and E
There is a Direct Relationship Between Tkelvin An
d Energy
Earths coldest Recorded Temp -132 deg C High
Antartic Polar Plateau
E
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V vs. T at Different P
V/T k (p,n held const.)
No matter what the initial P is all lines
intersect at Absolute zero
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Lets try a few problems.
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Problem 1 2
If the temperature of the gas in fig.1 is 35 deg.
C and the volume is 1/2L what is the temperature
in fig.2 and What is the temp in fig 3? (P,n are
constant)
Fig 1 Fig 2 Fig. 3
V1/T1 V2/T2 .5L/308 1L/T2 T2
1L/(.5L/308) T2 616 deg K V1/T1
V3/T3 .5L/3082L/T3 T3 2L/(.5L/308) T3 1232
deg. K
½ L 1 L 2L
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Problem 3
A sample of gas at 30 deg C and standard pressure
(1 atm) occupies a volume of 200 ml. Calculate
the temperature in deg. Celsius at which the gas
will occupy a volume of 5 ml at std pressure if
P is held constant.
V1/T1 V2/T2 T2 V2/(V1/T1) T2
5/(200/303) T2 7.58 deg K Whats this
temperature in deg. C? T2 -265.42 deg. C
(K C 273)