the gas laws
DESCRIPTION
The Gas Laws. Pressure Volume & Temperature. States of Matter. In liquids and solids, the primary particles (atoms or molecules) are always in contact with each other. In gases, particles move independently. - PowerPoint PPT PresentationTRANSCRIPT
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Pressure Volume & Temperatu
re
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In liquids and solids, the primary particles
(atoms or molecules) are always
in contact with each other.
In gases, particles move independently.
Because the atoms of gases are far apart
they are very compressible.
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When pressure is applied, the volume
occupied by a gas can be decreased.
Gases fill all of the space available to them.
In a contained sample (e.g. balloon) gases expand to fill the total volume of the balloon.
If not contained:
Gases expand indefinitely.
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If the cubic meter were divided into 1000 equal smaller parts, each part would be equal
to 1 Liter (slightly larger than a quart)
1 qt = 1.057 L
If each liter were divided into 1000 equal
smaller parts, each part would be equal to
1 milliliter (mL) or 1 cubic centimeter (cc) 1 mL = 1 cc
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Space occupied in 3 dimensions.
Units: liters
One liter is similar in volume to a quart
1 qt = 1.057 L
One liter is equal to 1,000 cubic centimeters
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Force per unit of area.
Force / area = lbs / sq.in
Pounds per square inch = psi 14.7 psi = 1 atm
1 mm Hg = 1 torr 1 atm = 760 mm Hg
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Increase the pressure
Volume decreases proportionally
Pressure x Volume = constant
Product of pressure and volume is fixed.
P x V = constant
P1 x V1 = P2 x V2
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Compressed gas cylinder
Pressure = 135 atm
Volume = 15.0 liters
What volume the gas will occupy at 1.00 atm ?
P1 = 135 atm
V1 = 15.0 L
P2 = 1.00 atm
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Determine V2
P1 x V1 = P2 x V2
V2 = ( P1 x V1 ) / P2
V2 = ( 135 atm ) ( 15.0 L ) / 1.00 atm
= 2,030 liters
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Increase the temperature
Volume will increase proportionally.
The volume of a sample divided by the
temperature is equal to a constant.
V / T
= constant
V1 / T1 = V2 / T2
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Determine the final volume of a
0.35 liter balloon which is heated from
room temperature to 100 degrees C.
V1 / T1 = V2 / T2
Convert all temperatures to Kelvins.
T1 = 25 °C + 273 = 298 K
T2 = 100 °C + 273 = 373 K
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V1 / T1 = V2 / T2
V2 = ( V1 x T2 ) / T1
= V1 x ( T2 / T1 )
= ( 0.35 L ) ( 373 K / 298 K)
= ( 0.35 ) ( 1.25)
= 0.44 liters
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Pressure is proportional to the temperature
The ratio of the absolute temperature
to the pressure is always constant.
P1 / T1 = P2 / T2
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The pressure inside a compressed gas cylinder is 134 atm @ 25 °C. Calculate the new pressure inside the cylinder if it is heated to 48 °C.
P1 = 134 atm
T1 = 25 + 273 = 298 K
T2 = 48 + 273 = 321 K
Determine P2
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P1 / T1 = P2 / T2
P2 = ( P1 x T2 ) / T1
P2 = ( 134 atm ) ( 321 K ) / 298 K
= 144 atm
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The pressure of CO2 inside a bottle of carbonated soda pop is approximately 1.35 atm @ 25 °C (298 K).
Determine the pressure inside the bottle if it is chilled to 0 °C (273 K) .
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P1 / T1 = P2 / T2
P2 = ( P1 x T2 ) / T1
P2 = (
1.34 atm ) ( 273 K ) / 298 K
= 1.23 atm
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We can combine all of these laws
to get a combined gas law:
P V / T = constant
P1 x V1 / T1 = P2 x V2 / T2
This law holds for a fixed amount of gas (or a fixed number
of moles, n ).
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Start with 2.37 liters of gas
@ 25.0 °C ( 298 K ) and 1 atmosphere
Heat it to 297 °C ( 570 K ).
Increase the pressure to 10 atmospheres.
What is the final volume?
*Note: Upon heating, volume will increase.
But on compression, volume will decrease.
Opposing forces
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P1 x V1 / T1 = P2 x V2 / T2
Solve for V2 (isolate the variable): V2
= [ P1 x V1 / T1 ] x ( T2 / P2 )
Express as a product of ratios: V2
= V1 x [ P1 / P2 ] x [ T2 / T1 ]
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P1 / P2 = 1 / 10
T2 / T1 = 570 / 298
V2 = ( 2.37 ) ( 1 / 10 ) ( 570 / 298)
V2 = ( 2.37 ) ( 0.19 ) = 0.453 L
*Note: Ratio of pressures = 0.10 < 1
Ratio of temps = 1.91 > 1
They offset each other.
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P V = n R T
n = # of moles of gas
R = 0.0821 liter * atm / mol * K
PV / nT = constant
( P1 x V1 ) / ( n1 x T1 )
= ( P2 x V2 ) / ( n2 x T2 )
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Calculate the volume of 1 mole of Ideal gas
@ Room temp (298 K) and pressure (1 atm).
P V = n R T
V = n R T / PV
= ( 1.0 ) ( 0.0821 ) ( 273 ) / 1.0
= 22.4 L
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11.2 L tank of gas is found in the coldest
part of the refrigerator (0 °C = 273 K).
It contains 4
moles of gas: (1 mole of oxygen and
3 moles of neon).
What is the pressure in the tank?
P = nRT / V =
= ( 4.0 )( 0.0812 ) ( 273 ) / 11.2
= 7.91 atm