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Gas Laws
Why does a gas station sell liquid fuel?
Values and preferred units
• P—atmospheres
• T—kelvins
• V—Liters
• n—moles
Conversions
• P: 1 atm =760 mmHg=760torr
=101.3 kPa=101,325 Pa
• T: T(k) = T(oC) + 273
• V: 1L=1000 ml=.001 m3
Convert!
25oC=_______k
0oC=_______k
100oC=_______k
98k=_______oC
417k=_______oC
1809k=_______oC
Convert!
633 mmHg = ___________ atm
724 mmHg = ___________ atm
.83 atm = ___________mmHg
.95 atm = ___________mmHg
87 kPa = ___________ atm
122 kPa = ___________ mmHg
Boyle’s Law
• Pressure & volume are inversely related
• PV=k
• P1V1=P2V2
• When the pressure goes up, volume goes down.
P
V
At a constant temperature!
State it!
• If you double the pressure, you __________ the volume.
• If you reduce the pressure to 1/3 of the original, you __________ the volume.
• If you double the volume, you __________ the pressure.
• If you increase the pressure 20 times, you __________ the volume
For example:
If a sample of air has a volume of 120 ml at a pressure of 2.0 atm, what will its volume be if the pressure is increased to 4.0 atm?
For example:
If a sample of helium has a volume of 433 ml at a pressure of 88 kPa, what will its volume be if the pressure is increased to 2.8 atm?
Charles’ Law
• Temperature & volume are directly related
• V/T=k
• V1/T1=V2/T2
• When the temperature goes up, volume goes up.
T
V
At a constant pressure!
Charles’ Law
• Temperature & volume are directly related
• V/T=k
• V1/T1=V2/T2
• When the temperature goes up, volume goes up.
T
V
At a constant pressure!
Is it hot in here?
Charles’ Law
• Temperature & volume are directly related
• V/T=k
• V1/T1=V2/T2
• When the temperature goes up, volume goes up.
T
V
At a constant pressure!
You must use absolute temperatures
For example:
If a sample of oxygen has a volume of 2.4 m3 at 19oC, what will its volume be if the temperature is increased to 155oC?
For example:
If a sample of chlorine has a volume of 12 L at 38oC, at what temperature will its volume be 17 L?
Gay-Lussac’s Law
• Temperature & pressure are directly related
• P/T=k
• P1/T1=P2/T2
• When the temperature goes up, pressure goes up.
T
P
At a constant volume!
For example:
A tire is fairly flat (P=1200 mmHg) at -5oC on a cold morning. At what temperature would it reach its normal 3.5 atmospheres if you were to heat it up instead of pumping more air in?
Avogadro’s Law
• Volume & # of particles are directly related
• V/n=k
• V1/n1=V2/n2
• When the number of particles goes up, volume goes up.
n
V
At a constant pressure and temperature!
For example:
N2(g) + 3H2(g)2NH3(g)
If 30 L N2 and 90L of H2 are mixed, what would the final volume be if all of the reactants formed ammonia (at constant pressure and temperature)?
Combined Gas Law
• Pressure, volume & temperature relationship
• PV/T=k
P1V1/T1=P2V2/T2
For example:
If a sample of hydrogen has a volume of 56 ml
at STP, what will its volume be 19oC and
.84 atm?
For example:
If a sample of hydrogen has a volume of 56 ml
at STP, what will its volume be 19oC and
.84 atm?
STP =standard temperature and pressure
= 273k, 1.00 atm
P.S.
• The standard molar volume for an ideal gas is:
at STP
22.4L/mol
22.4 L/mol
P.S.
is about22.4 L
P1V1=P2V2
V1/T1=V2/T2
V1/n1=V2/n2
P1V1=P2V2
V1/T1=V2/T2
V1/n1=V2/n2
P1V1
n1T1
=P2V2
n2T2
always, for any sample of gas.
What is ? P1V1
n1T1
P1V1
n1T1
The molar volume of a gas is 22.4 L at STP
1.00 mol 273 k
22.4 L1.00 atm
Ideal Gas Law
• Pressure, volume, temperature & mole relationship
• PV/nT=R
• P1V1/n1T1=P2V2/n2T2=R
PV=nRT
Ideal Gas constant
.0821 L atm/mol k
An ideal gas has particles of zero volume, with no attraction to each other! It doesn’t even matter which gas is there
Ideally…
A ? 38 ml .12 mol 58oC
B 725 mmHg
? 4.9 mol 198oC
C 325 kPa .29 m3 ? 457 k
D 1.2 atm 9.1 L .85 mol ?
