combined and ideal gas laws gases have mass gases diffuse gases expand to fill containers gases...
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Gases Have MassGases DiffuseGases Expand To Fill
ContainersGases Exert PressureGases Are CompressiblePressure & Temperature
Are Dependent
Gases Have MassGases DiffuseGases Expand To Fill
ContainersGases Exert PressureGases Are CompressiblePressure & Temperature
Are Dependent
Gas propertiesGas properties
VOLUME (V)– UNITS OF VOLUME (L)
AMOUNT (n)– UNITS OF AMOUNT (MOLES)
TEMPERATURE (T)– UNITS OF TEMPERATURE (K)
PRESSURE (P)–UNITS OF PRESSURE (mmHg)–UNITS OF PRESSURE (kPa)–UNITS OF PRESSURE (atm)–UNITS OF PRESSURE (torr)
VOLUME (V)– UNITS OF VOLUME (L)
AMOUNT (n)– UNITS OF AMOUNT (MOLES)
TEMPERATURE (T)– UNITS OF TEMPERATURE (K)
PRESSURE (P)–UNITS OF PRESSURE (mmHg)–UNITS OF PRESSURE (kPa)–UNITS OF PRESSURE (atm)–UNITS OF PRESSURE (torr)
Gas variablesGas variables
P1V1 = P2V2
P1V1 = P2V2
BOYLE’S LAW–PRESSURE & VOLUME–AS P THEN V–AT CONSTANT T, n
BOYLE’S LAW–PRESSURE & VOLUME–AS P THEN V–AT CONSTANT T, n
A little reviewA little review
A Little reviewA Little reviewCHARLES’ LAW:
–TEMPERATURE & VOLUME
–AS T THEN V–AT CONSTANT P, n
CHARLES’ LAW: –TEMPERATURE & VOLUME
–AS T THEN V–AT CONSTANT P, n
V1V1
T2T2
==T1T1
V2V2
A Little reviewA Little reviewGAY-LUSSAC’S LAW:
–TEMPERATURE & PRESSURE
–AS P THEN T–AT CONSTANT V, n
GAY-LUSSAC’S LAW: –TEMPERATURE & PRESSURE
–AS P THEN T–AT CONSTANT V, n
P1P1
T2T2
==T1T1
P2P2
Another step up…Another step up…
PV=k1PV=k1 V/T=k2V/T=k2 P/T=k3P/T=k3
If we combine all of the relationships from the 3 laws covered thus far (Boyle’s, Charles’s, and Gay-Lussac’s) we can develop a mathematical equation that can solve for a situation where 3 variables change :
If we combine all of the relationships from the 3 laws covered thus far (Boyle’s, Charles’s, and Gay-Lussac’s) we can develop a mathematical equation that can solve for a situation where 3 variables change :
Combined gas law
Combined gas lawAMOUNT IS HELD
CONSTANTIS USED WHEN YOU HAVE A CHANGE IN VOLUME, PRESSURE, OR TEMPERATURE
AMOUNT IS HELD CONSTANT
IS USED WHEN YOU HAVE A CHANGE IN VOLUME, PRESSURE, OR TEMPERATURE P1V1P1V1
T1T1
= k= kP2V2P2V2
T2T2
= k= k
Combined gas law
Combined gas lawAMOUNT IS HELD CONSTANT
IS USED WHEN YOU HAVE A CHANGE IN VOLUME, PRESSURE, OR TEMPERATURE
AMOUNT IS HELD CONSTANT IS USED WHEN YOU HAVE A
CHANGE IN VOLUME, PRESSURE, OR TEMPERATURE
P1V1P1V1
T1T1
P2V2P2V2
T2T2
==
P1V1T2P1V1T2 P2V2T1P2V2T1==
A GAS WITH A VOLUME OF 4.0L AT STP. WHAT IS ITS VOLUME
AT 2.0ATM AND AT 30°C?
A GAS WITH A VOLUME OF 4.0L AT STP. WHAT IS ITS VOLUME
AT 2.0ATM AND AT 30°C?
Example problemExample problem
P1 P1 V1 V1 T1 T1
P2P2V2 V2 T2 T2
1atm1atm4.0 L4.0 L273K273K
2.0 atm
2.0 atm??
30°C + 273
30°C + 273=
303K= 303K
SO FAR WE’VE COMPARED ALL THE VARIABLES EXCEPT THE AMOUNT OF A GAS (n).
There is a lesser known law called avogadro’s law which relates v & n.
It turns out that they are directly related to each other.
As # of moles increases then v increases.
SO FAR WE’VE COMPARED ALL THE VARIABLES EXCEPT THE AMOUNT OF A GAS (n).
There is a lesser known law called avogadro’s law which relates v & n.
It turns out that they are directly related to each other.
As # of moles increases then v increases.
V/n = k
V/n = k
ideal gas lawideal gas lawWHICH LEADS US TO THE
IDEAL GAS LAW – SO FAR WE HAVE ALWAYS
HELD AT LEAST 1 OF THE VARIABLES CONSTANT.
WE CAN SET UP A MUCH MORE POWERFUL EQN, WHICH CAN BE DERIVED BY COMBINING THE PROPORTIONS EXPRESSED BY THE PREVIOUS LAWS.
WHICH LEADS US TO THE IDEAL GAS LAW –
SO FAR WE HAVE ALWAYS HELD AT LEAST 1 OF THE VARIABLES CONSTANT.
WE CAN SET UP A MUCH MORE POWERFUL EQN, WHICH CAN BE DERIVED BY COMBINING THE PROPORTIONS EXPRESSED BY THE PREVIOUS LAWS.
IF WE COMBINE ALL OF THE LAWS TOGETHER INCLUDING AVOGADRO’S LAW MENTIONED EARLIER WE GET:
IF WE COMBINE ALL OF THE LAWS TOGETHER INCLUDING AVOGADRO’S LAW MENTIONED EARLIER WE GET:
PVPVTTnn
= R= R
WHERE R IS THE
UNIVERSAL GAS
CONSTANT
WHERE R IS THE
UNIVERSAL GAS
CONSTANTNORMALLYWRITTEN
AS
NORMALLYWRITTEN
ASPVPV=nRT=nRT
Ideal gas lawIdeal gas law
Ideal gas constant(R)
Ideal gas constant(R)R IS A CONSTANT THAT
CONNECTS THE 4 VARIABLES R IS DEPENDENT ON THE
UNITS OF THE VARIABLES FOR P, V, & T–TEMP IS ALWAYS IN KELVIN–VOLUME IS IN LITERS–PRESSURE IS IN EITHER atm OR mmHg OR kPa
R IS A CONSTANT THAT CONNECTS THE 4 VARIABLES
R IS DEPENDENT ON THE UNITS OF THE VARIABLES FOR P, V, & T–TEMP IS ALWAYS IN KELVIN–VOLUME IS IN LITERS–PRESSURE IS IN EITHER atm OR mmHg OR kPa
BECAUSE OF THE DIFFERENT PRESSURE UNITS THERE ARE 3 POSSIBILITIES FOR OUR R
BECAUSE OF THE DIFFERENT PRESSURE UNITS THERE ARE 3 POSSIBILITIES FOR OUR R
R=.0821R=.0821L•atmL•atmmol•Kmol•K
– IF PRESSURE IS GIVEN IN mmHg
– IF PRESSURE IS GIVEN IN mmHg
R=62.4R=62.4L•mmHgL•mmHgmol•Kmol•K
– IF PRESSURE IS GIVEN IN kPa
– IF PRESSURE IS GIVEN IN kPa
R=8.314R=8.314L•kPaL•kPamol•Kmol•K
– IF PRESSURE IS GIVEN IN atm
– IF PRESSURE IS GIVEN IN atm
Using Ideal gas law
Using Ideal gas lawEG #1: WHAT VOL DOES 9.45g
OF C2H2 OCCUPY AT STP?EG #1: WHAT VOL DOES 9.45g
OF C2H2 OCCUPY AT STP?
P P
V V T T
1atm1atm
?? 273K273K
R R
n n =.3635 mol
=.3635 mol
.0821 .0821L•atmL•atmmol•Kmol•K
9.45g9.45g
26g26g
PV = nRTPV = nRT(1.0at
m)(1.0at
m)(V)(V)
(.3635mol)(.3635mol) (273K)(273K)
V = 8.15LV = 8.15L
==(.0821 )(.0821 )L•atm
mol•KL•atmmol•K
(1.0atm)
(1.0atm)
(V)(V) (8.147L•atm
)
(8.147L•atm
)
==
Using Ideal gas law
Using Ideal gas lawEG #2: A CAMPING STOVE
PROPANE TANK HOLDS 3000g OF C3H8. HOW LARGE A CONTAINER
WOULD BE NEEDED TO HOLD THE SAME AMOUNT OF PROPANE AS A GAS AT 25°C AND A PRESSURE OF
303kPa?
EG #2: A CAMPING STOVE PROPANE TANK HOLDS 3000g OF C3H8. HOW LARGE A CONTAINER
WOULD BE NEEDED TO HOLD THE SAME AMOUNT OF PROPANE AS A GAS AT 25°C AND A PRESSURE OF
303kPa?
Using Ideal gas law
Using Ideal gas law
P P
V V T T
303kPa
303kPa?? 298K298K
R R
n n =68.2 mol
=68.2 mol
8.314 8.314L•kPaL•kPa
mol•Kmol•K
3000g3000g44g44g
PV = nRTPV = nRT