Combined and ideal gas
laws
Gas properties
 Gases Have Mass
 Gases Diffuse
 Gases Expand To Fill Containers
 Gases Exert Pressure
 Gases Are Compressible
 Pressure & Temperature Are Dependent
Gas variables
 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)
A little review
 BOYLE’S LAW
–PRESSURE & VOLUME
–AS P THEN V
–AT CONSTANT T, n
P1V1 = P2V2
A Little review
CHARLES’ LAW:
–TEMPERATURE & VOLUME
–AS T THEN V
–AT CONSTANT P, n
V1
T1
=
V2
T2
A Little review
GAY-LUSSAC’S
LAW:
–TEMPERATURE & PRESSURE
–AS P THEN T
–AT CONSTANT V, n
P1
T1
=
P2
T2
Another step up…
 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 :
PV=k1
V/T=k2
P/T=k3
Combined gas law
AMOUNT IS HELD CONSTANT
IS USED WHEN YOU HAVE A CHANGE IN
VOLUME, PRESSURE, OR TEMPERATURE
P1V1
=k
T1
P2V2
=k
T2
Combined gas law
 AMOUNT IS HELD CONSTANT
 IS USED WHEN YOU HAVE A CHANGE IN
VOLUME, PRESSURE, OR TEMPERATURE
P1V1
P2V2
=
T1
T2
P1V1T2 = P2V2T1
Example problem
A GAS WITH A VOLUME OF 4.0L AT STP. WHAT IS
ITS VOLUME AT 2.0ATM AND AT 30°C?
P1  1atm
V1  4.0 L
T1  273K
P2 2.0 atm
V2  ?
T2 
30°C + 273
= 303K
PLUG & CHUG
P1V1
P2V2
=
T1
T2
2.22L = V2
 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
ideal gas law
 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.
Ideal gas law
 IF WE COMBINE ALL OF THE LAWS TOGETHER
INCLUDING AVOGADRO’S LAW MENTIONED
EARLIER WE GET:
PV
nT
=R
NORMALLY
WRITTEN AS
WHERE R IS THE
UNIVERSAL GAS
CONSTANT
PV=nRT
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
 BECAUSE OF THE DIFFERENT PRESSURE UNITS
THERE ARE 3 POSSIBILITIES FOR OUR R
L•atm
mol•K
L•mmHg
– IF PRESSURE IS GIVEN
R=62.4
IN mmHg
mol•K
– IF PRESSURE IS GIVEN R=8.314 L•kPa
IN kPa
mol•K
– IF PRESSURE IS GIVEN IN
R=.0821
atm
Using Ideal gas law
EG #1: WHAT VOL DOES 9.45g
OF C2H2 OCCUPY AT STP?
P  1atm
R .0821
V ?
T  273K
9.45g
n
26g
L•atm
mol•K
=.3635 mol
PV = nRT
(1.0atm) (V) =
(.3635mol)
(.0821 L•atm )
mol•K
(273K)
(1.0atm) (V) = (8.147L•atm)
V = 8.15L
Using Ideal gas law
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
P  303kPa R  8.314
V ?
3000g
n
44g
L•kPa
mol•K
T  298K
PV = nRT
=68.2 mol
(303kPa) (V) =
(8.314 L•kPa )
(68.2mol)
(303kPa)
mol•K
(V)
=
(298K)
(168,970.4L•kPa)
V = 557.7L