Combined and ideal gas laws

PV=k 1 V/T=k 2 P/T=k 3  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  AMOUNT 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 P1V1P1V1 T1T1 T1T1 = k P2V2P2V2 P2V2P2V2 T2T2 T2T2

Combined gas law  AMOUNT 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 P1V1P1V1 T1T1 T1T1 P2V2P2V2 P2V2P2V2 T2T2 T2T2 = = P1V1T2P1V1T2 P1V1T2P1V1T2 P2V2T1P2V2T1 P2V2T1P2V2T1 = =

A GAS WITH A VOLUME OF 4.0L AT STP. WHAT IS ITS VOLUME AT 2.0ATM AND AT 30°C? Example problem P1 P1  P1 P1  V 1  T 1  P2P2 P2P2 V2 V2  V2 V2  T 2  1atm 4.0 L 273K 2.0 atm ? ? 30°C = 303K

PLUG & CHUG P1V1P1V1 P1V1P1V1 T1T1 T1T1 P2V2P2V2 P2V2P2V2 T2T2 T2T2 = = 2.22L = V 2

 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

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.  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: PV T T n n = R WHERE R IS THE UNIVERSAL GAS CONSTANT NORMALLY WRITTEN AS NORMALLY WRITTEN AS PV =nRT Ideal gas law

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 R=.0821 Latm molK –IF PRESSURE IS GIVEN IN mmHg R=62.4 LmmHg molK –IF PRESSURE IS GIVEN IN kPa R=8.314 LkPa molK –IF PRESSURE IS GIVEN IN atm

Using Ideal gas law EG #1: WHAT VOL DOES 9.45g OF C 2 H 2 OCCUPY AT STP? EG #1: WHAT VOL DOES 9.45g OF C 2 H 2 OCCUPY AT STP? P  V  T T  T T  1atm ? ? 273K R  n n  n n  =.3635 mol.0821 Latm molK 9.45 g 26 g

PV = nRT (1.0atm) (V)(V) (V)(V) (.3635 mol ) (273K) V = 8.15L = = (.0821 ) Latm molK Latm molK (1.0atm) (V)(V) (V)(V) (8.147Latm) = =

Using Ideal gas law EG #2: A CAMPING STOVE PROPANE TANK HOLDS 3000g OF C 3 H 8. 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  V  T T  T T  303kPa ? ? 298K R  n n  n n  =68.2 mol LkPa molK 3000g 44 g PV = nRT

(303kPa) (V)(V) (V)(V) (68.2 mol ) ( 298K ) = = (8.314 ) LkPa molK LkPa molK (303kPa) (V)(V) (V)(V) (168,970.4LkPa) = = V = 557.7L