System constants varied `Law’ Balloon n, P T, V Piston n, T P, V Pressure n, V P,T Cooker EMPIRIC=SIMPLE GAS LAWS SUMMARIZED V 1 /T 1 =V 2 /T 2 P 1 V 1 =P 2 V 2 P 1 /T 1 =P 2 /T 2 CHARLES BOYLE GAY-LUSSAC

How Boyle, Gay-Lussac and Charles Laws are reflected in the Combined Gas Law (when n is constant) P 1 V 1 = P 2 V 2 T 1 T 2 constant n,P P 1 V 1 = P 2 V 2 T 1 T 2 Charles’ Law (P 1 =P 2 ) constant n, T Boyle’s Law (T 1 =T 2 ) constant n, V Gay-Lussac’s Law (V 1 =V 2 ) Combined Gas Law constant n P 1 V 1 = P 2 V 2 T 1 T 2 P 1 V 1 = P 2 V 2 T 1 T 2 ConditionsName of Gas Law Gas Law Equation

An ideal gas at constant V and P=2 atm is heated from 300 to 600 K. What is the final P ? A.1 atm B.2 atm C.3 atm D.4 atm

1.A sample of oxygen gas is expanded from 20 to 50 liters at constant temperature. The final pressure is 4 atm. What was the initial pressure ? P 1 =10 atm COMBINED GAS LAW PROBLEMS…BOARD WORK

A sample of ideal gas arrives at 300K when expanded from 3 to 9 L at constant P. What was the original temperature ? A.900 K B.100 K C.600 K D.150 K

2. A child’s balloon originally occupies 5 liters at sea level (P=1 atm) and room temperature (300 K). It is released and is allowed to rise to an altitude where the pressure is 0.25 atm and the temperature is 150 K. What is the balloon’s new volume ? 10 L COMBINED GAS LAW PROBLEMS…BOARD WORK (CONT.)

An ideal gas in a fixed volume and an initial pressure of 10 atm and initial T of 177 C has a final pressure of 3.33 atm. What is the final T(K) (K=C+273) A.150 K B.59 K C.450 K D.531 K

3.The volume of a piston at fixed pressure changes as it is cooled from 500 o C to 250 o C. If the final volume is 6.76 L, what is the initial volume ? V 1 =10 L COMBINED GAS LAW PROBLEMS…BOARD WORK (CONT.)

4. Autoclaves are essentially pressure cookers. At 1 atm, steam has a temperature of 100 o C. Would you expect the pressure to double if the autoclave to attains a steam temperature of 200 o C ? a) NO…must convert C  K…ratio is not 200/100 What pressure do you actually expect to reach at 200 o C? =1.73 atm COMBINED GAS LAW PROBLEMS…BOARD WORK (CONT.)

Trickier problem…2 MOL $ IF YOU CAN DO IT FOR CLASS 2.00 L H 2 at atm 1.00 L N 2 at atm Stopcock closed Stopcock open Final P = ??? atm

Combined Gas Law Reviewed As long as n=moles is held constant: P 1 V 1 = P 2 V 2 T 1 T 2

What happens if we let n vary too ??

P (piston head) n V (varies T Heating/cooling coils piston walls Hypothetical Gas Property testing apparatus Ideal Gas Law: letting T,P,V, n and gas ID all vary (pp ) GASGAS GAS VALVE insulatio n

0 o Vary gas and fix three out of four gas variables… Gas varied H 2 (2) He(4) N 2 (28) CO 2 (44) SF 6 (146) T( O C) P(atm) n(moles) V(obs) Variables fixed at constant values (`STP’) STP =Standard Temperature & Pressure ( and n=1)..see what happens Gas ID (and size) not important Ideal Gas derived: Why gas identity not important 0 o

What happens if we hold different sets of three variables constant and watch the fourth for a given gas ? P(atm) V(L) T(K)n(moles) PV/nT Anything constant ?? Ideal Gas Law derived (cont.): origin of R

PV = nT =R (atm L) (mol K ) PV =nRT Or…

The ideal gas law lead to : molecular masses verification of stoichiometries

1. An 11 gram sample of a gas occupies 2.0 liters at atm and 200 K. What is the molecular mass of the gas ? (R= ) 44 g/mol