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Chemistry Lecture ’94 B. Rife CHS
Text: Modern Chemistry; Holt, Rinehart & Winston 1993
Gas Stoichiometry Chapter 12
Homework: DUE DATE
1Section Reviews (pg 350,355,360,365)Thur. 2/17
2Reviewing Concepts:(all) (pg 366)Tue. 2/22
3Problems (all black / red EC) (pg 366-69)Thur 2/24
4Chapter/Section Review (Handout)
Exam Date _ Wed 3/1
12.1 Volume - Mass Relationships of Gases
12.1A State the law of combining volumes. ( )
GAY-LUSSAC’S LAW OF COMBINING VOLUMES OF GASES STATES AT A CONSTANT TEMPERATURE AND PRESSURE, THE VOLUMES OF GASEOUS REACTANTS AND PRODUCTS CAN BE EXPRESSED AS RATIOS OF SMALL WHOLE NUMBERS.
12.1B State Avogadro’s principle, and explain its significance. ( )
AVOGADRO’S PRINCIPLE STATES THAT EQUAL VOLUMES OF GASES AT THE SAME TEMPERATURE AND PRESSURE CONTAIN EQUAL NUMBERS OF MOLECULES. (THIS LAW MADE POSSIBLE THE FIRST RELIABLE DETERMINATION OF ATOMIC MASSES.)
O2 (g)+2 H2 (g)--->2 H2O (g)
1 MOLECULE2 MOLECULES2 MOLECULES
1 MOLE2 MOLES2 MOLES
1 VOLUME2 VOLUMES2 VOLUMES
12.1C Define standard molar volume of a gas, and use it as a conversion factor to calculate gas masses andvolumes. ( )
STANDARD MOLAR VOLUME OF A GAS IS THE VOLUME OCCUPIED BY ONE MOLE OF ANY GAS AT STP, AND HAS BEEN FOUND TO BE 22.4 L
HOW MANY MOLES IN ONE CUBIC METER OF AIR AT STP?
1 m3 = 103 dm3 = 103 L (1 mole / 22.4 L) = 44.64 moles air
HOW MANY LITERS IS OCCUPIED BY 2 MOLES OF H2 AT STP?
2 moles H2 (22.4 L / 1 mole) = 44.8 L H2
ELECTROLYSIS OF WATER PRODUCES 2 LITERS OF OXYGEN AT STP, HOW MANY GRAMS OF OXYGEN WAS PRODUCED?
2 L O2 ( 1 mole ) ( 32 g O2) = 2.86 g O2
22.4 L 1 mole O2
12.1D Calculate the molar mass and density of a gas by using standard molar volume. ( )
GAS DENSITY (AT STP) = MOLAR MASS = g_
MOLAR VOLUME L
DENSITY OF NITROGEN (N2) = 28 g / 22.4 L = 1.25 g/L
DENSITY OF CARBON DIOXIDE (CO2) = 44 g / 22.4 L = 1.96 g/L
12.2 The Ideal Gas Law
12.2A State the ideal gas law. ( )
THE IDEAL GAS LAW IS AN EQUATION OF STATE FOR A GAS, WHERE THE STATE OF THE GAS Is ITS CONDITION AT A GIVEN TIME.
12.2B Derive the ideal gas constant and discuss its units. ( )
A PARTICULAR STATE OF A GAS IS DESCRIBED BY ITS PRESSURE, VOLUME, TEMPERATURE (KELVIN), AND NUMBER OF MOLES (n) PRESENT.
AN IDEAL GAS IS ONE THAT OBEYS THE GAS LAWS EXACTLY.
MANY REAL GASES SHOW SLIGHT DEVIATIONS FROM IDEALITY, BUT AT NORMAL TEMPERATURES AND PRESSURES THE DEVIATIONS ARE SMALL ENOUGH TO BE IGNORED IN MOST CASES.
SUMMARIZING THE BEHAVIOR OF GASES IN A GENERAL WAY, WE HAVE:
BOYLE'S LAW V _ 1/P(AT CONSTANT T AND n)
CHARLES' LAW V _ T (AT CONSTANT P AND n)
AVOGADRO'S LAW V _ n (AT CONSTANT T AND P @ STP)
THEREFORE V _ nT/P OR REARRANGING PV _ nT
THE PROPORTIONALITY, PV nT, CAN BE CONVERTED INTO AN EQUALITY BY INTRODUCING A PROPORTIONALITY CONSTANT, FOR WHICH IT IS TRADITIONAL TO USE R
PV = nRT
THE RELATIONSHIP IS CALLED THE IDEAL GAS EQUATION OR THE IDEAL GAS LAW.
THE NUMERICAL VALUE OF R, THE PROPORTIONALITY CONSTANT, DEPENDS UPON THE CHOICES OF THE UNITS FOR P, V, AND T.
SOLVING THE IDEAL GAS LAW FOR R GIVES
R = PV / nT = (1.0 atm) (22.4 L) / (1.0 mol) (273 K) = 0.08206 L atm / mol K
R IS CALLED THE UNIVERSAL GAS CONSTANT.
THE IDEAL-GAS EQUATION SIMPLIFIES THE SOLUTION OF MASS-GAS VOLUME PROBLEMS UNDER NONSTANDARD CONDITIONS.
12.2C Using the ideal gas law, calculate one of the quantities: pressure, volume, temperature, amount of gas, when the other three are known. ( )
CAUTION:ALWAYS BE SURE TO MATCH THE UNITS OF THE KNOWN QUANTITIES AND UNITS OF R.
SAMPLE PROBLEM
WHAT IS THE VOLUME OF A GAS BALLOON FILLED WITH 4.0 MOLES OF HELIUM WHEN THE ATMOSPHERIC PRESSURE IS 748 TORR AND THE TEMPERATURE IS 30 oC.
P = 748 TORR (1 ATM / 760 TORR) = 0.984 ATM
n = 4.0T = 30 oC + 273 = 303 K
PV = nRT ---> V = nRT / P = (4.0 mol) (.08206) (303 K) / 0.984 ATM = 101 L
12.2D Reduce the ideal gas law to Boyle’s law, Charles’ law, and Avogadro’s principle. Describe the conditions under which each applies. ( )
V = nRT / P
V = R/P OR R = VP(AT CONSTANT T AND n) BOYLE'S LAW
ONE VERY IMPORTANT USE OF THE IDEAL GAS LAW IS IN THE CALCULATION OF THE MOLAR MASS OF A GAS FROM ITS MEASURED DENSITY.
MOLAR MASS (M) = dRT / P
SAMPLE PROBLEM
THE DENSITY OF A GAS WAS MEASURED AT 1.5 ATM AND 27 oC AND FOUND TO BE 1.95 g/L. CALCULATE THE MOLAR MASS OF THE GAS.
P = 1.5 ATMd = 1.95 g/LT = 27 oC + 273 = 300 K
(M) = dRT / P = (1.95 g/L) (.08206) (300 K) / 1.5 ATM= 32 g /mol
12.3 Stoichiometry of Gases
12.3A Explain how Gay-Lussac’s law and Avogadro’s principle apply to the volumes of gases in chemicalreactions ( )
O2 (g)+2 H2 (g)--->2 H2O (g)
1 MOLECULE2 MOLECULES2 MOLECULES
1 MOLE2 MOLES2 MOLES
1 VOLUME2 VOLUMES2 VOLUMES
12.3B Use a chemical equation to specify volume ratios for gaseous reactants and/or products. ( )
SAMPLE PROBLEM
ASSUME ALL VOLUME MEASUREMENTS ARE MADE AT THE SAME CONDITIONS OF TEMPERATURE AND PRESSURE, WHAT VOLUME OF HYDROGEN GAS IS NEEDED TO REACT COMPLETELY WITH 4.55 L OF OXYGEN TO PRODUCE WATER VAPOR?
4.55 L O2 ( 2 L H2) = 9.10 L H2
1 L O2
12.3C Use volume ratios, standard molar volume, and the gas laws where appropriate to calculate volumes, masses, or molar amounts of reactants or products in reactions involving gases. ( )
SAMPLE PROBLEM
WHEN LIME (CaO) IS HEATED TO INCANDESCENCE WITH A HOT FLAME, IT GIVES AN INTENSE, BRIGHT LIGHT. SUCH LIGHTS WERE USED BY 1800s’ THEATERS TO SPOTLIGHT ACTORS, ORIGINATING THE PHRASE “IN THE LIMELIGHT”
QUICKLIME (CaO) IS PRODUCED BY THE THERMAL DECOMPOSITION OF CALCIUM CARBONATE (CaCO3). CALCULATE THE VOLUME OF CO2 AT STP PRODUCED FROM THE DECOMPOSITION OF 152 g CaCO3 .
BALANCED REACTION
CaCO3 (s) ---> CaO (s) + CO2 (g)
152 g CaCO3 ( 1 mol CaCO3) (22.4 L CO2) = 34.1 L CO2
100.1 CaCO3 1 mol CO2
SAMPLE PROBLEM
A SAMPLE OF METHANE GAS HAVING A VOLUME OF 2.80 L AT 25o C AND 1.65 ATM WAS MIXED WITH A SAMPLE OF OXYGEN GAS HAVING A VOLUME OF 35.0 L AT 31 o C AND 1.25 ATM. THE MIXTURE WAS THEN IGNITED TO FORM CARBON DIOXIDE AND WATER. CALCULATE THE VOLUME OF CO2 FORMED AT A PRESSURE OF 2.50 ATM AND A TEMPERATURE OF
125 o C.
BALANCED EQUATION
CH4 (g) + 2 O2 (g) ---> CO2 (g) + 2H2O
LIMITING REAGENT
CH4 n = PV / RT = (1.65) (2.80) / (0.08206) (298) = 0.189 mol CH4 (1 mol CO2 / 1 mol CH4 ) = .189 mol CO2
O2 n = PV / RT = (1.25) (35.0) / (0.08206) (304) = 1.75 mol O2 (1 mol CO2 / 2 mol O2 ) = .875 mol CO2
SINCE THE CONDITIONS STATED ARE NOT STP, WE MUST USE THE IDEAL GAS LAW TO CALCULATE THE VOLUME.
V = nRT / P = (0.189 mol) (0.08206) (398) / (2.50) = 2.47 L
12.4 Effusion and Diffusion
DIFFUSION IS THE TERM USED TO DESCRIBE THE MIXING OF GASES
EFFUSION IS THE TERM USED TO DESCRIBE THE PASSAGE OF A GAS THROUGH A TINY ORIFICE INTO AN EVACUATED CHAMBER.
12.4A State Graham’s law of effusion or diffusion. ( )
GRAHAM’S LAW OF EFFUSION (OR DIFFUSION) STATES THAT THE RATES OF EFFUSION OF GASES AT CONSTANT TEMP. AND PRESSURE ARE INVERSELY PROPORTIONAL TO THE SQUARE ROOTS OF THEIR MOLAR MASSES.
RATE OF EFFUSION FOR GAS 1 = _ M 2
RATE OF EFFUSION FOR GAS 2 M 1
12.4B Determine the relative rates of effusion of two gases of known molar masses. ( )
SAMPLE PROBLEM
CALCULATE THE RATIO OF THE EFFUSION RATES OF HYDROGEN GAS (H2) AND URANIUM HEXAFLUORIDE (UF6), A GAS USED IN THE ENRICHMENT PROCESS TO PRODUCE FUEL FOR NUCLEAR REACTORS.
RATE OF EFFUSION FOR H2 = _ 352 = 13.26
RATE OF EFFUSION FOR UF6 2
THE EFFUSION RATE OF THE VERY LIGHT H2 MOLECULES IS ABOUT 13 TIMES THAT OF THE MASSIVE UF6 MOLECULES.