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Combined Gas Law. This is made by combining Charles’ and Boyle’s Law. V i P i / T i = V f P f / T f Temperature has to be in Kelvin (so it can never be 0) volume and pressure can be in any unit as long as it is the same on both sides. A problem. - PowerPoint PPT Presentation
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Combined Gas LawCombined Gas Law
This is made by combining This is made by combining Charles’ and Boyle’s Law.Charles’ and Boyle’s Law.
VVi i PPi i / T/ Tii = V = Vf f PPf f / T/ Tff
Temperature has to be in Kelvin Temperature has to be in Kelvin (so it can never be 0)(so it can never be 0)
volume and pressure can be in volume and pressure can be in any unit as long as it is the any unit as long as it is the same on both sides.same on both sides.
A problemA problem
If a gas occupies 34 L at 1.2 atm and If a gas occupies 34 L at 1.2 atm and 290 K, what volume will it occupy at 1.1 290 K, what volume will it occupy at 1.1 atm and 280 K?atm and 280 K?
VVi i PPi i / T/ Tii = V = Vf f PPf f / T/ Tff
34L (1.2atm) / 290 K = V (1.1atm)/280K34L (1.2atm) / 290 K = V (1.1atm)/280K V = 36 L V = 36 L
A problemA problem
If a gas occupies 24 mL at 115 kPa and If a gas occupies 24 mL at 115 kPa and 1313oo C, what volume will it occupy at 101 C, what volume will it occupy at 101 kPa and 0kPa and 0oo C? C?
24 mL (115kPa)/286 K24 mL (115kPa)/286 K
= V 101kPa)/273 K= V 101kPa)/273 K V = 26 mL (don’t forget to convert temp V = 26 mL (don’t forget to convert temp
to K)to K)
Standard Temperature and Standard Temperature and PressurePressure
Normally volumes are reported at Normally volumes are reported at standard conditions.standard conditions.
It is normally abbreviated STP It is normally abbreviated STP (standard temperature and (standard temperature and pressure)pressure)
Standard temperature is 273 K or Standard temperature is 273 K or 00oo C C
Standard pressure is 101 kPa, or Standard pressure is 101 kPa, or 760 torr, or 1.00 atm. 760 torr, or 1.00 atm.
Avogadro’s LawAvogadro’s Law
Avogadro discovered that the size or Avogadro discovered that the size or type of molecule or atom of a gas had type of molecule or atom of a gas had no effect on the volume of that gas.no effect on the volume of that gas.
His law states…His law states… ~equal volumes of ~equal volumes of differentdifferent gases at gases at
the same temperature and pressure the same temperature and pressure contain the same number of molecules.contain the same number of molecules.
1.00 mol of 1.00 mol of anyany gas at STP will occupy gas at STP will occupy 22.4 L22.4 L
To convert…To convert…
What volume will .67 mol of a What volume will .67 mol of a gas occupy at STP?gas occupy at STP?
.67mol 22.4 L (at STP).67mol 22.4 L (at STP) 1 mol1 mol = 15.008 = 15.008 15 L at STP15 L at STP What volume will .67 mol of a What volume will .67 mol of a
gas occupy at 740 torr and 295 gas occupy at 740 torr and 295 K?K?
Add this into combined gas Add this into combined gas lawlaw
VVi i PPi i / T/ Tii = V = Vf f PPf f / T/ Tff
What volume will .67 mol of a What volume will .67 mol of a gas occupy at 740 torr and 295 gas occupy at 740 torr and 295 K?K?
15.008 L (760 torr)/273 K15.008 L (760 torr)/273 K= V (740 torr)/295K= V (740 torr)/295K
V = 17 LV = 17 L
MoreMore
What volume will .83 mol of a gas What volume will .83 mol of a gas occupy at .82 atm and 264 K?occupy at .82 atm and 264 K?
.83 mol 22.4 L (at STP).83 mol 22.4 L (at STP) 1 mol1 mol = 18.592 L at STP= 18.592 L at STP 18.592 L (1.00 atm)/273 K18.592 L (1.00 atm)/273 K
= V (.82 atm)/264 K= V (.82 atm)/264 K V = 22 LV = 22 L
Combined Gas Law Combined Gas Law ProblemsProblems
Number 1Number 1
126 mL of nitrogen at 113 kPa 126 mL of nitrogen at 113 kPa and 39and 39oo C will occupy what C will occupy what volume at STP?volume at STP?
VP/T = VP/TVP/T = VP/T 126 mL (113 kPa)/312K 126 mL (113 kPa)/312K
= V 101 kPa/273K= V 101 kPa/273K V = V = 123 mL123 mL
Number 2Number 2 1.54 mol of helium will occupy 1.54 mol of helium will occupy
what volume at 92 kPa and 315 what volume at 92 kPa and 315 K?K?
1.54 mol x 22.4 L/1 mol1.54 mol x 22.4 L/1 mol =34.496 L at STP=34.496 L at STP VP/T = VP/TVP/T = VP/T 34.496…L (101 kPa)/273K 34.496…L (101 kPa)/273K
= V 92 kPa/315K= V 92 kPa/315K V = V = 44 L44 L
Number 3Number 3 2.14 g of NH2.14 g of NH33 ammonia will ammonia will
occupy what volume at 795 torr occupy what volume at 795 torr and 315 K?and 315 K?
2.14 g x 1 mol/17.034 g = .125mol2.14 g x 1 mol/17.034 g = .125mol .1256… mol x 22.4 L/1 mol.1256… mol x 22.4 L/1 mol =2.81… L at STP=2.81… L at STP VP/T = VP/TVP/T = VP/T 2.81…L (760 torr)/273K 2.81…L (760 torr)/273K
= V 795 torr/315K= V 795 torr/315K V = V = 3.10 L3.10 L
Number 4Number 4
126 mL of nitrogen at 143 kPa 126 mL of nitrogen at 143 kPa and 39and 39oo C will occupy 154 mL at C will occupy 154 mL at 101 kPa and what temperature?101 kPa and what temperature?
VP/T = VP/TVP/T = VP/T 126 mL (143 kPa)/312K 126 mL (143 kPa)/312K
= 154 mL 101 kPa/ T= 154 mL 101 kPa/ T V = V = 269 K or -4269 K or -4o o CC
Number 5Number 5
CHCH33OH + OOH + O22 → H→ H22O + COO + CO22
What volume of What volume of carbon dioxidecarbon dioxide will will 5.2 g oxygen produce at 1.2 atm 5.2 g oxygen produce at 1.2 atm and 299 K?and 299 K?
.108.. mol x 22.4 L/1 mol=2.42… L .108.. mol x 22.4 L/1 mol=2.42… L 2.426…L (1.00 atm)/273K 2.426…L (1.00 atm)/273K
= V 1.2 = V 1.2 atm/299Katm/299K
V = V = 2.2 L2.2 L
2 3 4 2
5.2 g O5.2 g O22 1 mol O1 mol O22 2 mol CO2 mol CO22
32.00 g O32.00 g O22 3 mol O3 mol O22
Number 6Number 6
HCl + Co HCl + Co → CoCl→ CoCl33 + H + H22
What volume of What volume of hydrogen gashydrogen gas will will 5.2 g cobalt produce at 97 kPa and 5.2 g cobalt produce at 97 kPa and 285 K?285 K?
.132.. mol x 22.4 L/1 mol=2.42… L .132.. mol x 22.4 L/1 mol=2.42… L 2.966…L (101 kPa)/273K 2.966…L (101 kPa)/273K
= V 97 = V 97 KPa/285KKPa/285K
V = V = 3.2 L3.2 L
6 2 2 3
5.2 g Co5.2 g Co 1 mol Co1 mol Co 3 mol H3 mol H22
58.93 g Co 58.93 g Co 2 mol Co2 mol Co
