i. the gas laws ch. 14 - gases. a. boyle’s law b the pressure and volume of a gas are inversely...
TRANSCRIPT
![Page 1: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/1.jpg)
I. The Gas Laws
I. The Gas Laws
Ch. 14 - GasesCh. 14 - Gases
![Page 2: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/2.jpg)
A. Boyle’s LawA. Boyle’s LawA. Boyle’s LawA. Boyle’s Law
The pressure and volume of a gas are inversely related
• at constant mass & temp
P
V
P1V1 = P2V2
![Page 3: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/3.jpg)
A. Boyle’s LawA. Boyle’s LawA. Boyle’s LawA. Boyle’s Law
![Page 4: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/4.jpg)
V
T
B. Charles’ LawB. Charles’ LawB. Charles’ LawB. Charles’ Law
The volume and absolute temperature (K) of a gas are directly related • at constant mass & pressure
V1 = V2
T1 T2
![Page 5: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/5.jpg)
B. Charles’ LawB. Charles’ LawB. Charles’ LawB. Charles’ Law
![Page 6: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/6.jpg)
V
n
A. Avogadro’s PrincipleA. Avogadro’s PrincipleA. Avogadro’s PrincipleA. Avogadro’s Principle
Equal volumes of gases contain equal numbers of moles• at constant temp & pressure• true for any gas
V1 = V2
n1 n2
![Page 7: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/7.jpg)
= kPVPTVT
PVnT
D. Combined Gas LawD. Combined Gas LawD. Combined Gas LawD. Combined Gas Law
P1V1
n1T1
=P2V2
n2T2
P1V1T2n2 = P2V2T1n1
![Page 8: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/8.jpg)
GIVEN:
V1 = 473 cm3
T1 = 36°C = 309K
V2 = ?
T2 = 94°C = 367K
WORK:
P1V1T2 = P2V2T1
E. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law Problems
A gas occupies 473 cm3 at 36°C. Find its volume at 94°C.
CHARLES’ LAW
T V
(473 cm3)(367 K)=V2(309 K)
V2 = 562 cm3
![Page 9: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/9.jpg)
GIVEN:
V1 = 100. mL
P1 = 150. kPa
V2 = ?
P2 = 200. kPa
WORK:
P1V1T2 = P2V2T1
E. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law Problems
A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa.
BOYLE’S LAW
P V
(150.kPa)(100.mL)=(200.kPa)V2
V2 = 75.0 mL
![Page 10: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/10.jpg)
GIVEN:
V1 = 2.00 L
n1 = 5.00 moles
n2 = 10.0 moles
V2 = ?
WORK:
V1n2 = V2n1
(2.00 L)(10.0 moles)
=(5.00 moles) V2
V2 = 4.00 L
E. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law Problems A sample of gas occupies 2.00 L with 5.00 moles present.
What would happen to the volume if the number of moles is increased to 10.0?
V n AVOGADRO’S LAW
![Page 11: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/11.jpg)
GIVEN:
V1 = 7.84 cm3
P1 = 71.8 kPa
T1 = 25°C = 298 K
V2 = ?
P2 = 101.325 kPa
T2 = 273 K
WORK:
P1V1T2 = P2V2T1
(71.8 kPa)(7.84 cm3)(273 K)
=(101.325 kPa) V2 (298 K)
V2 = 5.09 cm3
E. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law ProblemsE. Gas Law Problems
A gas occupies 7.84 cm3 at 71.8 kPa & 25°C. Find its volume at STP.
P T VCOMBINED GAS LAW
![Page 12: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/12.jpg)
Ch. 14 - GasesCh. 14 - Gases
II. Two More LawsII. Two More Laws
![Page 13: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/13.jpg)
B. Dalton’s LawB. Dalton’s LawB. Dalton’s LawB. Dalton’s Law
The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases.
Ptotal = P1 + P2 + ...When a H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor.
![Page 14: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/14.jpg)
GIVEN:
PH2 = ?
Ptotal = 94.4 kPa
PH2O = 2.72 kPa
WORK:
Ptotal = PH2 + PH2O
94.4 kPa = PH2 + 2.72 kPa
PH2 = 91.7 kPa
B. Dalton’s LawB. Dalton’s LawB. Dalton’s LawB. Dalton’s Law
Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.
Look up water-vapor pressure on p.899 for 22.5°C.
Sig Figs: Round to least number of decimal places.
The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor.
![Page 15: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/15.jpg)
GIVEN:
Pgas = ?
Ptotal = 742.0 torr
PH2O = 42.2 torr
WORK:
Ptotal = Pgas + PH2O
742.0 torr = PH2 + 42.2 torr
Pgas = 699.8 torr
A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas?
Look up water-vapor pressure on p.899 for 35.0°C.
Sig Figs: Round to least number of decimal places.
B. Dalton’s LawB. Dalton’s LawB. Dalton’s LawB. Dalton’s Law
The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.
![Page 16: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/16.jpg)
Ideal Gas LawIdeal Gas Law
Ch. 14 GasesCh. 14 Gases
![Page 17: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/17.jpg)
PV
TVn
PVnT
A. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas Law
= kUNIVERSAL GAS
CONSTANTR=0.0821 Latm/molK
R=8.315 dm3kPa/molK
= R
You don’t need to memorize these values!
Merge the Combined Gas Law with Avogadro’s Principle:
![Page 18: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/18.jpg)
A. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas Law
UNIVERSAL GAS CONSTANT
R=0.0821 Latm/molKR=8.315
dm3kPa/molK
PV=nRT
You don’t need to memorize these values!
![Page 19: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/19.jpg)
GIVEN:
P = ? atm
n = 0.412 mol
T = 16°C = 289 K
V = 3.25 LR = 0.0821Latm/molK
WORK:
PV = nRT
P(3.25)=(0.412)(0.0821)(289) L mol Latm/molK K
P = 3.01 atm
C. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law Problems Calculate the pressure in atmospheres of
0.412 mol of He at 16°C & occupying 3.25 L.
![Page 20: I. The Gas Laws Ch. 14 - Gases. A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2](https://reader034.vdocuments.net/reader034/viewer/2022042616/56649f085503460f94c1d3df/html5/thumbnails/20.jpg)
GIVEN:
V = ?
n = 85 g
T = 25°C = 298 K
P = 104.5 kPaR = 8.315 dm3kPa/molK
C. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law Problems
Find the volume of 85 g of O2 at 25°C and 104.5 kPa.
= 2.7 mol
WORK:
85 g 1 mol = 2.7 mol
32.00 g
PV = nRT(104.5)V=(2.7) (8.315) (298) kPa mol dm3kPa/molK K
V = 64 dm3