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Unit IX:Gases
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Behavior of GassesThe push or pull particles exert over a particular area is called pressurePressure plays a role in our everyday
livesExamples:
The pascal (Pa) is the SI unit of pressure
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A device that measures atmospheric pressure is called the barometerInvented in 1643 by Evangelista Torricelli
(Italian;1608-1647)Student of Galileo’s
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Units of Pressure
The SI unit for pressure is the Pascal (Pa)Sample EquationsNote: Solve by dimensional analysis, with the
correct number of significant figures! Not necessarily in standard scientific
notation.
1. 842 mm Hg → Pa2. 12.8 psi → atm3. 1.88 bars → torr4. 1.25 atm → kPa5. .78 atm → mm Hg
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Boyle’s LawThe first careful experiments on gases was conduced by Robert BoyleIrish (1627 – 1691)Performed J – Tube experiments
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Formula:P1V1 = P2V2
Pressure (before)(Can be in any units)
Volume (before)(Can be in any units)
Pressure (before)(units consistent with P1)
Volume (after)(units consistent with V1)
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Gas Law Problem SolvingSet-up an Information MatrixThe abbreviations STP or ST or SP are often
used in place of numbers1st set of
conditions (Before Change)
2nd set of conditions
(After Change)
Pressure
Volume
Temperature
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Sample Problem 1: A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. What is the new volume of the container if the pressure decreases to 1.87 atm?
P
V
T
Condition 1
Condition 2
3.54 atm
1.87 atm
23.1 L ?
V2 = P1V1
P2
V2 = (3.54 atm ● 23.1 L)
(1.87 atm)
= 43.7 L
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Charles’ LawJacques Charles was the 1st to fill a balloon with H2 gasFrench Physicist (1746 – 1823)Showed the volume of a given gas (at
constant pressure) increases with temperature
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Formula:V1T2 = V2T1
Volume (before)(Can be in any units)
Temperature (after)(Kelvin – K)
Volume (after)(units consistent with V1)
Temperature (before)(Kelvin - K)
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Sample Problem 2: Your are given 1.2 L of oxygen gas measured at 380 torr and 18°C. What will be the volume when the temperature goes up to 307°C?
P
V
T
Condition 1
Condition 2
380 torr
380 torr
1.2 L ?
V2 = V1T2
T1
V2 = (1.2 L ● 580 K)
(291 K)
= 2.4 L18°C
291 K
307°C
580 K
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Combined Gas LawBoyle’s and Charles’ Law can be combinedPressure, Volume, and Temperature are
inter-relatedFormula: P1V1 P2V2
T1 T2
=
OR P1V1T2 = P2V2T1
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Sample Problem 3A: A helium balloon with a volume of 410. mL is cooled from 27°C to -27°C. The pressure on the gas is reduced from 110. kPa to 25 kPa. What is the new volume of the gas?
P
V
T
Condition 1
Condition 2
110. kPa
25 kPa
410. mL
?
V2 = P1V1T2
P2T1
V2 = (110 kPa • 410. mL • 246 K)
(25 kPa • 300 K)
= 1.5 x 103 mL27°C
300 K
-27°C
246 K
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Sample Problem 3B: A gas sample is originally at STP. If the volume was originally 10.5 L, then what will happen to the pressure when the temperature rises to 109°F?
P
V
T
Condition 1
Condition 2
1.00 atm
?
10.5 L
P2 = P1V1T2
V2T1
P2 = (1.00 atm • 316 K)
(273 K)
= 1.16 atm273 K109°F
316 K
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The Ideal Gas LawThe Ideal Gas Law relates the number of particles to pressure, volume, and temperatureBased on Avogadro’s Principle
Equal volumes of gases at the same temperature and pressure contain equal numbers of particles
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Formula:
P V = n R T
Pressure (atm)
Volume (L)
Moles (mol)
Temperature (K)
Universal Gas Constant(0.0206 L • atm / K • mol)
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There are some limitations to the Ideal Gas Law1. Works well at low pressures & high
temperatures
2. Most gases do not behave ideally at 1 atm
3. Does not work well near the condensation conditions of a gas
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Remember the Gas Law Problem Solving Matrix
Condition 1
Condition 2
P
V
n
T
All Gas Law matrices should include mol (n) from this point!
You won’t necessarily know what Gas Law you will be solving!
The Ideal Gas Law will not use Condition 2!
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Sample Problem 4A: A 333 g sample of Radon gas has a volume of 2.1 x 104 mL at 33°C. What is the pressure of the gas?
P = n R T
V
P = (1.5 mol • .08206… • 306 K)
21 L
1.8 atm=
Condition 1
Condition 2
P
V
n
T
?2.1 x 104
mL
333 g Rn gas
33°C
21 L
1.5 mol
306 K
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Sample Problem 4B: Calculate the volume of hydrogen produced at 1.50 atm and 19°C by the reaction of 26.5 g of Zn with excess hydrochloric acid?
1 Zn (s) + 2 HCl (aq) → 1 ZnCl2 (aq) + 1 H2 (g)
1 2
PVn
T
1.50 atm
?
2.65 g Zn
19°C
?
.405 mol
292 K
1.50 atm
V = n R T
P
V = (.405 mol • .08206… • 292 K)
1.50 atm
6.5 L H2=
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The density of a gas can be determined by using the Ideal Gas LawFormula:
D=M P
R T
Density (g/L)
Universal Gas Constant(0.0206 L • atm / K • mol)
Temperature (K)
Pressure (atm)Molar Mass (g)