pressure, volume, temperature the gas laws. learning objectives understand the qualitative...
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Pressure, Volume, TemperatureThe Gas Laws
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Learning Objectives
• Understand the qualitative relationship between pressure (P) and volume (V) and temperature (T), when you have a gas
• Learn the three gas laws and how to apply them mathematically to solve problems
• Combine the gas laws into one equation, and solve problems where P, V, and T are no longer constant.
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Boyle’s Law• Robert Boyle, studied the relationship
between pressure, p, and volume, V, in the mid-1600s.
• When he doubled the pressure on a sample of gas at constant temperature, its volume was reduced by one-half.
pressure
volume
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Boyle’s Law: Graphically
-constant temperature-inverse relationship
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Connection To Your Math Class
Asymptote- A line that continually approaches a given curve but does not meet it at any finite distance.
Greek word that means “not falling together”
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Boyle’s Law: Formula
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
If you know three of the four, you can calculate the fourth.
P1V1 = P2V2
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Boyle’s Law: Sample Problems
P1V1 = P2V2
A sample of oxygen gas has a volume of 150. ml when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature does not change?
Standard Problem
More Difficult Problem
It is hard to begin inflating a balloon. A pressure of 800.0 kPa is required to initially inflate the balloon 225.0 mL. What is the final pressure in mm Hg when the balloon has reached it's capacity of 1.2 L??
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Boyle’s Law: Sample Problem
P1V1 = P2V2A sample of oxygen gas has a volume of 150. ml when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature does not change?
P1V1 = P2V2
P2 = P2
P1V1 = V2
P2
V2 = (0.947)(150.) = 144 ml of O2
(.987)
P1 = 0.947 atmV1 = 150. mlP2 = 0.987 atmV2 = what problem is looking for
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Charles’ Law• Jacques Charles discovered the relationship
between volume and temperature in 1787.
• The law states that the volume of a sample of gas at constant pressure varies directly with Kelvin temperature.
1783 - 1st hydrogen balloon
volume
temperature
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Charles’s Law: Graphically
-constant pressure-directly proportional
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Charles’s Law: Formula
V1
T1
= V2
T2
V1 = initial volume
T1 = initial temperature
V2 = final volume
T2 = final temperature
If you know three of the four, you can calculate the fourth.
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Charles’s Law: Sample Problem
A sample of neon gas occupies a volume of 752 ml at 25oC. What volume will the gas occupy at 50oC if the pressure remains constant?
T2V1 T2V2
T1 T2
T2V1
T1
V2 = (752)(273 +50) = 815 ml Ne (273 + 25)
V1
T1
= V2
T2
= = V2
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Gay-Lussac’s Law• Joseph Gay-Lussac is credited with discovering
relationship between pressure and temperature, but the discovery should actually go to Guillaume Amontons (1699).
• There is a Gay-Lussac's law but it has to do with the ratio of the volumes of gases in a chemical reaction, the "law of combining volumes".
pressure
temperature
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Gay-Lussacs Law: Graphically
-constant volume-direct relationship
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Gay-Lussac’s Law: Formula
P1
T1
= P2
T2
P1 = initial pressure
T1 = initial temperature
P2 = final pressure
T2 = final temperature
If you know three of the four, you can calculate the fourth.
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Gay-Lussac’s Law: Sample Problem
The gas in an aerosol can is at a pressure of 3.00 atm at 25oC. The can warns not to allow the temperature to get above 52oC. What would the pressure of the can be at 52oC?
T2P1 T2P2
T1 T2
T2P1
T1
P2 = (3.00)(273 +52) = 3.25 atm (273 + 25)
P1
T1
= P2
T2
= = P2
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LAWLAW RELATIONSHIRELATIONSHIPP
LAWLAW CONSTANTCONSTANT
Boyle’sBoyle’s PP V V PP11VV1 1 = P= P22VV22 T, nT, n
Charles’Charles’ VV T T VV11/T/T11 = V = V22/T/T22 P, nP, n
Gay-Gay-Lussac’sLussac’s PP T T PP11/T/T11 = P = P22/T/T22 V, nV, n
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The Combined Gas Law
The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.
2
22
1
11
T
VP
T
VP
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Sample Combined Gas Law Problem
A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature (°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?
Set up Data Table
P1 = 0.800 atm V1 = 180 mL T1 = 302 K
P2 = 3.20 atm V2= 90 mL T2 = ??
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Pressure, Volume, Temperature
Let’s see what we already know about these three variables …
Gas Law Program
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NOVA: Race for Absolute Zero
Try not to lose your head when you are doing chemistry
and
Why you should always wear your safety goggles