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Pressure, Volume, Temperature The 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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Boyles 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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Boyles 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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Boyles Law: Formula P 1 = initial pressure V 1 = initial volume P 2 = final pressure V 2 = final volume If you know three of the four, you can calculate the fourth. P 1 V 1 = P 2 V 2

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Boyles Law: Sample Problems P 1 V 1 = P 2 V 2 A sample of oxygen gas has a volume of 150. ml when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature does not change? Standard Problem More Difficult Problem It is hard to begin inflating a balloon. A pressure of kPa is required to initially inflate the balloon 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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Boyles Law: Sample Problem P 1 V 1 = P 2 V 2 A sample of oxygen gas has a volume of 150. ml when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature does not change? P 1 V 1 = P 2 V 2 P 2 = P 2 P 1 V 1 = V 2 P 2 V 2 = (0.947)(150.) = 144 ml of O 2 (.987) P 1 = atm V 1 = 150. ml P 2 = atm V 2 = what problem is looking for

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Charles Law Jacques Charles discovered the relationship between volume and temperature in The law states that the volume of a sample of gas at constant pressure varies directly with Kelvin temperature st hydrogen balloon volume temperature

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Charless Law: Graphically -constant pressure -directly proportional

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Charless Law: Formula V1T1V1T1 = V2T2V2T2 V 1 = initial volume T 1 = initial temperature V 2 = final volume T 2 = final temperature If you know three of the four, you can calculate the fourth.

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Charless Law: Sample Problem A sample of neon gas occupies a volume of 752 ml at 25 o C. What volume will the gas occupy at 50 o C if the pressure remains constant? T 2 V 1 T 2 V 2 T 1 T 2 T 2 V 1 T 1 V 2 = (752)( ) = 815 ml Ne ( ) V1T1V1T1 = V2T2V2T2 = = V2V2

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Gay-Lussacs 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-Lussacs Law: Formula P1T1P1T1 = P2T2P2T2 P 1 = initial pressure T 1 = initial temperature P 2 = final pressure T 2 = final temperature If you know three of the four, you can calculate the fourth.

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Gay-Lussacs Law: Sample Problem The gas in an aerosol can is at a pressure of 3.00 atm at 25 o C. The can warns not to allow the temperature to get above 52 o C. What would the pressure of the can be at 52 o C? T 2 P 1 T 2 P 2 T 1 T 2 T 2 P 1 T 1 P 2 = (3.00)( ) = 3.25 atm ( ) P1T1P1T1 = P2T2P2T2 ==P2P2

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LAW RELATIONSHI P LAWCONSTANTBoyles P V P V P 1 V 1 = P 2 V 2 T, n Charles V T V T V 1 /T 1 = V 2 /T 2 P, n Gay- Lussacs P T P T P 1 /T 1 = P 2 /T 2 V, 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.

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Sample Combined Gas Law Problem A sample of helium gas has a volume of L, a pressure of 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 P 1 = atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ??

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Pressure, Volume, Temperature Lets 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

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