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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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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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**P1V1 = P2V2 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.

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**Boyle’s Law: Sample Problems**

P1V1 = P2V2 Standard Problem 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? 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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**Boyle’s Law: Sample Problem**

P1V1 = P2V2 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? P1 = atm V1 = 150. ml P2 = atm V2 = what problem is looking for P1V1 = P2V2 P2 = P2 P1V1 = V2 P2 V2 = (0.947)(150.) = 144 ml of O2 (.987)

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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. volume temperature st hydrogen balloon

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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**

V1 T1 V2 T2 = 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? T2V T2V2 T T2 T2V1 T1 = = V2 V2 = (752)( ) = 815 ml Ne ( )

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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**

T1 P2 T2 = 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? T2P T2P2 T T2 T2P1 T1 = = P2 P2 = (3.00)( ) = atm ( )

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**Summary Boyle’s P V P1V1 = P2V2 T, n Charles’ V T V1/T1 = V2/T2**

LAW RELATIONSHIP CONSTANT Boyle’s P V P1V1 = P2V2 T, n Charles’ V T V1/T1 = V2/T2 P, n Gay-Lussac’s P T P1/T1 = P2/T2 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 P1 = atm V1 = 180 mL T1 = 302 K P2 = 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

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