Presentation on theme: "Pressure, Volume, Temperature The Gas Laws. Learning Objectives Understand the qualitative relationship between pressure (P) and volume (V) and temperature."— Presentation transcript:
Pressure, Volume, Temperature The Gas Laws
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.
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
Boyles Law: Graphically -constant temperature -inverse relationship
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
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
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??
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
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
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.
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
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
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.
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
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
The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.
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 = ??
Pressure, Volume, Temperature Lets see what we already know about these three variables … Gas Law Program
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