Gay-Lussac's Law

Joseph-Louis Gay-Lussac

In the early 1800’s,

Gay-Lussac

ascended to a height of approximately 23,000 ft in a

hot air balloon

to study variations in the Earth's

electro-magnetic

intensity relative to

altitude

. On this flight, he experienced the effects of oxygen deprivation but still managed to collect air samples at over 20,000 ft, study the variation of

pressure

and

temperature

, and continue his observations on

electro magnetism

.

What is Gay Lussac’s Law?

Gay-Lussac's Law states that the

pressure

of a sample of gas at constant

volume

, is

directly proportional

to its

temperature

in Kelvin.

Mathematically Gay Lussac’s Law can be expressed as P 1 T 1 = P 2 T 2

P

1

T

2 =

P

2

T

1 • P 1 • T 1 • P 2 • T 2 is the initial pressure is the initial temperature (in Kelvin) is the final pressure is the final temperature (in Kelvin)

Gay Lussacs’s Law Practice Problems

1. A tank of gas has a pressure of 2.75 atm at 20 °C. What will be the new pressure in the tank if its temperature is increased to 100 °C? P 1 T 2 = P 2 T 1 P 1: T 1 : P 2 : T 2 :

2. A gas system has initial pressure of 793 kPa and temperature of 34.5

°C If the pressure changes to 446 kPa, what will the resultant temperature be in K?

P 1 T 2 = P 2 T 1 P 1 : T 1 : P 2 : T 2 :

COMBINED GAS LAW

The combined gas law is a combination of

Boyle's Law

and

Charles's Law

; hence its name the combined gas law. In the combined gas law, the

volume

of gas is

directly proportional

to the absolute

temperature

and

inversely proportional

to the

pressure

.

Mathematically, Combined Gas Law

• P 1 • V 1 • T 1 • P 2 • V 2 • T 2

can be expressed as P

1

V

1

T

1

P

1

V

1

T

2 =

P

2

V

2 is the initial pressure

T

1 is the initial volume is the final pressure is the final volume

= P

2

V

2

T

2 is the initial temperature (in Kelvin) is the final temperature (in Kelvin)

P 1 : V 1 : T 1 : P 2 : V 2 : T 2 :

Combined Gas Law Practice Problems

1. A sample of gas occupies a volume of 75 mL at a pressure of 725 mmHg and a temperature of 18 °C. What volume would this sample of gas occupy at 800 mmHg and 298K?

P 1 V 1 T 2 = P 2 V 2 T 1

P 1 : V 1 : T 1 : P 2 : V 2 : T 2 : 2. A sample of gas occupies a volume of 3.75 L at a pressure of 1.15 atm and a temperature of 25 °C. At what temperature will the sample of gas occupy 4 L at a pressure of 1 atm?

P 1 V 1 T 2 = P 2 V 2 T 1

Abbreviations Combined Gas Law Worksheet: ISN p 127

atm – atmosphere mm Hg - millimeters of mercury

Conversions

K = ° C + 273 1 cm 3 (cubic centimeter) = 1 mL (milliliter) torr - another name for mm Hg Pa - Pascal (kPa = kilo Pascal) K - Kelvin ° C - degrees Celsius 1 dm 0.00 3 ° (cubic decimeter) = 1 L (liter) = 1000 mL

Standard Conditions

C = 273 K 1.00 atm = 760.0 mm Hg = 101.325 kPa = 101,325 Pa

Problems:

1. A gas has a volume of 800.0 mL at minus 23.00 ° C and 300.0 torr. What would the volume of the gas be at 227.0 ° C and 600.0 torr of pressure?

2.500.0 liters of a gas are prepared at 700.0 mm Hg and 200.0 ° C. The gas is placed into a tank under high pressure. When the tank cools to 20.0 ° C, the pressure of the gas is 30.0 atm. What is the volume of the gas?

3. What is the final volume of a 400.0 mL gas sample that is subjected to a temperature change from 22.0 ° C to 30.0 ° C and a pressure change from 760.0 mm Hg to 360.0 mm Hg?

4.What is the volume of gas at 2.00 atm and 200.0 K if its original volume was 300.0 L at 0.250 atm and 400.0 K.

5.At conditions of 785.0 torr of pressure and 15.0 ° C temperature, a gas occupies a volume of 45.5 mL. What will be the volume of the same gas at 745.0 torr and 30.0 ° C?

6.A gas occupies a volume of 34.2 mL at a temperature of 15.0 ° C and a pressure of 800.0 torr. What will be the volume of this gas at standard conditions? 7.The volume of a gas originally at standard temperature and pressure was recorded as 488.8 mL. What volume would the same gas occupy when subjected to a pressure of 100.0 atm and temperature of minus 245.0 ° C?

8.At a pressure of 780.0 mm Hg and 24.2 ° C, a certain gas has a volume of 350.0 mL. What will be the volume of this gas under STP