Gas Laws and Kinetic Molecular Theory

2. The Gas Laws

3. Kinetic Molecular Theory • Particles in an ideal gas… • have no volume. • have elastic collisions. • are in constant, random, straight-line motion. • don’t attract or repel each other. • have an avg. KE directly related to Kelvin temperature. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

4. many different molecular speeds molecules sorted by speed Molecular Velocities Fractions of particles the Maxwell speed distribution speed http://antoine.frostburg.edu/chem/senese/101/gases/slides/sld016.htm

5. Real Gases • Particles in a REAL gas… • have their own volume • attract each other • Gas behavior is most ideal… • at low pressures • at high temperatures • in nonpolar atoms/molecules Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

6. Characteristics of Gases Gases expand to fill any container. • random motion, no attraction Gases are fluids (like liquids). • no attraction Gases have very low densities. • no volume = lots of empty space Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

7. Characteristics of Gases • Gases can be compressed. • no volume = lots of empty space • Gases undergo diffusion & effusion. • random motion Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

8. Properties of Gases V = volume of the gas (liters, L) T = temperature (Kelvin, K) P = pressure (atmospheres, atm) n = amount (moles, mol) Gas properties can be modeled using math. Model depends on:

9. PT V P T V PT V 1 V Boyle’s P a ___ a Charles V T a Gay-Lussac’s P T Pressure - Temperature - Volume Relationship

10. P T V P n V 1 V Boyle’s P a ___ a Charles V T a Gay-Lussac’s P T Pressure - Temperature - Volume Relationship

11. Robert Boyle • Boyle: His Life • Born on January 25, 1627 in Ireland • His father was the wealthiest man in the British Isles • Youngest of fourteen children • Boyle was a very shy, devoutly religious man • He was once offered a position in the clergy, but turned it down because he was more interested in the sciences. • He died on December 30, 1691, and left the gist of his estate to charitable organizations.

12. Robert Boyle • Boyle:His Scientific Career • Known as the “Father of Modern Chemistry” • First scientist to perform controlled experiments and publish his reports and work. • Responsible for Boyle’s Law, which states that at constant temperature, the pressure and volume of a gas are inversely proportional to each other.

13. Robert Boyle Boyle: His Law Explained At constant temperature, the volume of a gas is inversely proportional to pressure. In other words, when temperature remains the same, as pressure is increased, the volume of the gas will decrease. This is an INVERSE relationship. The Formula is: P1V1=P2V2 P1=original pressureP2= New pressure V1= Original volumeV2= New Volume

14. Robert Boyle Example: The Volume of a gas is 50 ML at a pressure of 1 atm. If the volume increases to 100 ML, and the temperature remains constant, what will the new pressure be? P1=1 atm. P2= ? V1= 50 ML. V2= 100 ML Put the numbers in the equation: 1atm(50 ML)=P2(100 ML) Divide both sides by 100. 100 (P2) 50 ------------------------------ = ------------------------------ P2= 0.5 atm. 100 100 The New Pressure is .5 atm.

15. Robert Boyle Boyle’s law is important to Scuba Divers. They need to ascend slowly, because as they come closer to the surface, the pressure exerted by the water decreases, which means the volume of air in their lungs increases. If a diver were to ascend very quickly, the pressure would decrease rapidly, causing the air in the lungs to increase rapidly, resulting in the Diver “exploding.”

16. Jacques Charles • Charles: His Life • Charles was born on November 23, 1746 in Beaugency, France. • As a child, he learned only basic math and hardly any science. • Charles became interested in science after the ambassador from the United States, Benjamin Franklin, visited Paris. • Although he is responsible for “Charles Law,” it was not published until 15 years after his initial discovery, by Josepgh Gay-Lussac.

17. Jacques Charles • Charles: His Scientific Career: • Although Charles is well known for his gas law, he was better known for his aeronautic research. • In 1783, he realized that Hydrogen was lighter than air and made the first balloon using hydrogen gas. • On August 27, 1783, Charles’s balloon ascended nearly 3,000 feet. Upon witnessing this, hordes of angry peasants destroyed the balloon after it landed, believing it was some type of evil or witchcraft. • In 1787, Jacques Charles discovered the relationship between the volume of gas and temperature (Charles’s law.)

18. Jacques Charles Charles: His Law Explained: At Constant pressure, the Volume of a gas is directly proportional to temperature (must be in Kelvin.) In other words, as temperature increases, so too, does volume. Notice that it’s absolutely imperative that the temperature is in degrees Kelvin (K=C+273) The Formula is: V1 V2 ---------- = ----------- T1 (Kelvin) T2 (Kelvin)

19. Jacques Charles Example: At 200K, the volume of a gas is 100 ML. The temperature is raised to 300K, what will the new volume be? V1=100 MLT1 =200K V2= ?T2=300K Substitute the numbers in the Equation: 100 V2 ------- = ------- 200 300 Cross Multiply: 200 (V2)= 30,000 Divide Both Sides By 200: 200 V2 30,000 30,000 ------------- = ------------ V2 = ---------- = 150 200 200 200 The New Volume is 150 ML.

20. Amedeo Avogadro • Avogadro: His Life: • Avogadro was born on August 9, 1776 in Turin, Italy. • He was born into a family of respected lawyers, and he intended to carry the family tradition, graduating with a degree in law at the age of twenty. He became interested in the sciences, however, and in 1800, he began studies in math and science. • He had six children and was very religious.

21. Amedeo Avogadro • Avogadro: His Scientific Career: • While employed as a teacher in Vericelli, Avogadro wrote a note, declaring the hypothesis, now known as Avogadro’s law. • His hypothesis wasn’t accepted until after his death, in 1858. • Avogadro is responsible for resolving the confusion surrounding atoms and molecules. • He believed that particles were composed of molecules, and that molecules were made up of smaller units; atoms. • Avogadro is also responsible for discovering the number of molecules in one mole. (6.02 x 10 23) Translation:(Good thing I take Italian) “Equal volumes of gas in the same conditions of temperature and pressure contain the same number of molecules”

22. Amedeo Avogadro Avogadro: His Law Explained: Equal Volumes of gases under the same conditions of temperature and pressure have the same number of molecules. Therefore, if more gas is added, the number of molecules will increase, as well, which will cause the volume to increase. One mole has 6.02 x 10 23particles, and one mole of gas occupies 22.4 L. .

23. Amedeo Avogadro Example: How many molecules are in 11.2 liters of a gas at STP? Since one mole of gas contains 22.4 L, 11.2 L is exactly half of that. Therefore, if one mole contains 6.02 x 1023 particles, than half of that is 3.01 x 1023. There are approximately 3.0 x 1023 molecules in 11.2 L. of a gas at STP.

24. John Dalton • John Dalton: His Life: • John Dalton was born in 1766, in Cumberland, England • For most of his life, Dalton was employed as a teacher and public lecturer. • He was very interested with weather, and kept daily weather records from 1787 until his death. • Dalton was a Quaker, meaning he believed in nonviolence. • He led a very modest life, although he received many honors for his accomplishments. • After he died, more than 40,000 people marched at his funeral procession.

25. John Dalton • John Dalton: His Scientific Career: • Known as one of the fathers of modern physical science. • Developed the atomic theory of matter. • Devised a system of chemical symbols • formulated the theory that a chemical combination of different elements occurs in simple numerical ratios by weight. • Discovered Butylene and determined the composition of ether • Developed an atomic theory, stating that all elements are composed of tiny, indestructible particles called atoms that are all alike and have the same atomic weight.

26. John Dalton Dalton: His Law Explained Dalton’s Law of partial pressures states that the sum of the partial pressures of all the components in a gas mixture is equal to the total pressure of the gas mixture. Pt= Pa+Pb+Pc Pt=The total pressure of a gas mixture. Pa+Pb+Pc= the individual pressures of each component

27. Joseph Louis Gay-Lussac • Lussac:His Life: • Born in 1778, in France. • Grew up during the French Revolution. • His father was a very successful lawyer, who, during the revolution was imprisoned. • selected to attend the École Polytechnique, an exclusive institution designed to create scientific and technical leadership.

28. Joseph Louis Gay-Lussac • Lussac:His Scientific Career: • Lussac’s study of gasses led him to make several trips nearly 7,000 meters above sea level in a Hydrogen balloon. • Gay-Lussac also participated in early electrochemical research. • With the help of other scientists, he decomposed boric acid by using fused potassium, thus discovering the element boron.

29. Joseph Louis Gay-Lussac Lussac: His Law Explained: As Temperature increases, Pressure increases, when volume remains constant. P1 P2 ------- = --------- T1 T2

30. Combined Gas Law P1 V1 P2 V2 ---------- = ----------- T1 T2

31. Ideal Gas Ideal Gases follow all laws perfectly. How to get a gas to behave like an ideal gas: LOW PRESSURE, so the molecules have lots of room to spread out. HIGH TEMPERATURE, They want a lot of kinetic energy to overcome Intermolecular forces

32. Boyle’s Law P1V1 = P2V2 Charles’ Law Combined V1 = V2 T1 = T2 P1V1 = P2V2 T1 = T2 Graham’s Law Gay-Lussac Density P1 = P2 T1 = T2 P1 = P2 diffusion vs. effusion T1D1 = T2D2 Gas Law Calculations Ideal Gas Law PV = nRT Dalton’s Law Partial Pressures PT = PA + PB 1 atm = 760 mm Hg = 101.3 kPa R = 0.0821 L atm / mol K