Unit 9 Notes – Gas Laws Background – Science Laws, Theories and Hypotheses Laws are generalizations or universal relationships related to the way that some aspect of the natural world behaves under certain conditions. Therefore, laws are different from hypotheses and theories in science. An initial investigation provides some evidence (data) that must be explained and tested further. This tentative explanation, or hypothesis, forms the foundation for further investigations. If the hypothesis is supported, more investigations are done. As it becomes stronger, it becomes more predictive and explanatory. At this point, the hypothesis becomes a theory: a broad explanation that has been supported with data and is a well substantiated, consistent explanation for a natural occurrence. Theories evolve as a result of continued testing. When evidences is found that is inconsistent with or not predicted by the theory, it must be changed. In some cases, a new theory must be proposed and tested further. I. Kinetic Theory of Gases This theory helps us understand why gases behave the way they do and give us insight into the behavior of solids and liquids. There are five basic postulates of this theory. 1.Particles in a gas have no volume and are very far apart. 2.Particles in a gas move in straight line paths and random directions. 3.Particles in a gas collide frequently with the sides of the container and less frequently with each other. All collisions are elastic (no energy is gained or lost as a result of the collisions). 4.Particles in a gas do not attract or repel one another. There is no intermolecular attractions. 5.The average kinetic energy of all of the gas particles in a sample is proportional to the temperature of that gas sample. II. Temperature Temperature is a measure of the average kinetic energy of a substance. Many problems we will be working use equations which include temperature, it is important to be able to convert between Celsius and Kelvin. 0 Kelvin is absolute zero; there are not negative numbers on the Kelvin scale. A. Converting between Celsius and Kelvin. Celsius to Kelvin K = oC + 273 Kelvin to Celsius oC = K – 273 B. Example: Convert: –167oC to Kelvin 1100oC to Kelvin 321 Kelvin to Celsius Unit 9 Notes: Gas Laws III. Pressure: defined as Force/Area. We will not be concerned with the mathematical aspect of finding pressure, but only using pressures and converting them to various other units. A. There are different UNITS of pressure used in chemistry and you must be able to convert between all of them. 1 atmosphere (atm) You must be able to = 760 mm Hg convert pressure units! = 14.7 psi = 101.3 kPa Example: Convert a pressure of 1.55 atm to kPa. Example: Which is higher pressure 1.45 atm or 1000 mm Hg? Example: Convert 753 psi to atmospheres. B. Pressure Measurement 1. Standard Temperature & Pressure (STP) is equal to 1 atm at 0°C III. Introduction to Gas Laws Based on the kinetic theory of gases, scientists were able to describe how gases behave and change using mathematical equations. There are 4 variables that work together to determine the behavior of gases – temperature, pressure, volume, and the number of particles. A. When you blow up a balloon, you are adding gas molecules & the pressure increases. This is because more molecules are colliding within a given space. Pressure and the number of gas molecules are directly related. Doubling the number of molecules of a gas, doubles the pressure. Gases naturally flow from areas of high pressure to low pressure until the pressure becomes equal. B. When you push on a bicycle pump or the end of a syringe, you change the size of the container creating a pressure that can be felt. In a smaller container, molecules have less room to move & hit the sides of the container more often. This creates pressure. 2 Unit 9 Notes: Gas Laws C. When you heat a gas, the temperature of a gas increases as a result of increased kinetic energy. This increase in energy causes the gas molecules to hit the walls of its container even harder – resulting in either increased pressure or increased volume. IV. Dalton’s Law of Partial Pressure – Equal amounts of gas at the same temperature and volume have equal pressure. The total pressure inside a container is equal to the partial pressure due to each gas. P total = P1 + P2 + P3 A. For instance, we can find the pressure in the fourth container by adding up the pressure in the first three containers. 2 atm 1atm 3atm ? atm B. Example: What is the total pressure in a balloon filled with air if the pressure of the oxygen is 170mmHg and the pressure of nitrogen is 620 mmHg? Example: In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mmHg? 3 Unit 9 Notes: Gas Laws V. Boyle’s Law – At constant temperature, pressure and volume are inversely related. In other words, as volume decreases, the pressure increases and vice versa. P1 x V1 = P2 x V2 Example: A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure changes to 1.5 atm, what is the new volume? Example: A balloon is filled with 73 L of air at 1.3 atm of pressure. What pressure is needed to change the volume to 43 L ? VI. Charles’ Law – The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. As temperature increases, volume also increases in a linear relationship. V1 / T1 = V2 / T2 Example: What is the temperature of a gas that is expanded from 2.5L at 25°C to 4.1 L at constant pressure? 4 Unit 9 Notes: Gas Laws Example: What is the final volume of a gas that starts at 8.3L and 290K and is heated to 369K? VII. Gay Lussac’s Law – If volume doesn’t change, then as temperature increases, pressure also increases. They are directly related. If a gas is in a fixed container, as the temperature increases the molecules collide more frequently with the walls of the container causing increased pressure. P1 / T1 = P2 / T2 Example: What is the pressure inside a 0.250L can of deodorant that starts at 0.250L and 1.2 atm if the temperature is raised to 100°C? Example: At what temperature will the can above have a pressure of 2.2 atm? VIII. Combined Gas Law – this law is a combination of the previous STUDY TIP gas laws. This law applies only when the number of molecules stays constant & everything else changes. All other gas laws can be derived from P1 x V1 = P2 x V2 this one equation T1 T2 Example: A 15L cylinder at 4.8 atm pressure at 25°C is heated to 75°C and compressed to 17 atm. What is the new volume? 5 Unit 9 Notes: Gas Laws Example: IF 6.2 L of gas at 723 mm Hg at 294K is compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas? IX. Ideal Gas Law A. In reality, an ideal gas does not exist. In this unit however, we are going to assume that gases behave ideally. This will make our math easier & is a close approximation. Real gases behave like an ideal gas at high temperature & at low pressure. B. Pressure (P) times volume (V) equals the number of moles (n) times the ideal gas constant (R) times the temperature in Kelvin (T) P x V = n x R x T where R = 0.0821 (Latm)/ (molK) or R = 62.4 (Lmm Hg) / (Kmol) Example: How many moles of air are there in a 2.0L bottle at 19°C and 747 mmHg? 6 .