Gas Laws. Heat and Temperature

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1 Gas Laws Heat and Temperature Often the concepts of heat and temperature are thought to be the same, but they are not. Perhaps the reason the two are incorrectly thought to be the same is because as human beings on Earth everyday experience leads us to notice that when you heat something up, say like putting a pot of water on the stove, then the temperature of that something goes up. More heat, more temperature - they must be the same, right? Turns out, though, this is not true. Temperature is a number that is related to the average kinetic energy of the molecules of a substance. If temperature is measured in Kelvin (K), then this number is directly proportional to the average kinetic energy of the molecules. K = o C A regular thermometer uses the expansion of a fluid to measure temperature. When the liquid (mercury or alcohol) in a thermometer is heated the average kinetic energy of the liquid particles increases, causing the particles to take up more space expanding them up the tube. There are three types of particle motion. Translational - whole atom or molecule changes its location, Rotational - whole molecule spins on its axis and Vibration - motion that changes the shape by causing the stretching, bending, or rotation of bonds. Translation and rotation occurs in liquids and gases and vibration only happens in solids. At 0K there is no motion (translation, rotation) or vibration of particles so the average kinetic energy is zero. The absolute temperature or Kelvin scale is an artificial scale. The Celsiusscale is based on the behavior of water molecules, with 0 o C being its freezing point of water or the point where the motion of the water molecules ceases. The Celsius scale has limited use when describing the motion of many substances, especially gases whose motions can cease at much lower temperatures. The mathematical conversion between o C and Kelvin is: C = K K -273 = C If Temperature is measured in Kelvin, then it is directly proportional to the average kinetic energy of the particles. Notice we did not say that temperature is the kinetic energy. We said it is a number, if in degrees Kelvin, proportional to the average kinetic energies of the molecules; that is, if you double the Kelvin temperature of a substance, you double the average kinetic energy of its molecules. KE α Absolute temp (K) Heat is a measurement of the total energy in a substance. That total energy is made up of not only of the kinetic energies of the molecules of the substance, but total energy is also made up of the potential energies of the molecules. It is measured in Joules (J). When heat energy goes into a substance one of two things can happen: 1 P a g e

2 1. The substance can experience a raise in temperature. That is, the heat can be used to speed up the molecules of the substance. 2. The substance can change state. Although heat is absorbed by this change of state, the absorbed energy is not used to speed up the molecules. The energy is used to change the bonding between the molecules. Heat comes in and there is an increase in the potential energy of the molecules. Their kinetic energy remains unchanged. So, when heat comes into a substance, energy comes into a substance. That energy can be used to increase the kinetic energy of the molecules, which would cause an increase in temperature. Or that heat could be used to increase the potential energy of the molecules causing a change in state that is not accompanied by an increase in temperature. 2 P a g e

3 An ideal gas is a model of how a perfect gas would behave according to the gas laws. They obey the ideal gas laws (Charles, Boyles, Gay-Lussacs, Avogadros, Combined). Gas that don t exactly obey the ideal gas laws are called real gases. No real gas can meet the ideal gas models criteria. Kinetic Theory Kinetic theory is a model used to describe the characteristics of a gas. According to kinetic theory gas particles (atoms/molecules): 1) are in constant random motion. There is no order. 2) have mass. 3) have no or negligible intermolecular forces between their particles. 4) have elastic collisions. This means that no attractive or repulsive forces are involved during collisions. Also, the kinetic energy of the gas molecules remains constant since there are no (negligible) intermolecular forces between them (IMF s). 5) do not have a fixed volume and will expand to fill the volume of the container. 6) the volume and pressure decreases proportionally with a decrease in temperature until both reach absolute zero. 7) the average K.E of the particles α absolute temperature (K). 8) the spaces between the particles is large so they can spread out and fill the container they occupy. 9) are in constant random motion they can create pressure when they collide with one another and the walls of the container. 10) have low densities. 11) diffuse (spread out) easily because of their relatively small masses and high velocity. 12) compress easily because the space between them and the particles is large. The volume occupied by the gas is greater than the volume occupied by the particles due to the large spaces between them. 13) expand on heating. Will expand without limit if they are not in a sealed container. Pressure occurs when gaseous molecules / atoms collide with the walls of the container. Many different experiments in the 17th and 18th centuries were carried out using kinetic theory to provide further evidence of how gases behave. The results of these experiments lead to the Boyles, 3 P a g e

4 Charles and Gay-Lussac/Pressure Laws. These laws explain the relationship between pressure, volume and temperature of an ideal gas mathematically. Boyles Law P α 1 when the temperature is constant V Equation P 1 V 1 = P 2 V 2 Explained at a molecular level using kinetic theory, as the volume increases the gas particles have more space and so collide with one another and the walls of the container less frequently, causing the pressure to decrease. 4 P a g e

5 Solving Gas Law problems The Steps: 1. Identify the law used to solve each problem 2. Identify the constant (P, V or T) 3. Identify the unknown 4. Do unit conversion where necessary 5. Show all the calculations/steps 6. Write the answer using the correct number of significant digits and the proper units Units Pressure, P in Pa (or atm) (1 atm = 1 x 10 5 Pa ; 1 Pa = KPa) Volume, V in m 3 or dm 3 (1m 3 = 1000 dm 3 ) Moles, n in mol Temperature, T in K ( C = K) Ideal Gas Constant, R is 8.31 J K -1 mol -1 (this unit is for when P is in KPa, V in dm 3, T in K and n in mol) NOTE: When using the ideal gas equations ensure that the correct units are used. If V is given in L or dm 3 convert to m 3 by dividing by Example 1 A perfectly elastic balloon has a volume of 1.2 dm 3 at a pressure of atm. Assuming the temperature remains constant, what volume will the balloon occupy if the pressure is reduced to atm. 5 P a g e

6 Charles Law Charles law states that V α T when the pressure is constant Equation V 1 = V 2 T 1 T 2 Explained at a molecular level using kinetic theory, as the temperature increases the average kinetic energy of the gas particles increases making them take up more space. The volume increases in order to keep the pressure constant. Example 2 A partially filled party balloon contains 2.6 dm 3 of helium gas at atmospheric pressure and a temperature of 12 C. Calculate the volume the balloon will occupy if it warms to a temperature of 20 C at atmospheric pressure? 6 P a g e

7 Gay Lussacs Law (Pressure Law) Gay-Lussacs law states that P α T when the volume is constant Equation P 1 = P 2 T 1 T 2 Explained at a molecular level, as the temperature increases the average kinetic energy of the gas particles increases. The particles collide with one another and the walls of the container with more force increasing the pressure. 7 P a g e

8 Ideal Gas Equation P V = n R T Formula for density d = m (g) v (dm 3 ) (gdm -3 ) Determining the volume of an ideal gas of known m or n, M, T, and P: n = m (g) M (gmo l-1 ) (mol) P V = n R T V = n R T P V = m R T M P Example 3 Determine the volume 52.0g of carbon dioxide will occupy at a temperature of 24 C and 206 KPa? 8 P a g e

9 Determining the molar mass, M of an ideal gas of known P, T, m or n and V: n = m (g) M (gmo l-1 ) (mol) P V = n R T n = P V R T m = PV M RT Molar Mass, M = m R T P V (M r is relative molar mass) Example cm 3 of an unknown gas has a mass of g at 25 C and 0.97 atmospheres. Determine the molar mass of the gas? 9 P a g e

10 Determining the density of a gas of known T, P, M and m or n: P V = n R T and d = m V V = n R T P m = n R T d P d = P m n R T or since n = m M d = P m m R T M d = P m M m R T d = P m M m R T d = P M (M can also be M r ) R T The Combined Gas Law A combination of Boyles, Charles and Gay-Lussacs laws. Is used to determine the fixed mass of an Ideal gas. P 1 V 1 = P 2 V 2 T 1 T 2 Boyles, Charles and Gay-Lussacs laws can be obtained from this law by holding one quantity (P, V or T) constant. 10 P a g e

11 Example 5 An expandable balloon contains 95.0dm 3 at 1.0 atm and 24 C. What volume will the balloon occupy when the pressure drops to atm and the temperature is 11 C. Questions 1. Which change in conditions would increase the volume of a fixed mass of gas? Pressure/kPa Temperature/K A. Doubled Doubled B. Halved Halved C. Doubled Halved D. Halved Doubled 2. All of the following are characteristic properties of gases EXCEPT A. They can expand without limit. B. They diffuse readily. C. They are easily compressed. D. They have high densities. 3. Which pressure expression represents the density of a gas sample of relative molar mass, M r, at temperature, T, and pressure, P? A. PM r T B. RT_ PM r C. PM r _ RT D. RM r PT 11 P a g e

12 4. The molar mass of an unknown gas is to be determined by weighing a sample. As well as its mass, which of the following must be known? I. Pressure II. Temperature III. Volume A. I only B. II only C. I and II only D. I, II, and III 5. Which of the following best accounts for the observation that gases are easily compressed? A. Gas molecules have negligible attractive forces for one another. B. The volume occupied by the gas is much greater than that occupied by the molecules. C. The average energy of the molecules in a gas is proportional to the absolute temperature of the gas. D. The collisions between gas molecules are elastic. 6. In which gas sample do the molecules have the greatest average kinetic energy? A. H 2 at 100 K B. CH 4 at 273 K C. H 2 O at 373 K D. CH 3 OH at 353 K 7. The temperature in Kelvin of 2.0 dm 3 of an ideal gas is doubled and its pressure is increased by a factor of four. What is the final volume of the gas? A. 1.0 dm 3 B. 2.0 dm 3 C. 3.0 dm 3 D. 4.0 dm 3 8. When the pressure is increased at constant temperature, the particles in a gas will: A. become smaller B. become larger C. move faster D. be closer together 9. Which quantity will not change for a sample of gas in a sealed rigid container when it is cooled from 100 C to 75 C at a constant volume? A. The average kinetic energy of the molecules B. The pressure of the gas C. The density of the gas 12 P a g e

13 10. A sample of gas has a certain volume at a temperature of 60 C. What must the temperature be in order to double the volume if the pressure is kept constant? A. 120 C B. 333 C C. 393 C D. 666 C 11. A 250 cm 3 sample of an unknown gas has a mass of 1.42 g at 35 C and 0.85 atmospheres. Which expression gives its molar mass, M r? (R = cm 3 atm K -1 mol -1 )? A X X X 0.85 B X X X 0.85 C X 250 X X 308 D X X X Which one of the following changes in conditions would give the greatest increase in the rate at which particles collide with the walls of the container? A. Increasing the temperature of the gas and increasing the volume of gas. B. Increasing the temperature of the gas and decreasing the volume of the gas. C. Decreasing the temperature of the gas and decreasing the volume of the gas. D. Decreasing the temperature of the gas and increasing the volume of the gas. 13. When a bicycle tire is pumped up with air at constant temperature, assuming any change in its volume can be neglected, the pressure increase comes from the fact that: A. The gas particles are moving faster. B. The collisions with the wall occur at a greater frequency. C. Each collision transfers more momentum to the wall than before. D. Two or three of the changes mentioned in A, B, and C occur simultaneously. 14. For which set of conditions does a fixed mass of an ideal gas have the greatest volume? Temperature Pressure A. low low B. low high C. high high D. high low (1) 13 P a g e

14 15. M00/420/S(2) (a) In hydrogen gas what happens to the average speed of the molecules if the temperature is increased? [1] (b) Explain in terms of molecules, what happens to the pressure of a sample of hydrogen gas if the volume is halved and the temperature is kept constant. [3] 16. N01/420/H(2) The mass of a gas sample is measured under certain conditions. List the variables that must be measured and show how these can be used to determine the molar mass of a gas. [4] 17. Floating balloons are filled with helium. Explain why these always deflate more quickly than those blown up with air. (2) 14 P a g e

15 Bibliography Clugston, Michael and Rosalind Flemming. Advanced Chemistry. Oxford: Oxford University Press, Derry, Lanna, Maria Connor and Carol Jordan. Chemistry for use for the IB Diploma Standard level. Melbourne: Pearson Education, Green, John and Sadru Damji. Chemistry for use with the International Baccalaureate Programme. Melbourne: IBID Press, Neuss, Geoffrey. IB Diploma Programme Chemistry Course Companion. Oxford: Oxford University Press, IB Study Guides, Chemistry for the IB Diploma. Oxford: Oxford University Press, Organisation, International Baccalaureate. Online Curriculum Centre. < "Chemistry Data Booklet." International Baccalaureate Organisation, March "Chemistry Syllabus." International Baccalaureate Organisation, March "IB Chemistry Examination Papers." Cardiff: International Baccalaureate Organisation, Answers 1. D 2. D 15 P a g e

16 3. C 4. D 5. B 6. C Temp average kinetic energy 7. A 8. D 9. C 10. A Charles law, when P is constant when you double the V the T will double 11. D 12. B 13. B 16 P a g e