Bloom s Taxonomy. Study Habits and Study Resources: Pause. Expectations: Develop a working knowledge of the topics.

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1 Dr. C. Weldon Mathews Chem 1 Office: 004 Evans Lab Telephone: mathews.6@osu.edu web: Office hours: TR 1:30 - :00 pm TR 4:00-5:00 pm or by appointment Chapters we ll cover in Chem 1: 10, 11, 13, 14, 15, 16, 17 ( ) First Week: Second Week: and First Quiz: Week of Jan 17 (third week) Review Chem 11, especially Chaps 8 and 9 Expectations: Develop a working knowledge of the topics. Knowledge Simple recall of facts Bloom s Taxonomy Comprehension Translate into your own words or equations. Application Apply concepts to specific situations; recognizing and solving a problem when the equations are not given. Analysis Application plus recognition of important parts of problem. Synthesis Assemble components into a form new to them, i.e. design a research plan or devise a synthetic scheme. Evaluation Judge the value of materials in terms of internal and external criteria. Grossly abbreviated adaptation from Bloom, B. S. (Ed.) (1956) Taxonomy of educational objectives;: The classification of educational goals: Handbook I, cognitive domain. New York; Toronto: Longmans, Green see also Study Habits and Study Resources: a) Lectures and Reading - minimal impact by themselves b) Chemistry is not a Spectator Sport! rof. Janet Tarino, OSU Mansfield c) Recitation and Laboratory TAs d) Ask questions and seek help whenever you need it! e) Web resources: /~mathews/chem1/ /~rbartosz/ /~rzellmer/ chemistry ->Undergraduate rogram->interactive Tutorials First Lab Experiment: Stoichiometry and Gas Volume KClO 3 (s) KCl (s) + 3 O (g) Apparatus is simple, shown in the next slide Depends on the Ideal Gas Equation, V = nrt Recall some of the results of applying this simple equation V = constant /T = constant These results work extremely well... OR DO THEY??? ause 1

2 Begin nd week? Chapter 10 Gases 9.1 Characteristics of Gases 9. ressure Atmosopheric ressure and the Barometer 9.3 The ressure-volume Relationships: Boyle s Law The Temperature-volume Relationship: Charles s Law 9.4 The Ideal-Gas Equation Relating the Ideal-Gas Equation and the Gas Laws 9.5 Further Applications of the Ideal-Gas Equation Gas Densities and Molar Mass Volumes of Gases in Chemical Reactions 9.6 Gas Mixtures and artial ressures artial ressures and Mole Fractions Collecting Gases over Water 9.7 Kinetic-Molecular Theory Application to the Gas Laws 9.8 Molecular Effusion and Diffusion Graham s Law of Effusion Diffusion and Mean Free ath 9.9 Real Gases: Deviations from Ideal Behavior The van der Waals Equation 10.1 Characteristics of Gases Gases are highly compressible and occupy the full volume of their containers. Contrast with liquids and solids. When a gas is subjected to pressure, its volume changes. Gases always form homogeneous mixtures with other gases. Gases only use about 0.01 % of the volume of their containers. Characteristics of Gases 10. ressure ressure is the force acting on an object per unit area: F = A Gravity exerts a force on the earth s atmosphere A column of air 1 m in cross section exerts a force of 10 5 N. The pressure of a 1 m column of air is about 100 ka. F = A F = ma = (10 4 kg)(9.8m/s ) = 1 x 10 5 kg-m/s = 1 x 10 5 N 5 F 1 x 10 N = = A 1 m = 1 x 10 5 N/m = 1 x 10 5 a = 1 x 10 ka = Newton ressure ressure Atmosphere ressure and the Barometer SI Units: 1 N = 1 kg.m/s ; 1 a = 1 N/m. Atmospheric pressure is measured with a barometer. If a tube is inserted into a container of mercury open to the atmosphere, the mercury will rise 760 mm up the tube. Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a column. Units: 1 atm = 760 mmhg = 760 torr = a = ka.

3 In our discussions about gases, we ll often use the gas cylinder with a movable piston as a helpful analogy. You also may think of a bicycle pump as an example. ressure Atmosphere ressure and the Barometer Notice that the top end of the BAROMETER is closed and that a Torricelli VACUUM exists above the mercury. ressure Atmosphere ressure and the Barometer The pressures of gases not open to the atmosphere are measured in manometers. A MANOMETER consists of a bulb of gas attached to a U-tube containing Hg: If gas < atm then gas + h = atm. If gas > atm then gas = atm + h. Note that h may be positive or negative! ressure Notice again the various units that may be used to measure ressure: Easiest to refer to the Standard Atmospheric ressure which is defined as 1 atm 1 atm = ka = x 10 5 a = = 760 mmhg = 760 torr And, this relationship will help you recall the conversion factors between the various units. End of Lecture, 1/4/ The ressure-volume Relationship: Boyle s Law Weather balloons are used as a practical consequence to the relationship between pressure and volume of a gas. As the weather balloon gets further from the earth s surface, the atmospheric pressure decreases. As a consequence, the volume of the balloon increases. Boyle s Law: the volume of a fixed quantity of gas is inversely proportional to its pressure. Boyle used a manometer to carry out the experiment. 3

4 The ressure-volume Relationship: Boyle s Law Mathematically: 1 V = constant = A plot of V versus is a hyperbola. Similarly, a plot of V versus 1/ must be a straight line passing through the origin. k V = constant V = k The ressure-volume Relationship: Boyle s Law V = k V = k/ The Temperature-Volume Relationship: Charles s Law We know that hot air balloons expand when they are heated. Charles s Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases. Mathematically: V = constant = kt T V T = constant = k These are typical of observations you might make in the lab. Notice that on this plot the equation is of the form y = a + b x and the volume does NOT go to 0 at x = 0!!! The Temperature-Volume Relationship: Charles s Law A plot of V versus T is a straight line. When T is measured in C, the intercept on the temperature axis is C. We define absolute zero, 0 K = C. Note the value of the constant reflects the assumptions: of a constant amount of gas and pressure. And now the equation is of the form y = bx, i.e. a = 0. 4

5 Gay-Lussac s Law of combining volumes: at a given temperature and pressure, the volumes of gases which react are ratios of small whole numbers. Avogadro s Hypothesis: equal volumes of gas at the same temperature and pressure will contain the same number of molecules. : the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas. Mathematically: V = constant n = k n We will show that.4 L of any gas at 0 C and 1 atm contain gas molecules = 1 mole of molecules The Ideal Gas Equation The Ideal Gas Equation Consider the three gas laws. 1 Boyle s Law: V (constant n, T ) Charles s Law: V T (constant n, ) : V n (constant, T ) We can combine these into a general gas law: nt nt V = k If the k is now defined as R, the proportionality constant of (called the gas constant), then nt V = R The ideal gas equation is: V = nrt R = L atm/mol K = J/mol K But how can you derive the value of R? 5

6 Recall this slide and how to convert grams to moles. The Ideal Gas Equation We define ST (standard temperature and pressure) = 0 C, K, 1 atm. And now we see the volume of 1 mol of gas at ST is: V = nrt nrt ( 1mol)( L atm/mol K )( K) V = = =.41L atm ( notice the > should be a / ) Fig shows the actual results for a number of gases. Notice that the ideal gas model does a pretty good job. The Ideal Gas Equation Relating the Ideal-Gas Equation and the Gas Laws If V = nrt and n and T are constant, then V = constant and we have Boyle s law. Other laws can be generated similarly. In general, if we have a gas under two sets of conditions, then V 1 1 V = n1t 1 nt 10.5 Further Applications of the Ideal-Gas Equation Gas Densities and Molar Mass Density has units of mass over volume. Rearranging the ideal-gas equation with M as molar mass we get V = nrt n = V RT nm M = d = V RT has units of mol L -1 And now the units are g L -1 6

7 Further Applications of the Ideal-Gas Equation Gas Densities and Molar Mass The molar mass of a gas can be determined as follows: drt M = Volumes of Gases in Chemical Reactions The ideal-gas equation relates, V, and T to number of moles of gas. The n can then be used in stoichiometric calculations. Further Applications of the Ideal-Gas Equation Volumes of Gases in Chemical Reactions Consider now the application of these ideas to chemical reactions. eg, NaN 3 (s) Na + 3 N (g) Given the mass of sodium azide that reacts, the number of moles of nitrogen gas generated may be calculated. From this, the volume may be calculated at a given temperature and pressure. What volume of gas at 760 torr and 0 o C would be generated from 3.51 g of sodium azide which decomposes according to the equation NaN 3 (s) Na + 3 N (g)? In order to answer this question, we need to know how many moles of nitrogen will be generated (see Chem 11). Then we apply the ideal gas law. 1mol NaN 3 3mol N 3.51g NaN3 = 0. 75mol N 65.0 g NaN 3 mol NaN 3 V = nrt or V = yields theequation V nrt = ( 0.75mol N )( 0.081L atm / mol K )( 73K ) = L of N gas 1 atm 10.6 Gas Mixtures and artial ressures Since gas molecules are so far apart, we can assume they behave independently. Dalton s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component: total = L Each gas obeys the ideal gas equation: RT i = ni V (Sorry about the mistake given in lecture!) Gas Mixtures and artial ressures Combing the equations ( ) RT total = n1 + n + n3 + L V artial ressures and Mole Fractions Let n i be the number of moles of gas i exerting a partial pressure i, then = Χ total where Χ i is the mole fraction (n i /n t ). i i A mixture of gases containing mol He(gas 1), mol Ne (gas), and mol Ar (gas 3) is confined in a 7.00-L vessel at 5 0 C. (a) Calculate the partial pressure of each gas. (b) Calculate the total (b)pressure in the vessel. (c) Calculate the mole fraction of each gas. 1 = n 1 RT / V = (0.538 mol)(0.081 L-atm/mol-K)(98 K) / (7.00 L) = 1.88 atm of He similarly, = 1.10 atm of Ne, and 3 = atm Ar The total pressure is just T = = i = = 3.34 atm The mole fraction of He is X 1 = 1 / T = 1.88/3.34 = (This also could be obtained from X 1 = n 1 / n T = 0.538/0.956 Likewise, X = 0.39 and X 3 = note that X i = 1.00 always (within error limits): =

8 Gas Mixtures and artial ressures Collecting Gases over Water It is common to synthesize gases and collect them by displacing a volume of water. To calculate the amount of gas produced, we need to correct for the partial pressure of the water: total = gas + water Gas Mixtures and artial ressures Collecting Gases over Water 10.7 Kinetic Molecular Theory Theory developed to explain gas behavior. Theory based on properties at the molecular level. Assumptions: Gases consist of a large number of molecules in constant random motion. Volume of individual molecules negligible compared to volume of container. Intermolecular forces (forces between gas molecules) negligible. 8