The religion of Islam (an Arabic word meaning “submission to God”) arose
among the people .... The use of tiles has a long history in the Middle East. The
art of ...
teachers find these notes useful, I would be happy to know that my work was ... (
Chapter, section, page, and formula numbers refer to the 6th edition of this text.).
SUTCLIFFE'S NOTES: CALCULUS 2 SWOKOWSKI'S CHAPTER 13. PLANE
CURVES AND POLAR COORDINATES. 13.1 Plane Curves. Definition A plane ...
y' = rw â y â xz (o, r, b are constant parameters) z' = xy â bz ... system, the trajectories in the phase plane ar
World War I and the Depression reduced monies available to support institutions.
2. ..... Trace the history of the treatment of people with psychological disorders,
and identify the major .... Answers to Practice Test Questions. Multiple Choice.
www.wiley.co.uk/go/gollmann. 2. Objectives. Brief survey of network security
challenges. Show how network security contributes to and depends on computer
...
Section 13F Chapter Summary. Section 13G Problems. Section 13H Solutions to
Practice Exercises. There are many ways to categorize analytical techniques, ...
In this chapter you will look at geometry as Euclid did. You will .... The next
example is Exercise 8 in your book. It takes ..... compare your answers to those
below.
(From Elkin, M.K., Perry, A.G., Potter, P.A. [2004]. Nursing interventions and
clinical skills. [3rd ed.]. ... Sterile technique is followed whenever the wound or.
The high voltage AC output from the twin electrostatic discs. 2. A moderate AC
...... invention incorporated an alternator from a 1997 Isuzu Trooper. The
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media. Record Date All persons whose names are recorded as stockholders on
the .... backdrop for discussion of the key arguments in support of dividend ...
Chapter 13. The Detection of ... and VP2 (58 kDa), which form the 20 nm diameter viral capsid (1). ... detection during PCR due to sequence differences between geno- types 1 and 3, means ... A number of parvoviruses, distantly related to the erythro-
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for a multicultural world by celebrating diversity in an inclusive classroom
environment, ... In this chapter, we choose to use the term English Language
Learner (ELL), as it ..... learn about the history and nature of science (Content
Standard G,
Does not account for the total costs of producing a product on a recurring basis and that full. (totally absorbed) costing, as in traditional accounting, is a better ...
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13-1. CHAPTER 13. Corporations: Organization and. Capital Stock Transactions
... 4. Explain the accounting for treasury stock. 7, 13,. 14, 15. 6. 5, 7, 8,. 11, 13.
Chapter 13 : Möbius Transformations page 2 of 13 .... A Möbius transformation, or
a bilinear transformation, is a rational function T : C → C of the form. T(z) =.
Ancient India. Chapter 13 Geography and the Early Settlement of India ... In Unit
2, you explored the world of the ancient Egyptians, the. Hebrews, and the ...
share, standardization of the product, and/or free entry and exit, explain your .....
The accompanying table presents prices for washing and ironing a man's shirt ...
Chapter 13. Are There ... 13-3. Background. • Fundamental rights guaranteed by
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sectarians, wherever they might have lived in Judah and the Judean hills, from where, ... Textual writing was first developed in Mesopotamia (Elam), where cuneiform ... Egyptians also started to write, making use of hieroglyphs and pictograms.
D. Genetics of organisms used in applied and medical science is important. E.
Many genetic systems in microbes have counterparts in prokaryotes (i.e. ...
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1. Chapter 13 - Chemical Equilibrium. Intro. A. Chemical Equilibrium. 1. The state
where the concentrations of all reactants and products remain constant with ...
Chapter 13 - Chemical Equilibrium Intro A. Chemical Equilibrium 1. The state where the concentrations of all reactants and products remain constant with time 2. All reactions carried out in a closed vessel will reach equilibrium a. If little product is formed, equilibrium lies far to the left b. If little reactant remains, equilibrium lies far to the right 13.1 The Equilibrium Condition A. Static Equilibrium does not occur in chemical systems 1. No reaction is taking place 2. All product molecules will remain product 3. All unused reactant molecules will remain unreacted B. Dynamic Equilibrium 1. Reactions continue to take place 2. Reactant molecules continue to be converted to product 3. Product continues to be converted to reactant (reverse reaction) 4. Forward and reverse reactions take place at the same rate at equilibrium C. Causes of Equilibrium 1. Beginning of reaction a. Only reactant molecules exist, so only reactant molecules may collide 2. Middle a. As product concentration increases, collisions may take place that lead to the reverse reaction 3. At equilibrium a. Rates of forward and reverse reactions are identical D. Example - The Haber Process 1.
N2(g) + 3H2(g) 2NH3(g) a. hydrogen is consumed at 3x the rate of nitrogen b. ammonia is formed at 2x the rate at which nitrogen is consumed
1
13.2 The Equilibrium Constant A. The Law of Mass Action 1. For the balanced equation: jA + kB
lC + mD
(j, k, l, m) are coefficients
The law of mass action is represented by the equilibrium expression: [C ]l [ D] m K= [ A] j [ B] k a. K is a constant called the equilibrium constant (1) K varies depending on temperature and upon the coefficients of the balanced equation b. [X] represents concentration of chemical species at equilibrium 2. For the reverse reaction lC + mD jA + kB The law of mass action is represented by the equilibrium expression: [ A] j [ B ] k 1 K' = = l m K [C ] [ D] B. Equilibrium Position 1. A set of equilibrium concentrations 2. There is only one value of K for a reaction at a given temperature, but an infinite number of possibilities for equilibrium positions C. Summary of the Equilibrium Expression 1. The equilibrium expression for a reaction is the reciprocal of that for the reaction written in reverse 2. When the balanced equation for a reaction is multiplied by a factor n, the equilibrium expression for the new reaction is the original expression raised to the nth power Knew = (Koriginal)n 3. For a particular reaction at a given temperature, the value of K is constant regardless of the amounts of gases that are mixed together (homogeneous rxn system) 13.3 Equilibrium Expressions Involving Pressure A. Derivation of Equilibrium Gas Laws n 1. PV = nRT therefore… P = RT V n/V is the molar concentration of the gas, represented by C P = CRT 2. For the reaction N2(g) + 3H2(g)
2NH3(g)
In terms of concentrations K c =
C NH 3
3
(C N 2 )(C H 2 )
In terms of partial pressures K p =
2
2
PNH 3
2 3
( PN 2 )( PH 2 )
B. Relationship between K and Kp 1. K p = K ( RT ) ∆n a. ∆n = (l + m) - (j + k) the difference in the sums of the coefficients for the gaseous products and reactants 13.4 Heterogeneous Equilibria A. The position of a heterogeneous equilibrium does not depend on the amounts of pure solids or liquids present B. If pure solids or liquids are involved in a chemical reaction, their concentrations are not included in the equilibrium expression for the reaction C. Pure liquids are not the same as solutions, whose concentration can change 13.5 Applications of the Equilibrium Constant A. Extent of a Reaction 1. Reactions with large equilibrium constants (K>>1) go essentially to completion a. Equilibrium position is far to the right b. Generally large, negative ∆E 2. Reactions with small equilibrium constants (K