reactant or the rate of increase of the concentration of a product. The rate law is an equation that expresses the rate of a reaction as a function of the concentration of all the species present in the overall chemical reaction at some time. The rate law is often found to be proportional to the concentration of the reactants raised to a power. For the depolymerization of diacetone alcohol the empirical rate equation is -∂x∂t=kxn[OH-]m (1) X= concentration of diacetone alcohol ‚ t=time ‚ k=rate
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* 9/4/12 12.3 - crystal structures crystalline structure: possess rigid and long-range order; its atoms‚ molecules‚ or ions occupy specific positions (Exs. wax ‚ice‚ sugar‚ salt‚ diamond‚ etc.) unit cell: basic repeating structural unit of crystalline solid -there are seven types of unit cells coordination number: number of atoms surrounding an atom in a crystal lattice -higher coordination number --> more tightly packed structure 3 types of cubic unit cells: -primitive cubic (sc) c#:
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Maxwell Cohen Table of functions used in ENGR 132 Type of equations General form The plot that shows your data as linear Linear y=mx + Linear Standard graph b Y vs. X Exponential X y=bemx ln(y) =mx+ln(b) Y = mx+B semilogy mx y=b10 log(y) =mx+log(b) log(Y) vs. X Logarithmic* x=bemy ln(x) =my+ln(b) X = my+B semilogx my x=b10 log(x) =my+log(b) Y vs. log(X) Power y=bxm ln(y)=m*ln(x)+ln(b) Y = mX+B log-log log(Y) vs. log(X) *logarithmic equations with calculations done in Excel or MATLAB you will have
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–––– Run ∆y y 2 - y1 ––– = ––––––– ∆x x 2 - x1 1- Solve for y to put the equation in slope intercept form. 2- Plot the y-intercept. 3- Using the slope as a fraction‚ rise y and run x to get second point. 4- Graph the line. Ex: 2x+3y=12 -2x -2x ––––––––– 3y=-2x+12 –– –––– 3 3 y= -2/3x+4 m= -2/3 b= 4 Horizontal and Vertical Lines: - A Horizontal Line has the form y=#. (In an equation of a horizontal line‚ there is no x) - The slope of a horizontal line is 0. Picture:
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Aristotle attributed the first of what could be called a scientific discussion on magnetism to Thales of Miletus‚ who lived from about 625 BC to about 545 BC.[1] Around the same time‚ in ancient India‚ the Indian surgeon‚ Sushruta‚ was the first to make use of the magnet for surgical purposes.[2] There is some evidence that the first use of magnetic materials for its properties predates this‚ J. B. Carlson suggests that the Olmec might have used hematite as a magnet earlier than 1000BC[3] [4] In
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mass-spring-damper system. The governing differential equation of a mass-spring-damper system is given by m x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system. Example 2 Consider the system given by the differential equation y + 4 y + 3 y = 2r (t )‚ where r(t) is the input to
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Point-Slope Form of the Equation of a Line 9 Section 2.3 Linear Functions and Slopes Write the point-slope form of the equation of the line with slope of 3 that passes through (-1‚2). Substitute into the point-slope form; y-y1 m( x x1 ) y 2 3( x 1) y 2 3( x 1) 10 Section 2.3 Linear Functions and Slopes Solving in Both Forms A. Write the equation in point slope form of the line with slope 4 that passes through the point (4‚-3). B. Then solve the equation for y. x1 y1 y-y1 = m(x-x1)
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Differential Equations 1 2 NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS Introduction Differential equations can describe nearly all systems undergoing change. They are ubiquitous is science and engineering as well as economics‚ social science‚ biology‚ business‚ health care‚ etc. Many mathematicians have studied the nature of these equations for hundreds of years and there are many well-developed solution techniques. Often‚ systems described by differential equations are so complex
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was weighed and the mass was measured. Then we calculated the moles of the precipitate. From these calculations‚ we established moles of the limiting reactant‚ were the same amount of moles in the product based on the stoichiometrically balanced equation. Next the percent yield of the limiting reactant was calculated. In Part B of this experiment‚ two solutions were added to the aqueous product in order to determine the limiting reactant. Once each solution was added‚ we were able to visibly see
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CHM 2330 Physical Chemistry Lab Winter 2015 Manual revised 2006 by Maude Boulanger (with Prof. P. Mayer and Prof. D. Bryce) Contact information: Prof. David Bryce dbryce@uottawa.ca -1- TABLE OF CONTENTS Schedule of experiments .......................................................................................................... - 3 General Lab Information ........................................................................................................ - 4 Guidelines for Laboratory
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