Chem 373 HW 1_math worksheet(1) - A’ and B’ are...

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Chem 373 HW 1 Due Tuesday Jan 29 th 1) Convert the x, y coordinates into polar coordinates a) (2,2) b) (4,-1) c) (1,5) 2) Convert the polar coordinates into x,y coordinates a) r = 6, Ө = 145º b) r = 3, Ө = 35º c) r = 3.16, Ө = 225º 3) Convert the x, y, z coordinates into spherical coordinates a) (3,2,1) b) (-1,0,4) c) (-3,-6,-12) 4) Determine the modulus |z| and phase angle for the following complex numbers. a) 3 b) 2 + 2i c) -4 -4i 5) Show that e - = cos(θ) i sin(θ ) using the infinate series expanstions for e x , sin x and cos x 6) Show that cos(θ) = ½ (e + e - ) and sin(θ ) = 1/(2i) {e - e - } 7) Find the values of m that satisfy the equation e 2πi m = 1 (Hint: Express the exponential in terms of sines and cosines.) 8) Show that A e ikx + Be -ikx , where A and B are arbitrary constants, is equivalent to the sum A’sin (kx) + B’cos (kx), where
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Unformatted text preview: A’ and B’ are different arbitrary constants. 9) Plot the followiing functions choosing suitable coordinats axes: a) E k = ½ mv 2 (constant m) b) V = -e 2 /r (e is a constant, not e x ) c) F = - e 2 /r 2 (e is a constant, not e x ) d) [A] = [A] o e-kt (A, A o , and k are constants) e) 1/[A] = kt + C (k and C are constants) f) k r = Ae E/RT (E, R, and A are constants) 10) Plot 9 a, and f choosing coordinates such that the result is a straight line 11)The apparent pH of an aqueous solution is defined by the equation pH = - log 10 (H + ). Find the apparent pH of the following solutions: a) (H + ) = 1.00 x 10-7 M b) (H + ) = 1.416M 12) Given the following values for the apparent pH, find the hydrogen ion concentrations. a) pH = 0 b) pH = 7.555...
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