# Download Applied Mathematics for Physical Chemistry (2nd Edition) by James R. Barrante PDF

By James R. Barrante

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Atmlmol . 0 liters. 00 liters. Determine the approximate area graphically by breaking up the area into four rectangles of equal width AV; compare your answer to that found by analytically integrating the function between these limits of integration. 5. Evaluate the following multiple integrals using the Table of Integrals, as needed: " " r Cardr 3. ' - d P ; R and Tconstants e dn, dny dn,; a,b, c, h, rn, k, and Tconstants 6. The equation of a straight line passing through the origin of a Cartesian coordinate system is y = mx, where m is the slope of the line.

I + x3 dy v v2 Problems I 93 9. Show that if we let x = cos 8, the solution to the associated Legendre's equation [Equation (6-4711 is y = cos 8, when l = l and m = 0, and is y = sin 8, when f! = 1 and m = l. 10. Show that if we let x = cos 8, the solution to the associated Legendre's equation [Equation(6-47)]isy= ~ ( 3 c o s 2 8 - l ) , w h e n e = 2 a n d m = 0 . 11. The Schrodinger equation for a particle in a three-dimensional box is (h) dV = nr2 dh + 2nrh dr + nRT v dV; (i) dq = nC, dT ti) PM d p = -dT R T~ ( k ) dE = nC, dT M +dP; RT n, C, and R are constants MandRareconstants.

5. Evaluate the following multiple integrals using the Table of Integrals, as needed: " " r Cardr 3. ' - d P ; R and Tconstants e dn, dny dn,; a,b, c, h, rn, k, and Tconstants 6. The equation of a straight line passing through the origin of a Cartesian coordinate system is y = mx, where m is the slope of the line. Show that the area of a triangle made up of this line and the x axis between x = 0 and x = a is A = :ay. 7. The Kirchhoff equation for a chemical reaction relating the variation of AH of a reaction with absolute temperature is where AC,, represents the change in the heat capacity at constant pressure for the reaction.