2. Diffusion and Reaction in a Sphere ( 25 pts) A sphere comprised of pure species B is exposed to species A at its surface, uniformly around the entire surface. Species A is soluble in the sphere at a mole fraction of xAo. Species A begins to diffuse into the sphere because of the concentration gradient from the outside to the inside of the sphere. There is no flow inside the sphere and no reaction occurs. From the table of the Equation of Continuity for Species A presented in lecture on Wednesday Jan. 25, 2023, a) Which of the equations would you choose? b) Write this equation down, and then decide which terms in the equation to keep and which terms to reject. State your reasons for keeping or rejecting terms in the equation. c) What is the final form of the equation of continuity for this problem? B.11 The Equation of Continuity for Species A in Terms of A for Constant AAB851 SB.11 THE EQUATION OF CONTINUITY FOR SPECIES A IN TERMS OF A FOR CONSTANT aaDAB [DA/Dt=DAB2A+rA] Cartesian coordinates (x,y,z) : (tA+vxxA+vyyA+vzzA)=DAB[x22A+y22A+z22A]+rA Cylindrical coordinates (r,,z) : (tA+vrrA+rvA+vzzA)=DAB[r1r(rrA)+r2122A+z22A]+rA Spherical coordinates (r,,) : (tA+vrrA+rvA+rsinvA)=DAB[r21r(r2rA)+r2sin1(sinA)+r2sin2122A]+rA a To obtain the corresponding equations in terms of xA, make the following replacements