Exercise Problems

Consider diffusion with a first order isothermal reaction in a rectangular pellet.[ll] [8]. The governing equation and boundary conditions for concentration in dimensionless form are  

Consider the diffusion reaction problem (problem 1) with a mass transfer resistance at the surface.[6] [11] The governing equation and boundary conditions for dimensionless concentration are  

Redo problem 4 if the boundary condition at x = 0 is c(0) = 1. Plot the concentration profiles for Pe = 5 and Da = 1. How does the exit concentration compare with problem 4 for low and high values of Peclet number (for Da = 1)  

A continuous-flow reactor A is to be designed to carry out a liquid-phase second-order irreversible reaction A + B C + D. The rate equation is (-Ca) = EC Cb. The concentrations of A and B in the feed solution are 5 kmol/m and 10 kmol/ m, respectively. The rate constant k = 0.1 m /kmol min. Calculate the space time required to achieve 80% conversion of A in (i) an ideal CSTR and (ii) an ideal PER. (Answer (i) 6.67 min (ii) 2.20 min) 

A total of 80% conversion of A is achieved when an irreversible reaction A B with rate equation (-Va ) = EC is carried out in an ideal CSTR having space time of 200 s. The conversion drops to a value of 73%, when the feed flow rate is doubled. Estimate the reaction order n and the rate constant k. 

A continuous-flow reactor is to be designed to carry out a non-elementary liquid-phase reaction A B -i- C whose rate equation is given by 

Calculate the space time required to achieve 95% of the equilibrium conversion of a first-order reversible reaction A B carried out in an ideal PER. The feed concentration of A is 1 kmol/m. The rate constant of the forward reaction is ki = 0.1 S and the equilibrium constant is X = 5. 

A third-order irreversible reaction A B with rate equation (r ) = kC is carried out in a battery of six numbers ideal CSTRs of equal volumes connected in series. The rate constant is fc = 0.1 (mVkmol) /min. The feed concentration of A is 2 kmol/m. The space time of each one of the CSTRs is 2 min. (i) What is the net conversion of A achieved in the battery of CSTRs (ii) What is the conversion in one single CSTR having space time equal to the sum of space times of all the six CSTRs  

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Similar treatments of base catalysis are left as an exercise (Problem 10-13). There is for specific base catalysis an additional mechanism, known as nucleophilic catalysis. 

Section 3 Exercises, Problems, and Solutions Review Exercises... 

Matrix multiplication is associative, that is, (AB)C = A(BC), assuming all the products are defined. The proof follows from (2.11) and is left as an exercise (Problem 2.2). 

The four normalized wave functions v//, f/2, f/3, f/4 that correspond to these four energies are found by solving the appropriate simultaneous equations the details are left as an exercise (Problem 8.8) the wave functions are... 

This case is known as partially competitive inhibition. The derivation of the rate equation is left as an exercise problem. 

In an earlier exercise (Problem 4.23) the structures of all the isomeric C5H120 alcohols were presented. Those that lack a stereogenic center and thus are achiral are... 

Written in an accessible style with numerous illustrations, exercises, problems and solutions to aid comprehension, this book is suitable for graduate students and researchers in inorganic chemistry, physical chemistry, materials science, and condensed matter physics. 

Consider potential distribution in porous electrode (Newman, 1991 [15] exercise problem 7 of chapter 3.1). For nonlinear Butler-Volmer kinetics dimensionless overpotential rj is governed by ... 

Complete the details missing in example 5.2.2. Consider chapter 5.1, exercise problem 9. 

Consider the cooling of spherical nuclear pellets (Rice and Do, 1995 [2] chapter 5.1, exercise problem 7). The dimensionless temperature distribution is governed by ... 

Consider the Graetz problem in planar geometry (chapter 5.1, exercise problem 11). The governing equations and boundary/initial conditions are ... 

Obtain an analytical solution for the Graetz problem described in example 5.6 and exercise problem 6 in chapter 7. 

Consider the fluid flow problem (Davis, 1984 [5] chapter 5.1, exercise problem 10 chapter 7, exercise problem 10) ... 

Consider the electrochemical discharge of spherical particles[6] (Subramanian and White, 2001 chapter 7, exercise problem 14). Governing equations, and boundary and initial conditions for this problem are ... 

Redo exercise problem 13, chapter 7 using the Laplace transform technique if the flux at the surface is a function of time. 

Consider diffusion with a second-order reaction in a cylindrical catalyst pellet (exercise problem 2 chapter 3). Solve this problem using recursion technique described in section 10.1.2. 

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