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Department of Chemical Engineering
University of California, Santa Barbara
Chemical Engineering
132B
Computational Methods
in Chemical Engineering
Fall 2011
Homework #4
Homework due: Friday, 28 October 2011
1. Suppose 3 moles of chemical A, 2 moles of chemical B, and 1 mole of chemical D are injected into a
oneliter reaction chamber and the coupled chemical reactions
A
+ 2
B
±
2
C
2
A
+
D
±
C
are allowed to proceed to equilibrium. The equilibrium constants for the reactions are
K
1
= 0
.
0100
and
K
2
= 0
.
0512. Use the multidimensional Newton method to ﬁnd how many moles of A, B, C, and
D are present at equilibrium to three signiﬁcant ﬁgures. (Don’t use a builtin
MatLab
function for
this; write your own program. You can use the
MatLab
backslash operator, however, for solving the
linear system at each iteration step.)
2. Employ the following methods to ﬁnd the maximum of
f
(
x
) = 4
x

1
.
8
x
2
+ 1
.
2
x
3

0
.
3
x
4
to a fractional relative error of 0.001
(a) Newton’s method with
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This note was uploaded on 12/29/2011 for the course CHE 132b taught by Professor Ceweb during the Fall '09 term at UCSB.
 Fall '09
 Ceweb
 Chemical Engineering, Mole

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