In the chemical reaction (CH3)CI + N aOH ? CH3OH + N aCI, for every molecule of

Question

In the chemical reaction (CH3)CI + N aOH ? CH3OH + N aCI, for every molecule of methyl chloride one molecule of sodium hydroxide is consumed, thus forming one molecule of sodium chloride. Let X(t) be denotes the amount of CH3OH at time t and ? and ? are the given amounts of the first two chemicals, then the instantaneous amounts that has not been converted are proportional to ? ? X and ? ? X, which is modeled by

X 0 = k(? ? X)(? ? X).

a ) Use the method of separation of variables to find the general solution of the model.

b ) Let ? = 250, ? = 40, X(0) = 0 gram and X(10) = 30 gram. USing part (a) find the value of k and the particular solution of the model.

(c)Find and classify the equilibrium solutions of the model

d ) Using part (c) sketch the direction field of the model.

e ) Using the matlab code dfield8.m in Blackboard confirm the sketch in part (d). In particular, you need to include a few graphs and indicate the specific values of ? and ? for each graph.

Explanation / Answer

The corrected text is:

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.