# Nonlinear Differential Equations : Chemical Reactions Problem

Question:

A Chemical X is produced from a reaction involving chemicals A and B. The rate of production of X varies directly as the product of the instantaneous amounts of A and B present. The formation of X requires 6 pounds of A for every 4 pounds of B. 30 pounds of A and 20 pounds of B are present initially and 10 pounds of X are formed in one hour.

a. Find the amount of X present at any time t.

b. Find the amount of X present after 6 hours.

c. Find the maximum amount of X that can be formed under these conditions.

I know that you would use dx/dt = k(Ao - A)(Bo - B). I'm just having problems keeping this straight.

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#### Solution Summary

Nonlinear Differential Equations and Chemical Reactions are investigated. The solution is detailed and well presented.