# Differential Equations

The topic is chemical reaction rate.

Two substances A and B are combined to form a product C. The formation of product is proportional to the time the reactants are combined. The final product is composed of three parts of A for every part of B. If initially A is 50 lbs and B is 60 lbs, and 10 lbs of the product is formed after 45 mins., find the time it takes for the reaction to form 25 lbs.

### As a KeMiST, I say we need

As a KeMiST, I say we need more (and clear) information.
"The formation of product is proportional to the time the reactants are combined" seems to mean that the reaction rate is constant. That is what we would call a zero order reaction.
If that were so, it would take 22.5 minutes to form 5 lb of product, and 112.5 minutes to form 25 lb.
If the answer is 135 minutes, the reaction rate is not constant.
it could be proportional to the amount or concentration of one or both reactants or, to a power of those amounts.
With the information, we could set up a differential equation. For many reaction mechanisms, the generic differential equation has been solved into a formula for chemists who cannot solve differential equations.

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