# Extraordinary Differential Equations #10

Calculus Level 3

Consider two reactants A and B in the following reaction in a 1:1 stoichiometric ratio to give product C: $A+B \rightarrow C$ The reaction is first order with respect to both A and B. You are given that the rate of formation of C is thus directly proportional to the concentrations of both A and B, i.e. we have the following differential equation: $Rate=\frac{d[C]}{dt}=k[A][B]$ where $$[C]$$ is the concentration of C (etc.), and $$k$$ is a proportionality constant called the rate constant. For this particular reaction $$k=2.50\times10^{-4} \text{ dm}^{3} \text{ mol}^{-1} \text{ s}^{-1}$$. If the initial concentrations of A and B are 3 $$\text{mol dm}^{-3}$$ and 1 $$\text{mol dm}^{-3}$$ respectively, and that there is no C in the beginning, calculate the concentration of C in $$\text{mol dm}^{-3}$$ after 1 hour.

(This problem is part of the set Extraordinary Differential Equations.)

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