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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