A chemical plant produces a product through a reaction that takes place in a packed bed reactor. The reaction rate is given by the equation:

-dC/dt = k * C^1.5

where C is the concentration of the reactant, k is the reaction rate constant, and t is time. The reactor is 100 cm long, and the inlet concentration of the reactant is 0.5 mol/L. The exit concentration of the reactant is 0.1 mol/L. Calculate the reaction rate constant, k, and the conversion of the reactant in the reactor.

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