A packed bed reactor is used to perform a chemical reaction. The reaction rate is given by the equation:

r = k * C^1.5

where r is the reaction rate, k is the reaction rate constant, and C is the concentration of the reactant. The reactor operates at a constant temperature and pressure, and the reaction is first order with respect to the reactant. The concentration of the reactant at the inlet of the reactor is 2 mol/L, and the outlet concentration is 0.5 mol/L. The volume of the reactor is 100 L. Calculate the reaction rate constant, k.

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