Final answer:
Whether a liquid A can reach 50% conversion depends on the order of the reaction. For first-order reactions, 50% conversion is achievable as the half-life is constant. For second-order or higher-order reactions, the half-life varies with concentration, and additional calculations would be needed.
Step-by-step explanation:
The question asks if a liquid A that undergoes nth-order kinetics in a batch reactor with the given rate law r = k can reach 50% conversion. The answer to this question depends on the specific reaction kinetics described by the order of the reaction (n).
For first-order reactions, the half-life is constant and does not depend on the initial concentration of reactants, meaning that the concentration of A would decrease by 50% over each half-life period. Therefore, it is always possible to reach a 50% conversion for first-order reactions.
In the case of second-order reactions or higher, the half-life depends on the initial concentration of reactants and changes as the reaction proceeds. Here, reaching exactly 50% conversion may not follow a simple half-life pattern, and determining whether 50% conversion is reached would require more information about the kinetics or direct calculations.