Rate constants have units of .

Question

Rate constants have units of                         .

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The question asks about the units of rate constants in chemical kinetics and provides four options to evaluate.
Option 1: 'none of these' would be incorrect if at least one of the other listed unit forms is valid for rate constants. Since rate constants do have units that depend on the reaction order, this option is unlikely to be correct on its own.
Option 2: 'reciprocal time' corresponds to first-order reactions, where k has units of s^-1 (or s^-1 in general, i.e., inverse time). This is a valid unit form for rate constants in first-order processes, so this option can be correct in the context of first-order kinetics.
Option 3: 'reciprocal time x reciprocal concentration' is equivalent to units of M^-1 s^-1, which are the standard units for second-order rate constants in reactions where the rate law is rate = k[A][B] or rate = k[A]^2. This is also a valid unit form for rate constants in second-order kinetics, so this option can be correct in the context of second-order processes.
Option 4: 'all of these' would be correct if every listed unit form can occur for rate constants in some legitimate scenario. Since first-order rate constants can have units of inverse time (s^-1) and second-order rate constants can have units of inverse concentration times inverse time (M^-1 s^-1), and since rate constants for other orders can adopt other unit forms (e.g., zero-order with units of concentration per time, M s^-1, in some contexts), the statement that rate constants have units that include both inverse time and inverse time × inverse concentration is consistent with the general statement that k is dimensionally dependent on reaction order.
In terms of conceptual accuracy, Option 2 reflects first-order kinetics correctly, Option 3 reflects second-order kinetics correctly, and Option 4 extends to acknowledge that rate constants can take on the appropriate unit forms for different orders. Option 1 is the strongest incorrect choice because it denies the validity of the unit forms described in Options 2 and 3, which are indeed correct in their respective contexts.
Therefore, discussing all the provided forms together as capturing the valid range of rate-constant units makes 'all of these' the inclusive and correct-sounding choice in this framework.
Note: Depending on the exact reaction order, k will have the corresponding units, and zero-order reactions involve different units; the emphasis here is on recognizing the commonly encountered units (s^-1 and M^-1 s^-1) and acknowledging that both can be correct in the appropriate contexts.

BIOC 440 A Lecture Concept Exercise | 12

Rate constants have units of .

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