Question

What are the units of k in the following expression: rate = k [A][B]?

Answer 1

The answer is B since it's a second order reaction.

Answer 2

Presumably, you meant to write:

rate = k*[a]*[b] ---- square brackets are used, by convention, to indicate the concentration of a species.

The

The rate gives the rate of change in concentration of the product per unit time, so is going to have units of concentration per unit time, e.g., mol/(L*s) or mol/(kg solvent * s). [a] and [b] both have units of concentration, i.e., M = molarity = mol/liter, or m = molality = mol/(kg solvent). The answer choices you gave used a lower-case "m" so I'll assume that meant molality

Putting this together yields:

m/s = k*m²

k = m/s * 1/m² = 1/(m*s) = m^-1 * s^-1