Question

the rate law for a reaction is rate = k[a]₂[b]. the units of the rate constant when the concentrations are measured in mol/l and the time in seconds are s-₁ m s-₁ m-₁ s-₁ m₂ s-1 m-₂ s-₁

Answer 1

The correct units for the rate constant k, given a rate law rate = k[A]2[B], are L2mol-2s-1, ensuring the rate has units of mol/L/s.

Step-by-step explanation:

The question requires us to determine the correct units for the rate constant (k), given the rate law for a reaction where rate = k[A]2[B]. When the concentrations are measured in mol/L and time in seconds, we must find the units for k that ensure that the rate has units of M/s (mol/L/s).

The rate law indicates that the reaction is third-order, with A being second-order and B first-order. According to dimensional analysis, the units for k will make the overall expression equal to mol/L/s. Thus we need the units for k to cancel out the units from the concentrations to end up with M/s.

If we multiply the units of k by the units of the concentration terms ([A]2 and [B]), we should get the units of the rate (mol/L/s). Therefore, the correct units for k are L2mol-2s-1 (M-2s-1).