If the reaction A + B→C has the rate law:
Rate = k [A]²[B], the units of the rate constant are:

Question

If the reaction A + B→C has the rate law: Rate = k [A]²[B], the units of the rate constant are:

Quizplus · Accepted Answer

By analyzing the given rate law, we can find the units of the rate constant (k) using dimensional analysis.

Rate = k [A]S1U1P12S1S1P0[B]

Rate has units of mol/L×s (as it is a rate of change of concentration with respect to time)

[A] has units of mol/L 
[B] has units of mol/L

Since the reaction order for A is (S1U1P12S1S1P0), the concentration of A has units of molS1U1P12S1S1P0/L 
Similarly, since the reaction order for B is (S1S1P0), the concentration of B has units of molS1S1P0/L

Substituting the units of the variables in the rate law:

mol/L×s = k × (molS1U1P12S1S1P0/L)S1S1P0 × (molS1S1P0/L)

mol/L×s = k × molS1U1P12S1S1P0molS1S1P0/L2

k = (mol/L×s)/(molS1U1P12S1S1P0molS1S1P0/L2)

k = LS1U1P12S1S1P0/molS1U1P12S1S1P0×s

Therefore, the answer is D.

If the Reaction a + B→C Has the Rate Law