The equation A + 2 B = C + D describes an elementary reaction, which takes place in a single step. Thus, the rate law must be
a. rate = k(A]2
b. rate = k(B]2
c. rate = k(A][B]
d. rate = k(A][B]2
e. none of the above represents the rate law for this elementary reaction.
To determine the rate law for an elementary reaction, we need to examine the stoichiometry of the reactants involved. The reaction equation A + 2B = C + D tells us that the reactant A appears only once, reactant B appears twice, and products C and D are formed.
Based on the stoichiometry of the reactants, we can write the rate law as follows:
rate = k[A]^m[B]^n
Here, the rate is determined by the concentration of reactant A raised to the power of m, and the concentration of reactant B raised to the power of n.
Let's determine the values of m and n for the given reaction equation:
A + 2B = C + D
From the equation, we can see that for every molecule of A, two molecules of B are consumed. This implies that the rate of the reaction depends on A and B, and both A and B must be involved in the rate law.
Therefore, the correct rate law based on the given stoichiometric equation is:
rate = k[A][B]^2
Thus, the correct answer is d. rate = k(A][B]2.