Question

The reaction A + 2B + C -- >D + 2E is first order in reactant A, first order in B, and second order in C. What is the rate law equation for this reaction?
A) rate = [A][B]2[C]
B) rate = [A][B][C]2
C) rate = [A][B]/2[C]
D) rate = k[A][B][C]2
E) k = [A][B][C]2

Answer 1

The answer should be D.  A rate law needs to be rate equaling the rate constant which is represented as k (make sure you use a lower case k since an upper case K is for equilibrium) times the concentrations of each reactant raised to the power of what ever order it has. (if A was a zero order it would be [A]⁰ and if A was third order it would be [A]³).
Do not get the order the reactants are confused with the coefficients in the chemical equation. (just because the reaction has 2B does not mean the rate law will have [B]².  As shown in this example since it is first order therefore being [B] in the rate law)

I hope this helps. Let me know if anything is unclear in the comments.

Answer 2

Answer : The correct option is, (B) $\text{Rate}=k[A][B][C]^2$

Explanation :

Rate law : It is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.

The general reaction is:

$A+B\rightarrow C+D$

The general rate law expression for the reaction is:

$\text{Rate}=k[A]^a[B]^b$

where,

a = order with respect to A

b = order with respect to B

R = rate  law

k = rate constant

$[A]$ and $[B]$ = concentration of A and B reactant

Now we have to determine the rate law for the given reaction.

The balanced equations will be:

$A+2B+C\rightarrow D+2E$

In this reaction, A, B and C are the reactants and the 1st order of reaction for reactant A, 1st order of reaction for reactant B and 2nd order of reaction for reactant C.

The rate law expression for the reaction will be:

$\text{Rate}=k[A]^1[B]^1[C]^2$

or,

$\text{Rate}=k[A][B][C]^2$

Hence, the correct option is, (B) $\text{Rate}=k[A][B][C]^2$