KEY2CHEM

Dependence of Reaction Rate on Concentration

The relationship between how rate changes as a function of reactant concentration is called the rate law (or rate equation). For the reaction $$\require{mhchem}\ce{aA + bB -> cC + dD}$$, the rate law is written as $$\text{rate} = k[A]^x[B]^y$$, where $$k$$ is the rate constant (constant for a specific reaction at a given temperature), and $$x$$ and $$y$$ are the reaction orders (how the rate changes as a function of the concentration of $$A$$ and $$B$$, respectively). Note that the reaction orders ($$x$$ and $$y$$) are not necessarily related to the stoichiometric coefficients ($$a$$ and $$b$$).

Example 1.

The rate of the reaction $$\require{mhchem}\ce{2 X + Y -> Z}$$ is experimentally-determined to be first order with respect to $$X$$ and second order with respect to $$Y$$. What is the rate law of the reaction?

A. $$\text{rate} = k[X][Y]$$

B.  $$\text{rate} = k[X]^2[Y]$$

C. $$\text{rate} = k[X][Y]^2$$

Solution

C. $$\text{rate} = k[X][Y]^2$$

The rate law and its reaction orders are experimentally-determined. The reaction orders are not necessarily related to the stoichioimetric coefficients in the overall reaction.

Example 2.

For the rate law rate = k[A][B] $$\text{rate} = k[A][B]$$, what is the overall reaction order?

A. $$0$$

B. $$1$$

C. $$2$$

Solution

C. $$2$$

The overall reaction order is the sum of the individual reaction orders. In this case, $$1+1 = 2$$.

Example 3.

For the reaction $$\require{mhchem}\ce{A -> B}$$, the following plot of reactant concentration vs time was observed. What statement about the reaction rate is true?

A. The rate is zero order with respect to $$[A]$$.

B. The rate is first order with respect to $$[A]$$.

C. The rate is second order with respect to $$[A]$$.

Solution

A. The rate is zero order with respect to $$[A]$$.

Since the rate does not change as $$[A]$$ changes, the rate is zero order with respect to $$[A]$$ ($$\text{rate} \propto [A]^0$$).