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 \([A]\) (\(\text{rate} \propto [A]^0\)).