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