Answer to Question #164001 in General Chemistry for Melissa Rodriguez

Question

Consider the following reaction: NO (g) + O3 (g) → NO2 (g) + O2 (g)

The reaction has an activation energy of 63.0 kJ/mol and a frequency factor of 8.70x1012. Calculate the value of the rate constant

of the reaction at 75 oC. The reaction is first order with respect to both NO and O3, write a rate law for the reaction and give the

rate constant with the appropriate units.

Answer 1

The rate constant of a reaction can be determined by the Arrhenius equation:

$k=Ae^{\frac{-E_a}{RT}}$ ,

where A is a frequency factor, $E_a$ is activation energy (J/mol), R is the gas constant (8.314 J/mol K) and T is a temperature (K). The units of a frequency factor depend on the order of a reaction. As we know from conditions, the reaction is the first order, so units for A are $s^{-1}$ and its rate law has the following form:

$Rate = k [NO][O_3]$

So the rate constant is:

$k = 8.70\times10^{12} s^{-1} e^{\frac{-63.0\times10^3 j/mol}{8.314 J/mol.K*(75+273)K}}$

$k=2.5\times 10^{22} s^{-1}$