Question #164001

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.

Expert's answer

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}"

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