Question

M^-1 s^-1 at 737 °C and 0.0815 M^-1 s^-1 at 947 °C. a. Calculate the activation energy for this reaction. b. Calculate the half-lifetime of this reaction at 947 °C if the initial concentration of NO is 2.23x10-5 M. c. If the exhaust gases in a car's exhaust pipe are at 947 °C explain on the basis of your answer in (b) whether a catalytic converter would be necessary to convert the NO in the exhaust gases.

Answer 1

In this chemistry question, we calculate the activation energy for a reaction at different temperatures, find the half-life of the reaction at a given temperature, and determine whether a catalytic converter is necessary based on the half-life.

Step-by-step explanation:

a. To calculate the activation energy for this reaction, you can use the Arrhenius equation: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2), where k1 and k2 are the rate constants at different temperatures (here, 737 °C and 947 °C, respectively), Ea is the activation energy, R is the gas constant, and T1 and T2 are the temperatures in kelvin. Rearranging the equation, you can calculate Ea as follows:

Ea = ((ln(k2/k1))/(1/T1 - 1/T2)) * R

b. The half-life of a reaction can be calculated using the equation: t1/2 = (ln2)/(k * [A]0), where t1/2 is the half-life, k is the rate constant, and [A]0 is the initial concentration of the reactant. Plugging in the given values, you can calculate the half-life at 947 °C.
c. Based on the calculated half-life in (b), if the half-life is very short, it indicates that the reaction proceeds quickly and no significant amount of the reactant (NO) will be left in the exhaust gases by the time they reach the catalytic converter. Therefore, a catalytic converter would not be necessary in this case to convert the NO in the exhaust gases.

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