At a certain temperature this reaction follows second-order kinetics with a rate constant of 14.1 M-1s-1 : --->2SO3g+2SO2gO2g Suppose a vessel contains SO3 at a concentration of 1.44M . Calculate the concentration of SO3 in the vessel 0.240 seconds later. You may assume no other reaction is important.

Approximately . (Moles-per-liter.)

Explanation:

.

is the only reactant in this reaction. Only the concentration of

Let (that's the concentration of .) By "second-order" kinetics, the question likely means that the rate of change in (with respect to time ) is proportional to . In other words,

,

where is the rate constant of the reaction. Note the negative sign in front of the fraction. Reactants are consumed in a reaction, so their concentrations would become smaller.

Rearrange the equation to separate the variables:

.

Integrate both sides using the power rule for integration:

.

.

The value of here is fixed; its exact value depends on the initial concentration of the reaction. Rearrange to obtain an equation for (concentration) with respect to (time.)

.

The concentration of was at the beginning of the reaction. As a result, should ensure that at .

Let , , and solve for :

.

.

According to the question, . Calculate the value of when :

.

Hence, the concentration of is approximately after .

the answer is d. 74.02

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