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In a first order reaction, the concentration of reactant decreases from 400 mol L ^ - 1 to 25 mol L ^ - 1 in 200 seconds. The rate constant for the reaction is?
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In a first order reaction, the concentration of reactant decreases fro...
First Order Reaction:

A first-order reaction is a type of chemical reaction where the rate of reaction is directly proportional to the concentration of one reactant. This means that the rate of reaction decreases exponentially with time.

Rate Equation for a First Order Reaction:

The rate equation for a first-order reaction can be expressed as:

Rate = k[A]

where Rate is the rate of reaction, k is the rate constant, and [A] is the concentration of the reactant.

Given Information:

In this problem, the concentration of the reactant decreases from 400 mol L^-1 to 25 mol L^-1 in 200 seconds.

Determining the Rate Constant:

To determine the rate constant for the reaction, we can use the rate equation and the given information.

Using the initial concentration ([A]0 = 400 mol L^-1), final concentration ([A]t = 25 mol L^-1), and time (t = 200 s), we can rearrange the rate equation to solve for the rate constant (k):

Rate = k[A]

k = Rate / [A]

k = (ln([A]0) - ln([A]t)) / t

k = (ln(400) - ln(25)) / 200

k = (ln(16) - ln(1)) / 200

k = ln(16) / 200

k ≈ 0.038 s^-1

Therefore, the rate constant for the reaction is approximately 0.038 s^-1.

Conclusion:

In a first-order reaction, the rate constant can be determined by using the rate equation and the given concentrations and time. In this case, the rate constant was found to be approximately 0.038 s^-1.
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There are many reactions which obey a first order rate equation although it reality they are bi- or ter-molecular. As an example of these may be taken the decomposition of Carbonyl sulfide in water, namely, COS + H20 002 + H2SAccording to the law of mass action this reaction should be second order with the rate dependent on the concentration of both the carbonyl sulfide and the water. Actually however, the rate is found to be first order with respect to the carbonyl sulfide and independent of the water Reactions exhibiting such behaviour are said to be pseudo-molecular.The pseudo-unimoecuar nature of this reaction is explainable by the fact that water is present in such excess that its concentration remains practically constant during the course of the reaction. Under these condition b x = b, and the rate equation becomesOn integration this leads towhich is the equation for a first order reaction. It is evident, however, that the now constant k is not independent of the concentration, as is the case with true first order constants, but may vary with b if the latter is changed appreciably, When such is the case, the true constant k2 can be obtained from k by dividing the latter by b. pseudo-molecular reactions are encountered whenever one or more of the reactants remain constants during the course of an experiment. This is the case with reactions conducted in solvents which are themselves one of the reactants, as in the decomposition of carbonyl sulfide in water, or in the esterification of acetic anhydride in alcohol(CH3C0)20 + 2C2H5OH 2CH3C00C2H5 + H20Again, this is also true of reactions subject to catalysis, in which case the concentration of the catalyst does not change. The decomposition of diacetone alcohol to acetone in aqueous solution is catalysed by hydroxyl ions, with the rate proportional to the concentration of the alcohol and that of the base. Since the concentration of the base does not change within any one experiment, however, the rate equation reduces to one of first order with respect to the alcohol. But the rateconstant k obtained for various concentrations of base are not identical, as may be seen from table. To obtain from these the true second order velocity constant, the ks must be divided by the hydroxyl ion concentration. When this is done excellent k2 values result, as column 3 indicatesTable : Decomposition of diacetone alcohol in water at 25C (Catalyst : NaOH)Q.By what factor does the rate of reaction of diacetone alcohol in water solution change if p0H is increased by 2 units other things remaining same ?

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In a first order reaction, the concentration of reactant decreases from 400 mol L ^ - 1 to 25 mol L ^ - 1 in 200 seconds. The rate constant for the reaction is?
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