In a first-order decomposition reaction, 50.0% of a compound decomposes in 10.5 min. a. what is the rate constant of the reaction? b. how long does it take for 75.0% of the compound to decompose?

In a decomposition reaction, the reactant breaks into two or more products. The rate of reaction is 0.066 per minute and the time required is 21 minutes.

The rate constant relates the reaction rate with the molar concentration of the reactants and is called reaction rate coefficient (k).

In the reaction 50 % compound decomposed in 10.5 minutes, that will be its half-life

Calculate the rate constant of the reaction by the formula:

Hence the rate constant for the reaction will be 0.066 per minute.

Calculate the time taken for 75 % decomposition of the compound:

The rate of the first-order reaction is given as:

Given,

Substituting values in the above equation:

Hence, for 75 % decomposition 21 minutes will be required.

Therefore, 0.066 per minute is the rate constant and 21 minutes is the time required for 75 % decomposition.

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In this reaction 50% of the compound decompose in 10.5 min thus, it is half life of the reaction and denoted by symbol .

(a) For first order reaction, rate constant and half life time are related to each other as follows:

Thus, rate constant of the reaction is .

(b) Rate equation for first order reaction is as follows:

now, 75% of the compound is decomposed, if initial concentration is 100 then concentration at time t will be 100-75=25.

Putting the values,

On rearranging,

Thus, time required for 75% decomposition is 21 min.

b. accuracy of the data matters alot more than its number of digits, organization or amount of detail. quantitative observation is more accepted than the qualitative observation.