For a first order reaction \(A → B\), the rate constant, \(k = 5.5×10^{–14}s^{–1}\). The time required for 67% completion of reaction is \(x×10^{–1}\) times the half life of reaction. The value of \(x\) is _____. (Nearest integer)
Correct Answer: 16
Solution and Explanation
\(∵ kt = ln \frac {A_0}{A}\)
\(\frac {ln2}{t_{\frac 12}}\) \(t\)67% \(=ln\frac {A_0}{0.33A_0}\)
\(\frac {log\ 2}{t_{\frac 12}}\)\(t\)67% = \(log \frac {1}{0.33}\)
\(t\)67% \(= 1.566 t_{\frac 12}\)
\(x = 15.66\)
Nearest Integer \(= 16\)
So, the answer is \(16\).
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Concepts Used:
Order of Reaction
The Order of reaction refers to the relationship between the rate of a chemical reaction and the concentration of the species taking part in it. In order to obtain the reaction order, the rate equation of the reaction will given in the question.
Characteristics of the reaction order
- Reaction order represents the number of species whose concentration directly affects the rate of reaction.
- It can be obtained by adding all the exponents of the concentration terms in the rate expression.
- The order of reaction does not depend on the stoichiometric coefficients corresponding to each species in the balanced reaction.
- The reaction order of a chemical reaction is always defined with the help of reactant concentrations and not with product concentrations.
- Integer or a fraction form the value of the order of reaction will be there and it can be zero.