The rate constant for the first order decomposition of \(H_2O _2\) is given by the following equation:
\(log\ k = 14.34 - 1.25 \times 10^4\ K/T \)
Calculate \(E_a\) for this reaction and at what temperature will its half-period be 256 minutes?
The rate constant for the first order decomposition of \(H_2O _2\) is given by the following equation:
\(log\ k = 14.34 - 1.25 \times 10^4\ K/T \)
Calculate \(E_a\) for this reaction and at what temperature will its half-period be 256 minutes?
Solution and Explanation
\(Arrhenius \ equation \ given\ by, \)
\(k = Ae^{\frac {-E_a}{RT}}\)
\(ln\ k = ln \ A - \frac {E_a}{RT}\)
\(ln\ k = log \ A - \frac {E_a}{RT}\)
⇒\(log\ k = log \ A - \frac {E_a}{2.303\ T}\) .....(i)
The given equation is
\(log\ k = 14.34-1.25×10^4\ K/T\) ......(ii)
From equation (i) and (ii), we obtain
\(\frac {E_a}{2.303 \ RT} = 1.25×10^4\ K/T\)
⇒ \(Ea=1.25×10^4K×2.303×R\)
= \(1.25 × 10^4K × 2.303 × 8.314 J K^{- 1}mol^ {- 1}\)
= \(239339.3 \ J mol^{-1} (approximately)\)
= \(239.34\ kJ mol^{-1}\)
Also, when \(t_{\frac 12}=256 \ minutes\),
\(k = \frac {0.693}{t_{1/2}}\)
\(k = \frac {0.693}{256}\)
\(k= 2.707×10^{-3} min^{-1}\)
\(k= 4.51 × 10^{-5} s^{-1}\)
It is also given that, \(log\ k= 14.34 - 1.25 × 10^4 K/T\)
⇒\(log(4.51×10^{-5})=14.34-1.25×10^4 K/T\)
\(log \ (0.654-05)=14.34-1.25×10^4 K/T\)
\(\frac {1.25×10^4K}{T} = 18.686\)
⇒\(T =\frac {1.25 \times 10^4 \ K}{18.686}\)
\(T = 668.95 \ K\)
\(T = 669\ K\ (approximately)\)
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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.