The rate constant for the first order decomposition of H 2 O 2 is given by the following equation- log k -14-34-1-25 - 104 K - T- Calculate E a for this reaction and at what temperature will its half-life period be 256 minutes-

(a) Calculation of activation energy E_a According to Arrhenius equation; k = Ae^ E_a/RT log k = log A E_0/2.303 RT log k = 14.34 1.25 × 10^4 K/T On compar ...

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Standard XII

Chemistry

Arrhenius Equation

The rate cons...

Question

The rate constant for the first order decomposition of $H_{2} O_{2}$ is given by the following equation, $l o g k = 14.34 - 1.25 \times 10^{4} K / T$ . Calculate $E_{a}$ for this reaction and at what temperature will its half-life period be 256 minutes?

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Solution

(a) Calculation of activation energy $E_{a}$
According to Arrhenius equation; $k = A e^{\frac{- E_{a}}{R T}}$
$l o g k = l o g A - \frac{E_{0}}{2.303 R T} l o g k = 14.34 - \frac{1.25 \times 10^{4} K}{T}$
On comparing both equations.
$\frac{E_{a}}{2.303 R T} = \frac{1.25 \times 10^{4} K}{T} E_{a} = 1.25 \times 10^{4} K \times 2.303 \times 8.314 (J K^{- 1} m o l^{- 1}) = 23.93 \times 10^{4} J m o l^{- 1} = 239.3 K J m o l^{- 1}$

(b) Calculation of required temperature if $t_{\frac{1}{2}} = 256 m i n$
For 1st order reaction;
$k = \frac{0.693}{t_{\frac{1}{2}}} = \frac{0.693}{(256 m i n)} = \frac{0.693}{256 \times 60 s} = 4.51 \times 10^{- 5} s^{- 1}$
According to Arrhenius theory,
$l o g k = 14.34 - \frac{1.25 \times 10^{4} K}{T} l o g (4.51 \times 10^{- 5}) = 14.34 - \frac{1.25 \times 10^{4} K}{T} - 4.35 = 14.34 - \frac{1.25 \times 10^{4} K}{T} \frac{1.25 \times 10^{4} K}{T} = 14.34 + 4.35 = 18.69 T = \frac{1.25 \times 10^{4} K}{18.69} = 669 K E_{a} = 239.3 K J m o l^{- 1} T = 669 K$

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The rate constant for the first order decomposition of H2O2 is given by the following equation, log k=14.34−1.25×104 K/T. Calculate Ea for this reaction and at what temperature will its half-life period be 256 minutes?

The rate constant for the first order decomposition of $H_{2} O_{2}$ is given by the following equation, $l o g k = 14.34 - 1.25 \times 10^{4} K / T$ . Calculate $E_{a}$ for this reaction and at what temperature will its half-life period be 256 minutes?