The value of rate constant for the decomposition of HI into $I_{2}$ and $H_{2}$ at different temperature are given below.
$T (K)$ 633 667 710 738
$10^{4} K (M^{- 1} s^{- 1}$ 0.19 1.00 8.31 25.1
The value of Arrhenius parameter is:

A = 2.64 \times 10^{9} M^{- 1} s^{- 1}

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A = 2.24 \times 10^{9} M^{- 1} s^{- 1}

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A = 2.34 \times 10^{9} M^{- 1} s^{- 1}

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Solution

The correct option is A $A = 2.64 \times 10^{9} M^{- 1} s^{- 1}$
The figure below shows a plot between in k against 1/T. It can be seen that it is a straight line with slop = -20.62 K and therefore, its activity energy.
$E_{a} = - (- 20.62) \times 8.314 J m o l^{- 1} K^{- 1}$
$= 171400 J m o l^{- 1} o r 171.4 k J m o l^{- 1}$
We can now calculate the value of A From the value ofk at 667 K.
In A = In $k + \frac{E_{a}}{R T} = l o g A = l o g k + \frac{E_{a}}{R T}$
log A = log $(- 9.2103) + \frac{171400 J m o l^{- 1}}{(8.314 J m o l^{- 1} K^{- 1}) \times 667 K}$
Solve for log A and then take antilog
$∴ A = 2.64 \times 10^{9} M^{- 1} s^{- 1}$

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$T (K)$	633	667	710	738
$10^{4} K (M^{- 1} s^{- 1}$	0.19	1.00	8.31	25.1

The value of rate constant for the decomposition of HI into I2 and H2 at different temperature are given below.T(K)633667710738104K(M−1s−10.191.008.3125.1The value of Arrhenius parameter is:

The value of rate constant for the decomposition of HI into $I_{2}$ and $H_{2}$ at different temperature are given below.
$T (K)$ 633 667 710 738
$10^{4} K (M^{- 1} s^{- 1}$ 0.19 1.00 8.31 25.1
The value of Arrhenius parameter is: