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# The rate constant for the decomposition of N_2 O_5 at various temperatures is given below:

4.22   The rate constant for the decomposition of N2O5 at various temperatures
is given below:

Draw a graph between ln k and 1/T and calculate the values of A and
$E_a$. Predict the rate constant at 30° and 50°C.

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From the above data,

 T/$C^{0}$ 0 20 40 60 80 T/K 273 293 313 333 353 $1/T$$/$$K^{-1}$ ($\times 10^{-3}$) 3.66 3.41 3.19 3 2.83 $10^{5}*K/S^{-}$ 0.0787 1.7 25.7 178 2140 $ln\ K$ -7.147 -4.075 -1.359 -0.577 3.063

Slope of line  = $\frac{y2-y2}{x2-x1} = -12.30\ K$

According to Arrhenius equations,

Slope = $-E_{a}/R$
$E_{a}=$ 12.30 $\times$8.314
= 102.27 $KJ mol^{-1}$

Again,

When T = 30 +273 = 303 K and 1/T =0.0033K
$\ln k= -2.8$

$\therefore$  k = $6.08\times 10^{-2}\ s^{-1}$

When T = 50  + 273 = 323 K  and 1/T = 3.1 $\times 10^{-3}$ K
$\ln k = -0.5$
$\therefore$ k = 0.607 per sec

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