The rate constant for the decomposition of N 2 O 5 at various temperatures is given below-beginarray -c-c-c-c-c-c-Wlineend array Draw a graph between ln k and 1- T and calculate the values of A and E a- Predict the rate constant at 50- and 30-

(a) To draw the graph between log k versus 1/T we rewrite the data as follows. [ T(K) amp; 273 amp; 293 amp; 313 amp; 333 amp; ...

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Standard XII

Chemistry

Rate Constant

The rate cons...

Question

The rate constant for the decomposition of $N_{2} O_{5}$ at various temperatures is given below:

$\begin{matrix} T /^{\circ} C & 0 & 20 & 40 & 60 & 80 10^{5} \times K / s^{- 1} & 0.0787 & 1.70 & 25.7 & 178 & 2140 \end{matrix}$

Draw a graph between ln k and $\frac{1}{T}$ and calculate the values of A and $E_{a}$ . Predict the rate constant at $50^{\circ}$ and $30^{\circ}$ .

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Solution

(a) To draw the graph between log k versus $\frac{1}{T}$ we rewrite the data as follows.
$\begin{matrix} T (K) & 273 & 293 & 313 & 333 & 353 \frac{1}{T} & 0.003663 & 0.003413 & 0.003213 & 0.003003 & 0.002833 l o g k & - 6.1040 & - 4.7696 & - 3.5900 & - 2.7496 & - 1.6996 \end{matrix}$

(b) From the graph, we find the slope.
Slope $\frac{- 2.4}{0.00047} = \frac{- E_{a}}{2.303 R}$
$∴$ Activation energy $(E_{a}) = \frac{2.4 \times 2.303 \times 8.314 J m o l^{- 1}}{0.00047}$
$= 97875 k J m o l^{- 1} E_{a} = 97.875 k J m o l^{- 1}$

(c) We know that
$l o g k = l o g A \frac{- E_{a}}{2.303 R T}$
On comparing it with y = mx + c, the equation of line in intercept form;
$l o g k = (- \frac{E_{a}}{2.303 R T}) \frac{1}{T} + l o g A$
log A = Value of intercept on y-axis, i.e., on the log k-axis
$= (- 1 + 7.2) = 6.2 [y_{2} - y_{1} = - 1 - (7.2)]$
Frequency factor A = Antilog 6.2 = 1585000
$= 1.585 \times 10^{6} c o l l i s i o n s s^{- 1} A = 1.585 \times 10^{6} c o l l i s i o n s s^{- 1}$

(d) Value of rate constant k can be find by the study of graph.
$\begin{matrix} T (K) & \frac{1}{T} & V a l u e s o f l o g k f r o m & V a l u e s o f k g r a p h 303 & 0.003300 & - 4.2 & 6.31 \times 10^{- 5} s^{- 1} 323 & 0.003096 & - 2.8 & 1.585 \times 10^{- 3} s^{- 1} \end{matrix}$

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Similar questions

Q. The rate constant for the decomposition of

N_{2} O_{5}

at various temperatures is given below:

$T /^{\circ} C$	$0$	$20$	$40$	$60$	$80$
$10^{5} \times k / s^{- 1}$	$0.0787$	$1.70$	$25.7$	$178$	$2140$

Draw a graph between ln

k

and

1 / T

and calculate the values of A and

E_{a}

. Predict the rate constant at

30^{\circ}

and

50^{\circ} C

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

T/°C	0	20	40	60	80
	0.0787	1.70	25.7	178	2140

Draw a graph between ln k and 1/T and calculate the values of A and E_a.

Predict the rate constant at 30º and 50ºC.

Q. For decomposition of

N_{2} O_{5}

, rate constant were determined at two different temperature. At

27^{\circ} C,

rate constant was

2 \times 10^{- 4} {sec}^{- 1}

, at

47^{\circ} C

the rate constant is

6 \times 10^{- 4} {sec}^{- 1}

.
Then identify the correct statement(s).
(Given

l n 3 = 1.1

)

For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained. Calculate the rate constant.
$\begin{matrix} t (s) & p (m m o f H g) 0 & 35.0 360 & 54.0 720 & 63.0 \end{matrix}$

The experimental data for decomposition of $N_{2} O_{5}$ $[2 N_{2} O_{5} \to 4 N O_{2} + O_{2}]$ in gas phase at 318 K are given below:

$\begin{matrix} t / s & 0 & 400 & 800 & 1200 & 1600 & 2000 & 2400 & 2800 & 3200 10^{- 2} \times [N_{2} O_{5}] / & 1.63 & 1.36 & 1.14 & 0.93 & 0.78 & 0.64 & 0.53 & 0.43 & 0.35 m o l L^{- 1} \end{matrix}$

Plot $[N_{2} O_{5}]$ against t

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The rate constant for the decomposition of N2O5 at various temperatures is given below: T/∘C020406080105×K/s−10.07871.7025.71782140 Draw a graph between ln k and 1T and calculate the values of A and Ea. Predict the rate constant at 50∘ and 30∘.