Determining Activation Energy The reaction 2N2O5(g) → 4NO2(g) + O2(g) was studied at several temperatures and the following values of k were obtained: Calculate the value of Ea for this reaction.

Question

Determining Activation Energy
The reaction

[latex] 2 N_{2}O_{5} (g) → 4 NO_{2} (g) + O_{2} (g) [/latex]

was studied at several temperatures and the following values of k were obtained:

[latex]k ( s ^{- 1 } ) [/latex]	T (° C )
[latex] 2.0 × 10 ^{-5}[/latex]	20
[latex]7.3 × 10 ^{-5} [/latex]	30
[latex] 2.7 × 10 ^{-4}[/latex]	40
[latex]9.1 × 10 ^{-4}[/latex]	50
[latex]2.9 × 10 ^{-3}[/latex]	60

Calculate the value of [latex] E_{a} [/latex] for this reaction.

Accepted Answer

To obtain the value of [latex] E_{a} [/latex], we need to construct a plot of [latex] \ln (k) [/latex] versus 1/T. First, we must calculate values of [latex] \ln (k) [/latex] and 1/T:

T ( ° C)	T ( K )	1 / T ( K )	[latex] k (s ^{-1}) [/latex]	[latex] \ln (k) [/latex]
20	293	[latex]3.41 × 10 ^{-3}[/latex]	[latex] 2.0 × 10 ^{-5}[/latex]	- 10.82
30	303	[latex]3.30 × 10 ^{-3}[/latex]	[latex] 7.3 × 10 ^{-5}[/latex]	- 9.53
40	313	[latex]3.19 × 10 ^{-3}[/latex]	[latex] 2.7 × 10 ^{-4}[/latex]	- 8.22
50	323	[latex]3.10 × 10 ^{-3}[/latex]	[latex]9.1 × 10 ^{-4}[/latex]	- 7.00
60	333	[latex]3.00 × 10 ^{-3}[/latex]	[latex]2.9 × 10 ^{-3}[/latex]	- 5.84

The plot of [latex] \ln (k) [/latex] versus 1/T is shown in Fig. 15.14 ▼. The slope is found to be [latex] - 1.2 × 10^{4} [/latex] K. Since

Slope = - [latex] \frac{E_{a}}{R} [/latex]

then

[latex] E_{a} = - R (slope ) = - (8.3145 J K ^{-1} mol^{-1}) (- 1.2 × 10^{4} K)[/latex]

= [latex] 1.0 × 10^{5} J / mol[/latex]

Thus the value of the activation energy for this reaction is [latex] 1.0 × 10^{5} J / mol[/latex]

T ( ° C)	T ( K )	1 / T ( K )	$k (s ^{-1})$	$\ln (k)$
20	293	$3.41 × 10 ^{-3}$	$2.0 × 10 ^{-5}$	– 10.82
30	303	$3.30 × 10 ^{-3}$	$7.3 × 10 ^{-5}$	– 9.53
40	313	$3.19 × 10 ^{-3}$	$2.7 × 10 ^{-4}$	– 8.22
50	323	$3.10 × 10 ^{-3}$	$9.1 × 10 ^{-4}$	– 7.00
60	333	$3.00 × 10 ^{-3}$	$2.9 × 10 ^{-3}$	– 5.84

Question 15.8: Determining Activation Energy The reaction 2N2O5(g) → 4NO2(g...

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