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In the Arrhenius equation for a certain reaction, the value of A and Ea (activation energy) are 4 x 1023 sec–1 and 98.6 kJ mol–1 respectively. If the reaction is of first order at what temperature will its half life period be ten times.


By using the half life equation, we get 

K=0.693t1/2K = 0.69310×60 s = 1.155 × 10-3s-1

log K = log A - Ea2.303 RT



log 1.155 × 10-3 = log 4 × 10-13J                                                  98.6 kJ mol-12.303 × 8.314 J K-1 mol-1 × Tor           3.0616 = 13.6021 -                                         98.600 kJ mol-12.303×8.314 J K-1 mol-1×T

or    -2.9384 = 13.6021 - 98.600 K2.303 × 8.314 ×Tor       16.5405 = 98.600 K 2.303 × 8.314 × Tor     16.5405 = 5149.6 KTor        T = 5149.6 K16.5405 = 311.333 K.


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The reaction:
SO2 + Cl2 SO2 + Cl2
is a first order reaction with k1 = 2.2 x 10–5 s–1 at 575 K. What percentage of a initial amount of SO2 Clwill get decomposed in 90 minutes when the reaction is carried out at 575 K?


The reaction:
SO2 + Cl2 SO2 + Cl2
is a first order reaction with k1 = 2.2 x 10–5 s–1 at 575 K
Thus using the first order equation

k = 2.303tlogA0A


2.2×10-5 = 2.30390log100Alog100A = 2.2 × 10-5 × 90 × 602.303                = 198 × 10-5×602.303                = 19.8 × 10-4×602.303                = 8.597 × 6 × 10-3                 = 51.482 × 10-3


100A = 051482 Antilog = 1.126A = 1001.126 = 88.8%% of SO2Cl2 decomposed            = 100 -88.8 = 11.2%.
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The activation energy of a reaction is 75.2 kJ mol–1 in the absence of a catalyst and 50.14 kJ mol–1 with a catalyst. How many times will the rate of reaction grow in the presence of the catalyst if the reaction proceeds at 25°C?
(R = 8.314 J K–1 mol–1)

By using the Arrhenius equation, we obtained 


In k1 = In A - Ea1RTIn k2 = In A - Ea2RTIn k2-In k1 = 1RT(Ea1-Ea2)   logk2k1 = 1RT(75.10 kJ - 50.14 kJ)  logk2k1 = 12.303 RT(25.10 kJ)           = 25.10 × 1000 J mol-12.303 × 298 k × 8.314 J K-1 mol-1logk2k1 = 251005705.8 = 4.40     k2k1 = Antilog 4.40 = 2.5 × 104.

The rate of reaction will grow up by 25000 times in presence of catalyst. The decrease in activation energy takes place by 25.1 kJ mol
–1.
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The reaction
SO2Cl2 → SO2 + Cl2
is a first order reaction with k = 2.2 x 10–5 s–1 at 320° C. Calculate the percentage of SO2Cl2 that is decomposed on heating this gas for 30 minutes.


The reaction
SO2Cl2 → SO2 + Cl2
is a first order reaction with k = 2.2 x 10–5 s–1 at 320° C
Thus by using the first order equation

k = 2.303tlogA0A           

 
 = log100A= 2.2 × 10-5×30×602.303

log100A = 39.6 × 10-32.303                 = 3.96 × 10-22.303                 = 1.1719 × 10-2 = 0.0172      100A = 1.040       A = 1001.04=96.15%
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A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in the presence of catalyst at the same rate, the temperature required is 400 K. Calculate the activation energy of the reaction if catalyst lowers the activation energy barrier by 20 kJ mol–1.

Suppose in the absence of catalyst and in the presence of catalyst the value of activation of energies are Ea1 and Ea2 at the temperature T1 and T2 respectively.
Thus,
           In k = In A - Ea1RT1                           (in the presence of catalyst)And   In k = In A - Ea2RT2                            (in the presence of catalyst)But    Ea1RT1 = Ea2RT2or        Ea1RT1 = Ea1-20RT2                                        [  Ea1-Ea2 =20 kJ]

Put, the values of T1 (=500 k) and T2 (=400 k)Thus,   Ea1500 = Ea1-20400or           Ea1 = 100 kJ mol-1.

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