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NCERT Class XII Chemistry
Chapter - Chemical Kinetics
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Question : 22 of 39
Marks: +1, -0
The rate constant for the decomposition of N2O5\mathrm{N_2O_5} at various temperatures is given below:
 T/°C  0  20  40  60  80
 105×ks−1\frac{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 value of A and Ea._{a}.Predict the rate constant at 30°C and 50°C.
Solution:  
The values of rate constants for the decomposition of N2O5 at varioustemperatures are given below :
 T(°C)  T (K)  1/T  k (s−1^{-1})  ln k (= 2.303 log k)
 0  273  3.6 ×10−3^{-3}  7.87 ×10−7^{-7}  -14.06
 20  293  3.4 ×10−3^{-3}  1.70×10−5^{-5}  -10.98
 40  313  3.19 ×10−3^{-3}  25.7 ×10−5^{-5}  -8.266
 60  333  3.00 ×10−3^{-3}  178×10−5^{-5}  - 6.332
 80  353  2.8 ×10−3^{-3}  2140 ×10−5^{-5}  -3.844
Slope of the line = tan θ
=y2−y1x2−x1= \frac{y_{2} - y_{1}}{x_{2} - x_{1}}
=−10.98−(−14.08)3.4−3.6×103= \frac{-10.98 - (-14.08)}{3.4 - 3.6} \times 10^{3}
=−15.5×103= -15.5 \times 10^{3}
Ea=−E_{a} = - slope ×R\times R
=−(−15.5×103×8.314)= - ( -15.5 \times 10^{3} \times 8.314 )
=128.86 kJ K−1 mol−1= 128.86\ \text{kJ}\ \text{K}^{-1}\ \text{mol}^{-1}
Again ln⁡A=ln⁡k+EaRT\text{Again}\ \ln A = \ln k + \frac{E_{a}}{R T}
=−14.06+128.86×103 J K−1 mol−18.314×273= -14.06 + \frac{128.86 \times 10^{3}\ \mathrm{J\,K}^{-1}\,\mathrm{mol}^{-1}}{8.314 \times 273}
=−14.06+56.77=42.71= -14.06 + 56.77 = 42.71
or, log⁡A=18.53\log A = 18.53
or, A=A = antilog 18.5318.53
=0.3388×1019= 0.3388 \times 10^{19}
or,A=3.388×1018A = 3.388 \times 10^{18}
Value of rate constant k at 303 K and 323 K can be obtained from graph.First of all ln k is obtained corresponding to1303 K\frac{1}{303}\ \mathrm{K}and 1323 K\frac{1}{323}\ \mathrm{K}and thenk is calculated.
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