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CBSE Class 12 Chemistry 2014 Delhi Set 1 Solved Paper

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Question : 22 of 30
Marks: +1, -0
The following data were obtained during the first order thermal decomposition of SO2Cl2\mathrm{SO}_2\mathrm{Cl}_2 at a constant volume: SO2Cl2(g)→SO2(g)+Cl2(g)\mathrm{SO}_2\mathrm{Cl}_2(\mathrm{g}) \rightarrow \mathrm{SO}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g})
 Experiment  Time /s−1/ \mathrm{s}^{-1}  Total pressure/atm
 1  0  0.4
 2  100  0.7
Calculate the rate constant.
(Given: long 4=0.6021,log⁡2=0.30104=0.6021, \log 2=0.3010 )
Solution:  
The given reaction is,
SO2Cl2(g)→SO2(g)+Cl2(g)\mathrm{SO}_2\mathrm{Cl}_2(\mathrm{g}) \rightarrow \mathrm{SO}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g})
Pi=0.4 atm, P=0.7 atm, t=100 sP_i=0.4\,\text{atm},\ P=0.7\,\text{atm},\ t=100\,\text{s}
Thus, according to the integrated rate law for gas phase
K=2.303t×log⁡10Pi2Pi−PK=\frac{2.303}{t}\times \log_{10} \frac{P_i}{2P_i-P}
K=2.303×10−2×log⁡100.40.1K=2.303\times10^{-2}\times \log_{10} \frac{0.4}{0.1}
K=2.303×10−2×log⁡10(4)K=2.303\times10^{-2}\times \log_{10}(4)
K=2.303×10−2×0.6021K=2.303\times10^{-2}\times0.6021
K=1.3866×10−2 s−1K=1.3866\times10^{-2}\ \mathrm{s}^{-1}
Thus, the rate constant for the above reaction is 1.3866×10−2 s−11.3866\times10^{-2}\ \mathrm{s}^{-1}.
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