For the first order thermal decomposition reaction, the following data were obtained : {\C}_2 {\H}_5 {\Cl}( {\g}) \to {\C}_2 {\H}_4( {\g})+ {\HCl}( {\g}) \table \Time \/ {\sec} ,\Total \pressure \/ \atm ; 0,0.30 ; 300,0.50 Calculate the rate constant (Given : \log 2=0.3010, \log 3=0.4771, \log 4= 0.6021 )

CBSE Class 12 Chemistry 2016 Outside Delhi Set 1 Solved Paper

Question : 12 of 26

Marks: +1, -0

For the first order thermal decomposition reaction, the following data were obtained :

{\C}_2 {\H}_5 {\Cl}( {\g}) → {\C}_2 {\H}_4( {\g})+ {\HCl}( {\g})

\table \Time \/ {\sec} ,\Total \pressure \/ \atm ; 0,0.30 ; 300,0.50

Calculate the rate constant
(Given :

\log 2=0.3010, \log 3=0.4771,

\log 4= 0.6021 )

Solution:

\text " Given : Initial pressure, "

{\P}_0\;=0.30 {\atm}

{\P}_t\;=0.50 {\atm}

t\;=300 {\ s}

\text " Rate constant, "\; k\;=\;{2.303}/{t} \log \;{ {\P}_0}/{2 {\P}_0- {\P}_t}

= {2.303}/{300 {\ s}} \log \;{0.30}/{2 × 0.30-0.50

\;=\;{2.303}/{300 {\ s}} \log \;{0.30}/{0.60-0.50}

\;=\;{2.303}/{300 {\ s}} \log \;{0.30}/{0.10}

\;=\;{2.303}/{300 {\ s}} \log 3

\;=\;{2.303}/{300 {\ s}} × 0.4771

\;=\;{1.099}/{300 {\ s}}

\;=0.0036 {\ s}^{-1}

\;=3.6 × 10^{-3} {\ s}^{-1}

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