The following data were obtained during the first order thermal decomposition of ` SO_2 Cl_2 ` at a constant volume :
` SO_2 Cl_2 (g) to SO_(2 ) (g) + Cl_(2(g))`

Calculate the rate constant
( given : log `4=0.6021 , log 2= 0.3010)`

Explanation

The given reaction is

where x is the decrease in pressure of `SO_2 Cl_2` due to its decomposition Total pressure at time t,
` P_t = ( 0.4 -x) atm +x+ x=(0.4 +x ) atm x=(p_t - 0.4 )`
Pressure of `SO_2 Cl_2` at timet will be
` therefore P_(SO_2)Cl_2 = 0.8 - 0.7 = 0.1 atm`
According to first order rate law,
` k=( 2.303 )/(t) log_(10) "" (p_(SO_2)Cl_2 (" inital ") )/( P_(SO_2 )Cl_2 " (After reaction )")`
`=( 2.303 )/(100 sec ) log ""((0.4 )/(0.1 )) = ( 2.303 )/( 100 sec ) log 4 `
`= ( 2.303 )/( 100 sec ) xx 0.6021 = 1.3 xx 10^(-2) s^(-1)`