The thermal decomposition of `HCO_2 H` is a first order reaction with a rate constant of `2.4 xx 10^(-3) s^(-1)` at a certain temperature. Calculate how long will it take for three-fourth of initial quantity of `HCO_2 H` to decompose. (log 0.25 =-0.6021)

Explanation

Let the initial quantity be = a
` x= 0.75 a , ( a-x) = a- 0.75 a= 0.25 a ,`
`k=2.4 xx 10^(-3) s^(-1)`
For a first order reaction,
` t=( 2.303 )/(k ) log "" (a)/((a-x))`
or ` t= ( 2.303 )/( 2.4 xx 10^(-3) s^(-1)) log "" (a)/( 0.25 a)`
`= 9.60 xx 10^(2) log "" (1)/( 0.25 )`
` = 9.60 xx 10^2 xx ( log 1- log 0.25 )`
` = 9.6 xx 10^2 xx 0.6021 = 577 sec .`