The thermal decomposition of `HCO_(2)H` is a first order reaction with a rate constant of `2.4xx10^(-3)s^(-1)` at a certain temmperature. Calculate how long will it take for three-fourths of initial quantity of `HCO_(2)H` to decompose. `" "[log 0.25= -0.6021]`

Explanation

Write the equation for the first order
`t=(2.303)/(k)"log"([R]_(0))/(R )`
When three-fourths of `HCO_(2)H` decomposes, the amount of `HCO_(2)H` that remains is one-fourth
`i.e., R=([R]_(0))/(4)`
Substituting the values in the first order equation, we have
`t=(2.303)/(2.4xx10^(-3)s^(-1)) "log"([R]_(0))/([R]_(0)//4)`
`=(2.303)/(2.4xx10^(-3)s^(-1))log4`
`=(2.303xx(0.6021))/(2.4xx10^(-3))=(2.303xx0.6021)/(2.4)xx10^(3)s`
`=578` seconds.