The reaction X `rarr` products is a first order reaction. In 40 minutes, the concentration of X changes from 1.0 M to 0.25 M. what is the initial rate of reaction when [X] = 0.1 M?
log 4 = 0.60 )

Options

A. `1.73 xx 10^(-3) "mol" L^(-1) min^(-1)`
B. `3.47 xx 10^(-4) "mol" L^(-1) min^(-1)`
C. `1.73 xx 10^(-4) "mol" L^(-1) min^(-1)`
D. `3.45 xx 10^(-3) "mol" L^(-1) min^(-1)`

Answer

D

Explanation

Given ,
(concentration ) a = 1.0 M, a - x = 0.25M, t = 40 minutes
For a first order reaction,
k = `(2.303)/(t ) log"" (a)/(a - x)`
`= (2.303)/(40) log " " (1)/(0.25) = (2.303)/(40) ` kog 4
= `(2.303 xx 2 xx 0.3010)/( 40) `
= 0.03466 `min^(-1)`
Now, Initial rate = K[A]
= 0.03466 (0.1)
= 0.003466 mol/L/min
= 3.466`xx 10^(-3) ` moL/L/ min
`= 3.47 xx 10^(-3)` mol /L / min
According to options given, any option cannot match with answer, But (d) can be the correct answer.