Q. For zero order reaction, the integrated rate equation is
A) $kt = \frac{\lbrack A\rbrack}{\lbrack A\rbrack_{0}}$
B) $kt = \lbrack A\rbrack - \lbrack A\rbrack_{0}$
C) $\lbrack A\rbrack = - kt + \lbrack A\rbrack_{0}$
D) $\lbrack A\rbrack = kt - \lbrack A\rbrack_{0}$
Explanation
(c)
For a zero order reaction,
$R \rightarrow$ product
Rate=$- \frac{d\lbrack R\rbrack}{dt} = k\lbrack R\rbrack^{0} = k$
$- d\lbrack R\rbrack = k.dt$
Integrating the above equation.
$- \int_{}^{}{d\lbrack R\rbrack = k\int_{}^{}{dt}}$
$- \lbrack R\rbrack = kt + I$ …(i)
Where, I is integration constant
At $t = 0,\ R = \lbrack R\rbrack_{0}$
$- \lbrack R\rbrack_{0} = k \times 0 + I$
$I = - \lbrack R\rbrack_{0}$
Put this value in Eq. (i)
$\ \ \ - \lbrack R\rbrack = kt - \lbrack R\rbrack_{0}$
or $\ \lbrack R\rbrack = - kt + \lbrack R\rbrack_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.