There are $0$-order reactions, such as certain decompositions in contact with a metal catalyst, such as
$2HI(g)$ $\longrightarrow$ $H_2(g)$ $+$ $I_2(g)$
in contact with gold $Au$.
Determine for these reactions
a) the rate law in relation to $HI$
b) the decomposition law of $HI$
c) the half-life time $\theta $
Let's call $HI(g)$ $=$ $A$
a)
$v_{A}=-k.[A]^o=-k$
b)
$\frac{\d [A]}{d t}$ $=$ $-k$
$d[A]$ $=$ $-k\;dt$
$\int_{[A]_o}^{[A]_t}d[A]$ $= $ $-k\;\int_{t_o}^tdt$
$[A]_t-[A]_o$ $=$ $-k(t-t_o)$
$[A]_t$ $=$ $[A]_o-kt$
c)
Si $[A]_t$ $=$ $\frac{[A]_o}{2}$, alors
$\frac{[A]_o}{2}$ $=$ $[A]_o-k\theta$
$\theta=\frac{[A]_o}{2\;k}$
