The hydrogen iodide $HI(g)$ decomposition follows second order kinetics.
The rate constant at a given temperature is $k =0.079 \frac{L}{mol\cdot s} $.
a) Calculate the half-life time, if the initial molarity is $0.050 \;M $.
b) Under the same conditions, calculate after how much time $\frac{3}{5}$ would be decomposed.
a)
Half-life time:
$\theta$ $=$ $\frac{1}{0.079\cdot 0.050}$ $\approx$ $253\;s$
b)
There remains:
$\frac{2}{5}$ de $0.050$ $=$ $0.020\;M$
Let $t$ be the desired time:
$\frac{1}{[A]_t}$ $-$ $\frac{1}{[A]_o}$ $=$ $kt$
$t$ $=$ $\frac{1}{k}(\frac{1}{[A]_t}$ $-$ $\frac{1}{[A]_o})$ $=$ $\frac{1}{0.079}(\frac{1}{0.020}-$ $\frac{1}{0.050})$ $=$ $380\; s $
