# Oxide layer formation on a metal is a $Rx_n$ which is of first order with rate constant $10^{-8}min^{-1}$ if maximum thickness can be $2mm$ then what time will be taken to form a oxide layer of thickness $1.5mm$

$\begin{array}{1 1} 1.386 \times 10^{8}\;min \\ 0.693 \times 10^{8}\;min \\ 10^{8}\;min \\ 4.238 \times 10^{8}\;min\end{array}$

Answer: $1.386 \times 10^{8}\;min$
This is very similar to the problems that involve calculating rate-constants for a partially completed reaction.
Out of a max thickness of 2mm, % complete when it forms an oxide layer of thickness 1.5mm $= \large\frac{1.5}{2}$$= 0.75 = 75\%$
$\Rightarrow$ The remaining $\% = 1 - 0.75 = 0.25 = 25\%$
$\Rightarrow ln\;A = -kt + ln\;A_0 \rightarrow ln 0.25 = -t \times 10^{-8}\;min^{-1} + ln \; 1$
$\Rightarrow -1.386 = -t \times 10^{-8}\;min^{-1} \rightarrow t = 1.386 \times 10^{8}\;min$
edited Jul 25, 2014