Question

A metal slowly forms an oxide film which completely protects the metal when the film thickness is 3.956 thousandths of an inch. If the film thickness is 1.281 thou. in 6 weeks, then the time it will take before it is 2.481 thou. is :(the rate of film formation follows first-order kinetics)

• A. 12 weeks
• B. 14 weeks
• C. 15 weeks
• D. 17 weeks

Answer 1

The correct option is A 12 weeks

When the film thickness is 3.956 thousandths of an inch., $a=\frac{3.956}{1000}$.
For $t=6weeks,a-x=\frac{(3.956-1.281)}{1000}$
$k=\frac{2.303}{t}log\frac{a}{a-x}=\frac{2.303}{6}log\frac{3.956}{3.956-1.281}$......(1)
For $t=?weeks$, $a-x=\frac{(3.956-2.481)}{1000}$
$k=\frac{2.303}{t}log\frac{a}{a-x}=\frac{2.303}{t}log\frac{3.956}{3.956-2.481}$......(2)
From equations (1) and (2),
$\frac{2.303}{6}log\frac{3.956}{3.956-1.281}=\frac{2.303}{t}log\frac{3.956}{3.956-2.481}$
Hence, $t=12weeks$.