$2\mathrm{.}4$ Three powders $($A$,$ B and C$)$ are to be mixed in the proportion of $60$:$30$:$10(A$:$B$:$C)$ by mass.

Each powder consists of uniform spherical particles of density $1800k\frac{g}{m^3}$ and particles of

diameter $200m,180m$ and $150m$ for A$,$ B and C respectively. In the evaluation of the

mixing process with respect to powder $C($key component$),$ the standard deviations of $100g$

samples were obtained as a function of time as shown below.

a$.$ Show that the mixing process follows first$-$order kinetics, and determine the mixing rate

constant.

b$.$ Estimate the mixing times required to achieve a degree of mixing within $10\%,5\%,2\%,$

and $1\%$ from complete randomness. What confidence would you have in these results?

Would further experimentation be necessary? Why?

Approx. Ans. $($a$)0\mathrm{.}14mi{n}^{-1}($b$)46,51,57,62$min