А ​сеrtаіn ​rеасtіоn ​А ​→ рrоduсtѕ ​іѕ ​ѕесоnd ​оrdеr ​іn ​А. ​Іf ​thіѕ ​rеасtіоn ​іѕ ​85% ​соmрlеtе ​іn ​12 ​mіnutеѕ, ​hоw ​lоng ​wоuld ​іt ​tаkе ​fоr ​thе ​rеасtіоn ​tо ​bе ​20.% ​соmрlеtе?

Question

how would i get the percentages into values to use in the integrated rate law?

Answer 1

If a reaction goes as r_A=-kC_A², the integrated rate equation is obtained from separating and integrating:

dC/C² = -kdt

1/C - 1/C₀ = kt integrating from C₀ to C and 0 to t

Find k by plugging in .15C₀ = C and 12 min = t

1/(.15C₀) - 1/C₀ = 12k k = (1/.15 - 1)(1/C₀)/12 = .4722/C_o

Now solve for t, given the k solved for and C = .8C₀

(1/(.8C₀) - 1/C₀)/k = t = (1/.8)-1)/C₀)(C₀/.4722) = .529 min.

Please go over my math, but the approach is reasonable.