Question

In a first-order process a blue dye reacts to form a purple dye. The amount of blue at the end of 1hr is 480g and at the end of 3hr is 120g. Graphically estimate the amount of blue present initially.

Answer 1

In a first-order process a blue dye reacts to form a purple dye. The amount of blue at the end of 1hr is 480g and at the end of 3hr is 120g. Graphically estimate the amount of blue present initially.

assume t = 1h, is actually initial time, so

A0 = 480 g at t = 0

then, Afinal = 120 g at t = 3-1 = 2

estimate K

ln(A) = ln(A0) - kt

ln(120) = ln(480) - k(2)

k = (ln(120 - ln(480) ) /(-2)

k = 0.6931

now

at t = -1

ln(A) = ln(480) - 0.6931(-1)

A = exp(ln(480) - 0.6931(-1))

A = 959.95 g initially at t = -1 . i.e. t = 0 hours