Biacetyl the flavoring that makes margarine taste just like

Biacetyl, the flavoring that makes margarine taste \"just like butter,\" is extremely stable at room temperature, but at 200°C it undergoes a first-order breakdown with a half-life of 9.0 min. An industrial flavor-enhancing process requires that a butter-flavored food be heated briefly at 200°C. How long can the food be heated at this temperature and retain 65% of its buttery flavor?

Solution

The first order reax has

k = ln2/T_1/2

So k = ln2/9 min^-1

And

kT = ln([A_o]/[A])

A = 65% of initial concentration

So A_o/A = 100/65 = 1.5384

=> kT = ln(1.5384)

So t = ln(1.5384)/(ln2/9)

t = 9 x ln(1.5384)/ln2

t = 5.592876 min

OR t = 5 min 36 sec (approx)