Question

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 74% of its buttery flavor?

Answer 1

Answer:

3.91 minutes

Explanation:

Given that:

Biacetyl breakdown with a half life of 9.0 min after undergoing first-order reaction;

As we known that the half-life for first order is:

$t__{1/2}}= \frac{0.693}{k}$

where;

k = constant

The formula can be re-written as:

$k = \frac{0.693}{t__{1/2}}$

$k = \frac{0.693}{9.0 min}$

$k = 0.077 min^{-1}$

Let the initial amount of butter flavor in the food be $(N_0)$ = 100%

Also, the amount of butter flavor retained at 200°C $(N_t)$= 74%

The rate constant $k = 0.077 min^{-1}$

To determine how long can the food be heated at this temperature and retain 74% of its buttery flavor; we use the formula:

$\frac{N_t}{N_0}= -kt$

$t = - (\frac{1}{k}*In\frac{N_t}{N_0} )$

Substituting our values; we have:

$t = - (\frac{1}{0.077}*In\frac{74}{100} )$

t = 3.91 minutes

∵ The time needed for the food to be heated at this temperature and retain 74% of its buttery flavor is 3.91 minutes