The conversion of sucrose (table sugar) to glucose and fructose is first order in the concentration of sucrose, which means that the rate of reaction is proportional to the concentration of the sucrose. The rate of disappearance of sucrose can be expressed as , where c represents the concentration of the sucrose, and k is called the rate constant and is mathematically identical to the negative of the decay constant. If it takes 4 hours for the sucrose concentration to drop by a factor of 8, what is the rate constant? A) 0.69 hour^-1 B) 0.50 hour^-1 C) 0.52 hour^-1 D) 2.00 hour^-1

Question

Quizplus · Accepted Answer

From the given information, we can use the formula:

ln(C0/Ct) = kt

where C0 is the initial concentration of sucrose, Ct is the concentration of sucrose after time t, and k is the rate constant.

Since it takes 4 hours for the sucrose concentration to drop by a factor of 8, we know that Ct/C0 = 1/8. Therefore, we can write:

ln(1/8) = k(4 hours)

Solving for k, we get:

k = ln(1/8)/4 hours ≈ 0.52 hour^-1

Thus, the answer is C.

The Conversion of Sucrose (Table Sugar) to Glucose and Fructose