Question

The hydrolysis of sucrose (C12H22O11) into glucose and fructose in acidic water has a rate constant of 1.8×10−4s−1 at 25 ∘C. Assuming the reaction is first order in sucrose, determine the mass of sucrose that is hydrolyzed when 2.55 L of a 0.160 M sucrose solution is allowed to react for 200 minutes.

Answer 1

To determine the mass of sucrose hydrolyzed in a first-order reaction, one must use the first-order rate equation with the given rate constant, initial concentration, and time. After solving for the concentration of sucrose at time t, the mass of sucrose hydrolyzed can be calculated by the change in concentration, molar mass of sucrose, and volume of the solution.

Step-by-step explanation:

The hydrolysis of sucrose (C12H22O11) into glucose and fructose is a first-order reaction, meaning that the rate of reaction depends linearly on the concentration of sucrose. Given the rate constant (k) of 1.8×10−4s−1 at 25 ℃, to determine the mass of sucrose hydrolyzed, we can apply the first-order rate equation:

ln([A]t/[A]0) = -kt

Where [A]t is the concentration at time t, [A]0 is the initial concentration, and t is time in seconds. As we're given [A]0 (0.160 M), and t (200 minutes, or 12000 seconds), we can find [A]t and then calculate the mass by using the molar mass of sucrose and the volume in liters.

To find the mass hydrolyzed, we subtract [A]t multiplied by the molar mass and volume from [A]0 multiplied by the same. Assuming complete reaction, the mass hydrolyzed would be:

Mass hydrolyzed = (0.160 M - [A]t) × 342.30 g/mol (molar mass of sucrose) × 2.55 L

Note that [A]t must be determined by plugging in the values into the first-order rate equation and solving for [A]t.