Decomposition of Sucrose Reacting with water in an acidic...

Decomposition of Sucrose Reacting with water in an acidic solution at $35^{\circ} \mathrm{C},$ sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ decomposes into glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ and fructose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)^{*}$ according to the law of uninhibited decay. An initial concentration of $0.40 \mathrm{M}$ of sucrose decomposes to $0.36 \mathrm{M}$ sucrose in 30 minutes. What concentration of sucrose will remain after 2 hours? How long will it take until only 0.10 M sucrose remains?

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Key Concepts

First-order Reaction Kinetics

This concept refers to reactions where the rate is directly proportional to the concentration of a single reactant. In such reactions, the concentration decreases exponentially over time, and the mathematical treatment simplifies to the use of a logarithmic relationship between concentration and time.

Law of Uninhibited Decay

Uninhibited decay describes a scenario in which the reactant decays naturally over time without any external inhibition or acceleration. This means that the process follows a predictable pattern solely based on the intrinsic properties of the reaction, typically corresponding to first-order kinetics.

Integrated Rate Law

The integrated rate law is used to relate reactant concentration to time and the rate constant in chemical kinetics. For first-order reactions, it takes the form ln([A]t/[A]0) = -kt, allowing calculation of unknown parameters such as remaining concentration at a given time or the time required to reach a specific concentration.

Rate Constant

The rate constant is a proportionality factor in the rate law that quantifies the speed of the reaction under given conditions. In first-order reactions, its value, expressed in inverse time units, directly influences how rapidly the concentration of the reactant decreases over time.

Transcript

00:01 In this problem, this is a problem of uninhibited decay, where the function says that the amount of the substance is equal to the starting amount and zero times e to the k times t power, where t is the time and k is the rate of decay.

00:18 In this case, because given that sucrose reacting with acidic solution at 35 degrees decomposes into two other.

00:30 Two new chemicals, according to law of uninhibited decay.

00:33 And we're given the information that initial concentration is 0 .4 molar, 0 .4, and it decomposes to 0 .36 molar in 30 minutes.

00:47 So 30 times k.

00:48 And now we're trying to solve for k, the value of the decomposition.

00:54 So divide both sides by 0 .4.

00:57 We get negative 0 .36 over 0 .4.

01:02 Take the natural log both sides.

01:16 And now we can just plug this into a calculator to divide both sides by 30.

01:24 And we have approximately negative 0 .0035.

01:35 We can use this value of k to solve the amount for the amount of concentric...

01:42 The amount of sucrose that will remain after two hours, the concentration.

01:45 So n of t is the concentration, and t stands for hours.

01:49 So in this case, 120, or t is 120.

01:57 Because t were reset to be equal to minutes.

02:02 So let's use 0 .4 is still the starting...

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