The desorption of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128>s at 150 K. a. What is the half-life of the desorption reaction? b. If the surface is initially completely covered with n-butane at 150 K, how long will it take for 25% of the molecules to desorb? For 50% to desorb? c. If the surface is initially completely covered, what fraction will remain covered after 10 s? After 20 s?

The concept of half-life is pivotal when studying first order reaction kinetics, particularly when analyzing processes like the desorption of n-butane from aluminum oxide.

Half-life, often symbolized by \( t_{1/2} \), is the time required for half of the reactant to be converted into product in a chemical reaction. For first order reactions, the half-life is constant because it doesn't depend on the initial concentration of the reactant. To calculate the half-life of a first order reaction, we use the equation: \[ t_{1/2} = \frac{\ln(2)}{k} \]where \( k \) is the rate constant of the reaction. In a simple form, half-life showcases how quickly a substance undergoes change during a reaction, providing students a time scale for the reaction's progress.

• To use this formula, one must have the value of the rate constant, which typically requires experimental data or calculations.
• The natural logarithm of 2 (\( \ln(2) \)) is a constant approximately equal to 0.693.

By understanding half-life, students can predict the time scale over which reactions occur and can prepare experiments or industrial processes accordingly.

Applying this to our textbook exercise, with a rate constant of 0.128/s at 150 K for n-butane desorption, the half-life would provide a clear sense of the adsorption process duration, revealing at a glance the efficiency of material's use in various conditions.

In reaction kinetics, the rate constant is an essential parameter that gives the speed of a chemical reaction, as well as its dependency on temperature and other factors. For first order reactions, which are reactions where the rate depends linearly on only one reactant concentration, the rate constant \( k \) can help predict how fast a reaction will proceed.

The rate constant, with units of s-1 in the case of a first order reaction, is obtained experimentally and used in the formula to calculate both the half-life and the change in concentration of reactants over time.

• Higher values of \( k \) indicate faster reactions, whereas lower values indicate slower processes.
• The rate constant is temperature-dependent, meaning that it will change as the reaction conditions change, which is why it's specified at 150 K for the desorption of n-butane in our exercise.

In our exercise, knowing the rate constant allowed us to calculate the half-life and to predict how long it would take for a certain percentage of n-butane molecules to desorb from the surface. In the industry, such information is critical for designing and controlling processes to ensure efficiency and safety.

A good grasp of rate constants enables students to move beyond rote learning to a deeper understanding of the temporal dynamics of chemical systems.

Desorption is the process in which a substance is released or removed from a surface. In our exercise, the desorption involves n-butane molecules leaving the surface of aluminum oxide, which can be quantified and modeled using reaction kinetics.

This process is the reverse of adsorption and is critical in various scientific fields such as surface science, catalysis, and materials engineering.

Key Points about Desorption:

• Desorption can be triggered by various factors, including temperature changes, pressure changes, or chemical reactions.
• The rate at which desorption occurs can be indicative of the strength of adsorption and the surface properties of the material.
• In practical terms, desorption must be well understood and controlled in applications such as catalysis, where the surface reactivity is crucial, or in pollutant removal from surfaces.

By learning about the desorption process and its kinetics, students can approach real-world problems with a scientific perspective. They can predict how changes in conditions, such as temperature, which we kept at a constant 150 K in our example, affect the rate and efficiency of desorption. It illustrates the interplay between theoretical concepts learned in class and their application in experimental and technological settings. Understanding desorption empowers students to design and predict the behavior of materials and processes of interest.