Looking ahead In Chapter 5, we explain that the equilibrium constant (Keq) for a reaction can be calculated based on the difference in energy between reactants and products, according to the following equation:Keq=e−ΔERTK_{eq}=$$e^{-\frac{\Delta E}$${RT}}Using this equation, calculate the equilibrium constant for the 'reaction' shown. [For the rest of the book, if not otherwise specified, assume room temperature (298K).]

Ch. 3 - Alkanes and Cycloalkanes: Properties and Conformational Analysis

Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition

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Mullins 1st Edition

Ch. 3 - Alkanes and Cycloalkanes: Properties and Conformational Analysis

Problem 64

Chapter 2, Problem 64

Looking ahead In Chapter 5, we explain that the equilibrium constant (K_eq) for a reaction can be calculated based on the difference in energy between reactants and products, according to the following equation:
$K_{e q} = e^{- \frac{Δ E}{R T}}$
Using this equation, calculate the equilibrium constant for the 'reaction' shown. [For the rest of the book, if not otherwise specified, assume room temperature (298K).]

Verified step by step guidance

Step 1: Understand the equation provided. The equilibrium constant (Kₑ_q) is calculated using the formula:

Kₑ_q = e ^ (-∆E / RT)

, where ∆E is the energy difference between reactants and products, R is the gas constant, and T is the temperature in Kelvin.

Step 2: Identify the values needed for the calculation. ∆E (energy difference) should be provided or calculated based on the reaction. R, the gas constant, is typically 8.314 J/(mol·K), and T is given as room temperature, 298 K.

Step 3: Substitute the values into the equation. Replace ∆E with the energy difference, R with 8.314 J/(mol·K), and T with 298 K in the formula:

Kₑ_q = e ^ (-∆E / (8.314 × 298))

Step 4: Simplify the exponent. Calculate the value of

-∆E / (8.314 × 298)

to determine the exponent for the base e.

Step 5: Compute the final value of Kₑ_q by evaluating the exponential function

e ^ (-∆E / RT)

. This will give the equilibrium constant for the reaction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (K_eq)

The equilibrium constant (K_eq) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It provides insight into the extent to which a reaction proceeds, with values greater than 1 indicating a tendency towards products, and values less than 1 indicating a preference for reactants.

Gibbs Free Energy (∆E)

Gibbs free energy (∆E) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. In the context of chemical reactions, a negative change in Gibbs free energy indicates that the reaction is spontaneous, while a positive change suggests non-spontaneity.

Temperature (T) and the Gas Constant (R)

Temperature (T) in the equation is typically expressed in Kelvin, and it influences the kinetic energy of molecules, affecting reaction rates and equilibria. The gas constant (R) is a proportionality constant that relates energy scales in thermodynamics, with a value of 8.314 J/(mol·K). Together, T and R are crucial for calculating K_eq using the relationship with Gibbs free energy.

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Related Practice

Textbook Question

Calculate the energy difference between each pair of conformations shown by drawing and comparing Newman projections down the indicated bonds in each.

(b)

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Textbook Question

In Chapter 5, we introduce reaction coordinate diagrams as a plot of potential energy versus the progress of a reaction. Consider the reaction coordinate diagram drawn for the 'reaction' of conformation A becoming conformation B. Which structure is present at the top of the hill?

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Textbook Question

Correct the following incorrect names using standard IUPAC nomenclature. [Draw a compound that corresponds to the incorrect name, and then rename it.]

(a) 4-methylhexane

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Textbook Question

For each structure shown, draw the two chair conformations and choose which is most stable. Be sure that your second chair is the flipped version of the first. [Make sure that wedged substituents are up in the chair, regardless of whether up is equatorial or axial.]

(g)

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Textbook Question

In contrast to ethane and other alkanes studied in this chapter, there is no free rotation around any bonds in cyclopentane (shown below). Why?

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Textbook Question

The normal C(sp³)–C(sp³) bond length is 1.54 Å. The normal bond angle for an sp³-hybridized carbon is 109.5°. The following molecule experiences large deviations from these normal values. Explain these deviations. [Molecular models would be helpful here.]

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