Gibbs Free Energy Practice Problems

The equilibrium constant (K_eq) of a reaction can be calculated using the following equation.

• K_eq = e^−∆E/RT

Calculate the equilibrium constant for the following reaction at room temperature (298K).

A. K_eq = 6.0

B. K_eq = 0.006

C. K_eq = 6000

D. K_eq = 6.066

Which of the following reactions would proceed at a higher rate? Consider the relative values of the frequency factor (A) to compare the rates.

Consider the following reaction of propan-2-ol and chloroethane:

This reaction occurs through the following mechanism:

Explain why this reaction mechanism is favored and estimate the value of K _eq based on the stability of the anions.

Given the keto-enol tautomerism below, the relevant bond dissociation energies (BDE), and no knowledge of the mechanism, estimate the equilibrium constant (in 3 s.f.) for the reaction at 298.15 K.

Relevant BDE values

C―C π bond = 65 kcal/mol
C―O π bond = 85 kcal/mol
2° C―H bond = 95 kcal/mol
RO―H bond = 102 kcal/mol

Assuming no knowledge of the mechanism of the equilibrium below and given the relevant bond dissociation energies (BDE), estimate the equilibrium constant (in 3 s.f.) for the equilibrium process at 298.15 K. 

Relevant BDE values

C―C π bond = 65 kcal/mol
3° C―H bond = 91 kcal/mol
2° C―H bond = 95 kcal/mol

Determine if the equilibrium constant is going to be greater than, equal to, or less than 1 for the following equilibrium reaction. Justify your answer.

Analyze the provided values below to ascertain whether the reaction would be favorable or unfavorable.

∆H° = +9.45 kcal/mol ; ∆S° = +80 cal/mol•K ; T = 425 K

A reaction has an enthalpy change of +12.8 kcal/mol and an entropy change of +75 cal/mol⋅K. (a) At which temperature will the process be in a state of neither being favored nor disfavored? (b) Will the process be favored or disfavored if the temperature exceeds the calculated value? (c) And what about if the temperature is lower than the calculated value?

Fill in the missing rates in the following table that represents the rotation around the single bond of butane. The rate of the reaction is independent of concentration.

Consider the rotation around the single bond of butan-2-ol. Based on experimental observations, what is the order of the reaction with respect to butan-2-ol?

Consider the following figure depicting the rotation around the single bond of 1-bromo-2-methylpropane. Determine the rate law expression for this reaction based on the provided experimental data.

Molecule X reacts in a two-step process to yield molecule Y, with the rate-determining step being the second step. On the other hand, molecule X undergoes a three-step process to yield molecule Z, with the rate-determining step being the first step. Sketch reaction coordinate diagrams for both reactions, clearly illustrating that the reaction leading to the formation of Y occurs at a faster rate compared to the reaction leading to the formation of Z.

Determine the rate law for the overall reaction if step 1 is the rate-determining step.

In the given reaction, which direction would be more favored with an increase in temperature?

If the temperature is increased, which direction of the reaction, if any, would be favored?

In the given acid-base reaction, determine the conjugate base-to-acid ratio. Assume that  the concentrations of the reactants are equal.

In the equilibrium (acid-base) reaction below, determine the Gibbs free energy (∆G°) at 289 K.

In the acid-base reaction below, determine the ∆G° in kcal/mol at 279 K.

In the acid-base reaction below, what is the ∆G° at 380 K?

(I) Identify the side of the reaction that is favored by entropy. (II) And if the change in entropy (∆S°) is zero for this reaction, calculate the change in Gibbs free energy (∆G°) using the assumption of a temperature (T) of 298 K.

Based on the data given below, determine the number of molecules involved in the rate-determining step.

For T₁ = 40°C and T₂ = 125°C, determine the equilibrium constants and ∆G° if a reaction has ∆H° = 10 kcal/mol and ∆S° = 0.14 kcal/(mol⋅K). How do ∆G° and K_eq change as T increases?

The reaction of methyl bromide with a base is linearly dependent on the concentrations of methyl bromide and OH ⁻. For T = 40°C, the rate constant for such a reaction is 1.2×10 ⁻⁸/(M•s). Determine the effects of increasing methyl bromide's concentration to 1.50 M on the:

1. Reaction rate

2. Rate constant

Given the changes in the concentrations of chloroethane and hydroxide ion, determine its effect on the rate of reaction.

Alkyl halide concentration is doubled and the hydroxide ion concentration is quadrupled.

Given the changes in the concentrations of chloropropane and hydroxide ion, determine its effect on the rate of the reaction.

Alkyl halide concentration is halved and the hydroxide ion concentration is quadrupled.

1. Which of the following reactions has a greater equilibrium constant?

2. A student starts both reactions with a reactant concentration of 1.0 M. Determine which reaction produces the most product after the reactions have reached equilibrium.

If the value of ΔGº for the following reaction is −2.0 kJ/mol (−0.48 kcal/mol), calculate K_eq at room temperature (25 °C).
CH₃CH₂Br + H₂S ⇌ CH₃CH₂SH + HBr

A. −0.81

B. 0.44

C. 0.81

D. 2.24

2-chloro-2-methylbutane reacts with methanol according to the following chemical equation.

Experimental results suggest that the reaction follows the rate equation shown below:
rate = k_t [2-chloro-2-methylbutane]
Determine the kinetic order with respect to 2-chloro-2-methylbutane.

2-chloro-2-methylbutane reacts with methanol according to the following chemical equation.

The reaction is found to follow the rate equation shown below
rate = k_t [2-chloro-2-methylbutane]
Determine the overall kinetic order.

Cyclopentene reacts with bromine according to the following chemical equation.

The reaction rate is found to follow the following rate law under certain conditions
rate = k_t [cyclopentene] [Br₂]²
Determine the kinetic order with respect to cyclopentene.

Cyclopentene reacts with bromine according to the following chemical equation.

The reaction rate is found to follow the following rate law under certain conditions
rate = k_t [cyclopentene] [Br₂]²
Determine the kinetic order with respect to bromine.

The following reaction takes place when a small piece of platinum is added to a mixture of propene and hydrogen (H₂).

Experimental results show that a change in the concentration of propene or H₂ has no effect on the reaction rate.
Determine the kinetic order with respect to propene and H₂. Find the overall order.

The value of ΔG° for the reaction below is −8.20 kJ/mol (−1.96 kcal/mol).

CH₃Cl + H₂S ⇌ CH₃SH + HCl

At 25.0°C, the initial concentrations of CH ₃Cl and H₂S are both 1.00 M. Determine the equilibrium concentrations of all species.