Gibbs Free Energy Calculations: Videos & Practice Problems

Understanding Gibbs free energy ($\mathrm{\Delta G}$) is crucial for predicting the spontaneity of chemical reactions. Under standard conditions (1 atmosphere pressure and 25 °C), the standard change in Gibbs free energy (${\mathrm{\Delta G}}^{\circ }$) is calculated using the formula:

${\mathrm{\Delta G}}^{\circ }={\mathrm{\Delta H}}^{\circ }-T{\mathrm{\Delta S}}^{\circ }$

where ${\mathrm{\Delta H}}^{\circ }$ is the change in enthalpy, $T$ is the temperature in Kelvin, and ${\mathrm{\Delta S}}^{\circ }$ is the change in standard entropy. For non-standard conditions, $\mathrm{\Delta G}$ varies and is not accompanied by the not sign. The standard Gibbs free energy of formation (${{\mathrm{\Delta G}}^{\circ }}_f$) for elements in their natural state is zero, and the ${\mathrm{\Delta G}}^{\circ }$ of a reaction can be determined by summing the Gibbs free energies of formation for all products and reactants, accounting for their respective moles. These values are typically provided in a chart, as they are unique for different compounds. This formula is a powerful tool for approximating whether reactions will be spontaneous at certain temperatures, guiding us through the thermodynamic landscape of chemical processes.

The Gibbs Free Energy Formula

The Gibbs free energy is a crucial concept in thermodynamics, allowing us to determine the spontaneity of a reaction. The formula for calculating the change in Gibbs free energy (\( \Delta G \)) is expressed as:\[\Delta G = \Delta H - T \Delta S\]where \( \Delta H \) represents the change in standard enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in standard entropy. It is important to distinguish between standard and non-standard conditions. The standard Gibbs free energy change (\( \Delta G^\circ \)) is calculated under standard conditions, which typically include a pressure of 1 atmosphere and a temperature of 25 degrees Celsius (298 K). In contrast, \( \Delta G \) without the superscript indicates the Gibbs free energy change under non-standard conditions. Understanding these distinctions is essential for accurately predicting the behavior of chemical reactions and their feasibility based on energy changes.

The Gibbs Free Energy Formula Example

In thermodynamics, the Gibbs free energy change (\( \Delta G \)) is a crucial indicator of a reaction's spontaneity. For a given reaction, if the standard enthalpy change (\( \Delta H \)) is -111.4 kJ and the standard entropy change (\( \Delta S \)) is -25 J/K, we can calculate \( \Delta G \) at a temperature of 298 K using the formula:

\( \Delta G = \Delta H - T \Delta S \)

Before substituting the values, it's important to ensure that the units are consistent. Since \( \Delta H \) is in kilojoules and \( \Delta S \) is in joules, we convert \( \Delta S \) to kilojoules by recognizing that 1 kJ = 1000 J. Thus, we have:

\( \Delta S = -25 \, \text{J/K} = -0.025 \, \text{kJ/K} \)

Now, substituting the values into the equation:

\( \Delta G = -111.4 \, \text{kJ} - (298 \, \text{K} \times -0.025 \, \text{kJ/K}) \)

Calculating the second term:

\( 298 \, \text{K} \times -0.025 \, \text{kJ/K} = -7.45 \, \text{kJ} \)

Now, substituting this back into the equation gives:

\( \Delta G = -111.4 \, \text{kJ} + 7.45 \, \text{kJ} = -103.95 \, \text{kJ} \)

Since \( \Delta G \) is less than 0, this indicates that the reaction is spontaneous at 298 K. In summary, a negative Gibbs free energy change signifies that the reaction can proceed without external energy input, confirming its spontaneous nature.

Standard Gibbs Free Energy and Temperature

In thermodynamics, the Gibbs free energy change (ΔG) is a crucial indicator of a reaction's spontaneity. The relationship can be expressed through the equation:

$$\Delta G = \Delta H - T\Delta S$$

Here, ΔH represents the change in enthalpy, T is the absolute temperature in Kelvin, and ΔS is the change in entropy. A reaction is considered spontaneous when ΔG is negative, indicating that the process can occur without external energy input.

When the values of ΔG are unknown, we can analyze the signs of ΔH and ΔS to predict the spontaneity of a reaction under varying temperature conditions. If both ΔH and ΔS are negative, the reaction is spontaneous at low temperatures. Conversely, if both are positive, the reaction is spontaneous at high temperatures. If ΔH is negative and ΔS is positive, the reaction is always spontaneous, while if ΔH is positive and ΔS is negative, the reaction is always non-spontaneous.

Understanding these relationships allows chemists to predict the behavior of reactions under different thermal conditions, facilitating the design of processes in various scientific and industrial applications.

Standard Gibbs Free Energy and Temperature Example

In the reaction where 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas to produce 2 moles of ammonia gas, the enthalpy change (ΔH) is -92.4 kJ, and the entropy change (ΔS) is -198 J/K. To determine if the reaction is spontaneous under standard conditions, we can use the Gibbs free energy equation:

$$\Delta G = \Delta H - T \Delta S$$

Setting ΔG to zero allows us to find the temperature at which the reaction is at equilibrium:

$$0 = -92.4 \text{ kJ} - T \left(-\frac{198 \text{ J}}{1000}\right)$$

Rearranging gives:

$$T = \frac{92.4 \text{ kJ}}{0.198 \text{ kJ/K}} \approx 466.67 \text{ K}$$

This temperature indicates the point of equilibrium. To assess spontaneity, we analyze the signs of ΔH and ΔS. In this case, both ΔH and ΔS are negative. According to the spontaneity criteria:

• If both ΔH and ΔS are negative, the reaction is spontaneous at low temperatures.
• If both are positive, it is spontaneous at high temperatures.
• If ΔH is positive and ΔS is negative, the reaction is non-spontaneous at all temperatures.
• If ΔH is negative and ΔS is positive, the reaction is spontaneous at all temperatures.

Since our reaction has both ΔH and ΔS negative, it will be spontaneous below the calculated temperature of 466.67 K. Therefore, any temperature below this threshold will result in a spontaneous reaction.

Calculate ∆G° for the following reaction: P₄ (s) + 5 O₂ (g) → P₄O₁₀ (s), ∆H° = −2940 kJ/mol, 25 °C.
Does the reaction favor reactants or products?

• A. 1419.3 kJ
• B. −2653 kJ
• C. −140.7 kJ
• D. 598.5 kJ

Answer: (B)

Determine if reaction is spontaneous under standard conditions, if not at what temperature will it be spontaneous?
3 A (g) + 5 B (s) → 3 AB (s) + B₂ (g)       ∆H° = 112.7 kJ, ∆S° = 78.3 J/K.

• A. 1439.3 K
• B. 274.6 K
• C. 1.439 K
• D. 719.65 K

Answer: (A)

Nickel has ∆H_vap = 370.4 kJ/mol and ∆S_vap = 123.3 J/mol•K. Will nickel boil at 2700 °C and 1 atm?

• A. Yes, nickel will boil at 2700 °C and 1 atm.
• B. No, the temperature is not high enough for nickel to boil.

Answer: (B)

Gibbs Free Energy of Reactions

The Gibbs free energy of a reaction is a crucial concept in thermodynamics, reflecting the spontaneity of a reaction under constant temperature and pressure. It can be calculated using the standard Gibbs free energy of formation values, denoted as ΔG_f⁰. These values are typically provided in a chart, as memorizing them for all compounds and elements would be impractical. Notably, the Gibbs free energy of formation for elements in their natural states is defined as zero, similar to the standard enthalpy of reactions.

The formula for calculating the change in standard Gibbs free energy of a reaction is expressed as:

ΔG_reaction⁰ = Σ(ΔG_f⁰ of products) - Σ(ΔG_f⁰ of reactants)

In this equation, ΔG_reaction⁰ represents the change in Gibbs free energy in kilojoules, while Σ indicates the summation of the Gibbs free energy of formation values for all products and reactants. The variable N refers to the moles of each substance involved in the reaction. The units for standard Gibbs free energy formation are kilojoules per mole (kJ/mol).

By applying this formula, one can determine whether a reaction is spontaneous. A negative value for ΔG_reaction⁰ indicates that the reaction can occur spontaneously, while a positive value suggests that the reaction is non-spontaneous under the given conditions. Understanding and utilizing this relationship is essential for predicting the behavior of chemical reactions in various contexts.

Gibbs Free Energy of Reaction Example

To determine the change in the standard Gibbs free energy for the reaction between nitric acid and ammonia to produce solid ammonium nitrate, we utilize the standard Gibbs free energy of formation values for each compound involved. The formula for calculating the standard Gibbs free energy change (\( \Delta G^\circ_{\text{reaction}} \)) is:

\( \Delta G^\circ_{\text{reaction}} = \Delta G^\circ_{\text{products}} - \Delta G^\circ_{\text{reactants}} \)

In this case, we have the following compounds:

• Ammonium nitrate (product): \( \Delta G^\circ_f = -183.8 \, \text{kJ/mol} \)
• Nitric acid (reactant): \( \Delta G^\circ_f = -73.5 \, \text{kJ/mol} \)
• Ammonia (reactant): \( \Delta G^\circ_f = -16.4 \, \text{kJ/mol} \)

Since the reaction involves one mole of each reactant and product, we can substitute these values into the equation:

\( \Delta G^\circ_{\text{reaction}} = (-183.8) - [(-73.5) + (-16.4)] \)

Calculating the reactants' contribution:

\( \Delta G^\circ_{\text{reaction}} = -183.8 - (-73.5 - 16.4) \)

Now, simplifying the equation:

\( \Delta G^\circ_{\text{reaction}} = -183.8 - (-89.9) \)

Thus, we find:

\( \Delta G^\circ_{\text{reaction}} = -183.8 + 89.9 = -93.9 \, \text{kJ} \)

Therefore, the standard Gibbs free energy change for the reaction is \( -93.9 \, \text{kJ} \), indicating that the reaction is spontaneous under standard conditions.

Fe₂O₃ (s) + 3 H₂ (g) → 2 Fe (s) + 3 H₂O (g) is a redox reaction. What would be its Gibbs Free energy change under standard conditions? Is the reaction spontaneous at 25 °C?

• A. 513.6 kJ; No, the reaction is not spontaneous at 25 °C.
• B. 56.4 kJ; No, the reaction is not spontaneous at 25 °C.
• C. −513.6 kJ; Yes, the reaction is not spontaneous at 25 °C.
• D. 56.4 kJ; Yes, the reaction is spontaneous at 25 °C.

Answer: (B)

Here’s what students ask on this topic:

How do you calculate standard Gibbs free energy?

To calculate the standard Gibbs free energy change (ΔG°) for a chemical reaction, you can use the following formula:

$\mathrm{\Delta G°}=\mathrm{\Delta H°}-T\mathrm{\Delta S°}$

Where:

• ΔG° is the standard Gibbs free energy change,
• ΔH° is the standard enthalpy change of the reaction,
• T is the temperature in Kelvin (K),
• ΔS° is the standard entropy change of the reaction.

All these values are typically given in joules per mole (J/mol). The standard enthalpy (ΔH°) and standard entropy (ΔS°) values can be found in tables or calculated from other data.

Another way to calculate ΔG° is by using the standard free energies of formation (ΔG_f°) for each reactant and product:

$\mathrm{\Delta G°}=\sum \left(\mathrm{\Delta G_f°}\text{products}\right)-\sum (\mathrm{\Delta G_f°}$

What is the standard Gibbs free energy?

The standard Gibbs free energy, denoted as ΔG^°, is a thermodynamic quantity that indicates the amount of energy available to do work during a chemical reaction at standard conditions (usually 1 bar pressure and 298.15 K temperature). It combines the enthalpy (ΔH^°) and entropy (ΔS^°) changes of a reaction into a single value. The equation for standard Gibbs free energy change is:

ΔG^° = ΔH^° - TΔS^°

Where:

• ΔG^° is the standard Gibbs free energy change,
• ΔH^° is the standard enthalpy change,
• T is the temperature in Kelvin,
• ΔS^° is the standard entropy change.

A negative ΔG^° value indicates that the reaction is spontaneous under standard conditions, meaning it can occur without the input of additional energy. Conversely, a positive ΔG^° means the reaction is non-spontaneous and requires energy to proceed. If ΔG^° is zero, the system is at equilibrium, and no net reaction occurs. This concept is fundamental in predicting the direction and extent of chemical reactions.

Which of the following correctly expresses the standard Gibbs free energy change of a reaction in terms of the changes in enthalpy and entropy?

The standard Gibbs free energy change (ΔG^°) of a reaction can be correctly expressed in terms of the changes in enthalpy (ΔH^°) and entropy (ΔS^°) using the following equation:

ΔG^° = ΔH^° - TΔS^°

In this equation, T represents the absolute temperature in Kelvin (K). The ΔG^° value predicts the spontaneity of a reaction under standard conditions (1 bar pressure and the substances involved being in their standard states). If ΔG^° is negative, the reaction is spontaneous; if it's positive, the reaction is non-spontaneous; and if it's zero, the system is at equilibrium. This relationship is fundamental in thermodynamics and helps to understand how changes in enthalpy, entropy, and temperature influence the spontaneity of a chemical reaction.