Gibbs Free Energy: Videos & Practice Problems

Gibbs free energy (ΔG) indicates the energy available for work in a reaction, with ΔG = 0 at equilibrium. Cellular reactions rarely reach equilibrium, necessitating the use of the reaction quotient (Q) to predict reaction direction. When Q < K (equilibrium constant), the reaction proceeds forward; when Q > K, it shifts backward. Under standard conditions (25°C, 1 atm, 1 M), ΔG can be calculated using ΔG° = -RT ln(K). Physiological conditions often differ, affecting ΔG, which can be calculated as ΔG = ΔG° + RT ln(Q), determining spontaneity in biological systems.

Gibbs Free Energy Equation

Gibbs free energy is a crucial concept in thermodynamics, representing the energy available to perform work in a chemical reaction. The standard Gibbs free energy equation is expressed as:

\[ \Delta G = \Delta H - T \Delta S \]

In this equation, \(\Delta G\) denotes the change in Gibbs free energy, \(\Delta H\) represents the change in enthalpy, \(T\) is the absolute temperature in Kelvin, and \(\Delta S\) signifies the change in entropy. Understanding this relationship is essential, as it illustrates how changes in enthalpy and entropy, along with temperature, influence the spontaneity of a reaction.

At equilibrium, the concentrations of reactants and products remain constant, leading to a situation where no net work is performed. In this state, the change in Gibbs free energy (\(\Delta G\)) equals zero, indicating that the system is at a balance where the forward and reverse reactions occur at the same rate.

This principle highlights the importance of concentration changes in determining the direction of a reaction. As we delve deeper into the topic, we will explore how these factors influence reaction direction and the implications for chemical processes.

Reaction Direction

In chemical reactions, the concentrations of reactants and products play a crucial role in determining the direction of the reaction. It is important to understand that cellular reactions are typically not at equilibrium due to various factors, such as changing conditions and the continuous addition or removal of reactants and products. When a reaction is not at equilibrium, we utilize the reaction quotient, denoted as q, which is calculated using the same expression as the equilibrium constant, K. The reaction quotient is defined as the ratio of the concentrations of products to the concentrations of reactants, but unlike the equilibrium constant, it applies to reactions that are not at equilibrium.

According to Le Chatelier's principle, when a system at equilibrium is disturbed, the reaction will shift in a direction that counteracts the disturbance, aiming to restore equilibrium. For example, consider the reaction between carbon monoxide (CO) and hydrogen gas (H₂) to produce methanol (CH₃

$$ q = \frac{[CH_3OH]}{[CO][H_2]^2} $$

Here, the concentration of methanol is in the numerator, while the concentrations of carbon monoxide and hydrogen gas are in the denominator, with the coefficient of hydrogen gas squared as it appears in the balanced equation.

By comparing the reaction quotient q with the equilibrium constant K, we can predict the direction of the reaction. If q is less than K, it indicates that the concentration of products is low compared to reactants, prompting the reaction to proceed in the forward direction to produce more products. Conversely, if q is greater than K, it suggests an excess of products, leading the reaction to shift in the reverse direction to generate more reactants. When q equals K, the system is at equilibrium, meaning the rates of the forward and reverse reactions are equal.

Understanding how concentrations affect the direction of reactions is essential, as these concentrations are integral to the conditions under which the reactions occur. In subsequent discussions, we will explore how standard conditions influence the Gibbs free energy equation, further enhancing our grasp of chemical thermodynamics.

Gibbs Free Energy (Standard Conditions)

In chemical reactions, predicting the direction of a reaction can be achieved by analyzing the equilibrium constant and the concentrations of the reactants and products. These concentrations are influenced by specific conditions, which is why scientists utilize standard conditions for comparison across different reactions. The symbol used to denote standard conditions is crucial for understanding these comparisons.

The equilibrium constant plays a significant role in calculating the change in free energy under standard conditions. The symbol Δ (delta) signifies change, while G represents free energy. When combined with a subscript "not" (‾), it indicates the change in free energy under standard conditions, denoted as ΔG‾. In contrast, ΔG without the "not" refers to the actual change in free energy under any conditions, which will be explored further in subsequent discussions.

Standard conditions are defined by specific parameters: a temperature of 25 degrees Celsius (298 Kelvin), a gas constant R of 8.315 joules per mole per Kelvin, and a pressure of 1 atmosphere. It is important to note that the value of the gas constant can vary based on the units used; for instance, it can also be expressed as 1.98 x 10^-3 kilocalories per mole per Kelvin.

The equation for calculating the change in Gibbs free energy under standard conditions is given by:

ΔG‾ = -R * T * \ln(K)

In this equation, ΔG‾ is the change in free energy, R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant. This formula will be applied in practice problems to deepen understanding.

Future discussions will focus on Gibbs free energy under physiological conditions, which differ from standard conditions, providing a broader context for these concepts.

Gibbs Free Energy (Physiological Conditions)

In scientific research, standard conditions are crucial for comparing different reactions, as they provide a controlled environment typically found in laboratory settings. However, biological systems often operate under varying physiological conditions, which can significantly differ from these standard conditions. Understanding the change in Gibbs free energy (ΔG) is essential for determining the spontaneity of reactions both in the lab and within living organisms.

The Gibbs free energy under any condition can be calculated using the equation:

ΔG = ΔG° + RT ln(Q)

In this equation, ΔG° represents the change in free energy under standard conditions, R is the gas constant (8.315 J/(mol·K)), T is the temperature in Kelvin, and Q is the reaction quotient, which is the ratio of the concentrations of products to reactants at any given moment.

For example, consider a reaction in glycolysis where dihydroxyacetone phosphate (DHAP) is converted into glyceraldehyde 3-phosphate (G3P). The equilibrium constant (K) for this reaction under standard conditions is given as 0.0475. To find ΔG° for this reaction, we can use the formula:

ΔG° = -RT ln(K)

Substituting the known values:

• R = 8.315 J/(mol·K)
• T = 298 K
• K = 0.0475

Calculating this gives:

ΔG° = -8.315 × 298 × ln(0.0475) = 7550 J/mol

This positive value indicates that the reaction is endergonic and non-spontaneous under standard conditions. However, glycolysis is a vital process that occurs continuously in cells, suggesting that the actual ΔG must be evaluated under physiological conditions.

To calculate ΔG under physiological conditions, we need the concentrations of DHAP and G3P. For this example, the concentrations are:

• [DHAP] = 2 × 10^-4 M
• [G3P] = 3 × 10^-6 M

Using these concentrations, we can determine the reaction quotient (Q):

Q = [G3P] / [DHAP] = (3 × 10^-6) / (2 × 10^-4)

Now, substituting into the ΔG equation:

ΔG = ΔG° + RT ln(Q)

Plugging in the values:

ΔG = 7550 + (8.315 × 298 × ln(Q))

After calculating Q and substituting it back into the equation, we find:

ΔG = -2856.32 J/mol

This negative value indicates that the reaction is spontaneous and exergonic under physiological conditions, aligning with the known behavior of glycolysis in living cells. Thus, while standard conditions suggest a non-spontaneous reaction, physiological conditions reveal the true spontaneity of the process, highlighting the importance of context in biochemical reactions.

Consider a reaction where K_eq=1.6 but Q = 3.19. What direction will the reaction proceed?

• A. Forward.
• B. Reverse.
• C. Forward & reverse reactions proceed equally.
• D. Not enough information provided to make conclusions.

Answer: (B)

At equilibrium, the reaction A ⇌ B + C has the following reactant concentrations: [A] = 3 mM, [B] = 4 mM, and [C] = 10 mM. What is the standard free energy change for the reaction & is it endergonic or exergonic?

• A. – 6418 J
• B. 6418 J
• C. 10,698 J
• D. – 10,698 J

Answer: (C)

ΔG˚=141.7 kJ for the following reaction. Calculate ΔG: T=10˚C, [SO ₃] = 25mM, [SO₂] = 50mM, & [O₂] = 75 mM. 
2 SO₃(g) ⇌ 2 SO₂(g) + O₂(g)

• A. – 6,437 J
• B. 39,938 J
• C. -155,127 J
• D. 138,865 J

Answer: (D)

Here’s what students ask on this topic:

What is Gibbs free energy and why is it important in chemical reactions?

Gibbs free energy (ΔG) is a thermodynamic quantity that represents the amount of energy available to do work in a chemical reaction. It is crucial because it helps predict whether a reaction will occur spontaneously. The equation for Gibbs free energy is:

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

where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous reaction, while a positive ΔG means the reaction is non-spontaneous.

How do you calculate Gibbs free energy under standard conditions?

To calculate Gibbs free energy under standard conditions (ΔG°), you can use the following equation:

$\mathrm{\Delta G°}=-RT\ln K$

where R is the gas constant (8.315 J/mol·K), T is the temperature in Kelvin (usually 298 K), and K is the equilibrium constant. This equation helps determine the spontaneity of a reaction under standard conditions, which include 25°C, 1 atm pressure, and 1 M concentration of reactants and products.

What is the difference between the reaction quotient (Q) and the equilibrium constant (K)?

The reaction quotient (Q) and the equilibrium constant (K) are both ratios of the concentrations of products to reactants, but they differ in their application. Q is used to describe the state of a reaction at any point in time, while K specifically describes the state at equilibrium. The expressions for Q and K are:

$Q=\frac{\mathrm{[products]}}{\mathrm{[reactants]}}$

$K=\frac{\mathrm{[products]}}{\mathrm{[reactants]}}$

If Q < K, the reaction proceeds forward; if Q > K, it proceeds backward; if Q = K, the reaction is at equilibrium.

How do physiological conditions affect Gibbs free energy calculations?

Physiological conditions often differ from standard conditions, affecting Gibbs free energy (ΔG). Under physiological conditions, ΔG can be calculated using:

$\mathrm{\Delta G}=\mathrm{\Delta G°}+RT\ln Q$

where ΔG° is the Gibbs free energy under standard conditions, R is the gas constant, T is the temperature in Kelvin, and Q is the reaction quotient. This equation accounts for the actual concentrations of reactants and products in a biological system, providing a more accurate measure of reaction spontaneity in living organisms.

What is the significance of ΔG being zero at equilibrium?

When ΔG is zero at equilibrium, it indicates that the system is in a state of balance, with no net change in the concentrations of reactants and products. This means that the forward and reverse reactions occur at the same rate, and no work can be done by the system. The equation for this state is:

$\mathrm{\Delta G}=0$

At equilibrium, the system has reached its lowest possible free energy state, and any deviation from this state will result in a shift to restore equilibrium, as described by Le Chatelier's principle.