Question

A reaction attains equilibrium state under standard conditions, then what is incorrect for this? (a) Equilibrium constant \(K=0\) (b) Equilibrium constant \(K=1\) (c) \(\Delta G^{\circ}=0\) and \(\Delta H^{\circ}=T \Delta S^{\circ}\) (d) \(\Delta G=0\) and \(\Delta H=T \Delta S\)

Short answer

The incorrect statement for a reaction at equilibrium under standard conditions is (d) \(\Delta G=0\) and \(\Delta H=T \Delta S\).

Step-by-step solution

Understanding Equilibrium State

In a chemical reaction, when the rate of the forward reaction equals the rate of the reverse reaction, the system is said to be in equilibrium. At this state, the concentrations of reactants and products remain constant over time.

Analyzing Answer Choice (a)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium. If K=0, it would suggest that no products are formed, which contradicts the definition of equilibrium. Therefore, K cannot equal zero.

Analyzing Answer Choice (b)

An equilibrium constant (K) of 1 indicates that the concentrations of reactants and products are equal at equilibrium. This is a possible scenario for a reaction at equilibrium.

Analyzing Answer Choice (c)

At equilibrium, the change in Gibbs free energy, \(\Delta G^\circ\), is zero, which is in line with the given choice. Also, according to the Gibbs-Helmholtz equation, \(\Delta H^\circ = T \Delta S^\circ\) describes a condition at equilibrium correctly. So, this option is correct.

Analyzing Answer Choice (d)

Again, \(\Delta G=0\) correctly states the condition for equilibrium. But the equation \(\Delta H = T \Delta S\) lacks the standard conditions superscript \(\circ\), which suggests it's referring to all conditions, not just standard. Therefore, it's not necessarily true for a reaction only under standard conditions and hence incorrect.

Key concepts

Equilibrium Constant K

Understanding the equilibrium constant, represented as K, is fundamental in the study of chemical reactions. It quantifies the balance between products and reactants in a chemical reaction at equilibrium. Specifically, K is a dimensionless quantity derived from the ratio of the concentration of products to the concentration of reactants, each raised to the power of their respective coefficients from the balanced equation.

For example, in a simple reaction where A and B react to form C and D, the equilibrium constant would be expressed as \( K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \) where \( [A] \) and \( [B] \) are the molar concentrations of reactants, \( [C] \) and \( [D] \) the molar concentrations of products, and a, b, c, d represent their coefficients in the balanced equation. This constant provides invaluable insight into the extent of a reaction—where a high K value suggests a greater concentration of products at equilibrium, signifying a reaction heavily favoring the product side, while a lower K value indicates a reaction favoring the reactants. It's important to note that K varies with temperature, emphasizing the need for standard conditions when comparing different K values.

Gibbs Free Energy

Gibbs free energy, denoted as \( \Delta G \), is integral to thermodynamics in chemistry and dictates whether a reaction is spontaneous. It combines enthalpy (\( \Delta H \) - a measure of the heat content) and entropy (\( \Delta S \) - a measure of disorder) within a system to determine the free energy change during a reaction. At a constant temperature and pressure, the change in Gibbs free energy is given by \( \Delta G = \Delta H - T\Delta S \).

A negative \( \Delta G \) indicates a spontaneous reaction, one that can occur without added energy. Conversely, a positive \( \Delta G \) suggests that energy must be added for the reaction to proceed, characterizing non-spontaneous processes. It's at the zero point of \( \Delta G \) that chemical equilibrium is achieved—neither the forward nor the reverse reaction is favored, and the system's composition remains static. In the context of standard conditions (denoted with a °), \( \Delta G^\circ = 0 \) signals that a reaction mixture is at equilibrium.

Reaction Equilibrium

Reaction equilibrium occupies a central place in chemical understanding and occurs when a chemical reaction proceeds at such a rate that the concentrations of reactants and products remain unchanged over time. Here, the forward and reverse reactions occur at the same rate. This concept is critical because it defines the point at which a reaction can do no more work – neither to produce more products nor to revert to reactants. At equilibrium, observable properties such as color, pH, and concentration stabilize.

As equilibrium is dynamic, reactions are still occurring, but there are no net changes in the overall concentrations of the reactant and product species. Furthermore, equilibrium does not imply that the concentrations of reactants and products are equal, but that their ratio remains constant, which is reflected in the equilibrium constant, K. The conditions for equilibrium can be affected by various factors, including temperature, pressure, and the presence of catalysts, which emphasize the delicacy and sensitivity of chemical systems.

Thermodynamics in Chemistry

Thermodynamics in chemistry is the study of energy changes accompanying chemical and physical processes. It is grounded in several fundamental laws that predict the flow of energy and the ability of energy to do work. The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed. This principle is crucial for understanding how energy is conserved in chemical reactions and processes.

The second law of thermodynamics adds another layer, stating that entropy, or disorder, always increases in a closed system. This law introduces the concept of spontaneity in a process. It underlies the rule that for a process to be spontaneous, it must increase the universe's overall entropy. Incorporating these principles, chemists can determine if reactions will occur spontaneously or require external energy input, helping to predict the feasibility and extent of chemical reactions.