Question

In your own words, define the following symbols: (a) $\mathrm{\Delta }{S}_{\text{univ }};$ (b) $\mathrm{\Delta }{G}_f^0;$ (c) $K$.

Short answer

$\mathrm{\Delta }{S}_{\text{univ }}$ stands for the change in entropy of the universe, $\mathrm{\Delta }{G}_f^0$ represents the standard free energy of formation, and 'K' denotes the equilibrium constant.

Step-by-step solution

Definition of $\mathrm{\Delta }{S}_{\text{univ }}$

We will start by defining $\mathrm{\Delta }{S}_{\text{univ }}$. The symbol $\mathrm{\Delta }{S}_{\text{univ }}$ denotes the change in entropy of the universe. Entropy, represented by 'S', is a thermodynamic property that measures the degree of randomness or disorder in a system. The 'univ' subscript indicates that the entropy change is for the universe, which includes both the system and its surroundings. The symbol 'Δ' in front of 'S' denotes change. So, $\mathrm{\Delta }{S}_{\text{univ }}$ represents the total change in entropy for a process, taking into account both the system and its surroundings.

Definition of $\mathrm{\Delta }{G}_f^0$

Next, we define $\mathrm{\Delta }{G}_f^0$. The symbol $\mathrm{\Delta }{G}_f^0$ represents the standard free energy of formation. 'G' stands for Gibbs free energy, which is the energy available in a system to do work. The subscript 'f' denotes formation, and the superscript '0' means under standard conditions (usually 298K and 1 bar pressure). The 'Δ' again denotes change. So, $\mathrm{\Delta }{G}_f^0$ represents the change in Gibbs free energy when one mole of a compound is formed from its elements in their standard states under standard conditions.

Definition of K

Lastly, we will define 'K'. 'K' represents the equilibrium constant. This constant expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of its coefficient in the balanced chemical equation. The value of 'K' depends on temperature and determines the direction and extent of a reaction.

Key concepts

Entropy Change

Entropy, symbolized as 'S', is a measure of disorder or randomness in a system. An increase in entropy indicates a system's progression towards more disordered states. In thermodynamic processes, we are often interested in the change in entropy, denoted as $\mathrm{\Delta }S$, which can tell us a lot about the nature of a process.

When considering entropy change on a universal scale, we use the term $\mathrm{\Delta }{S}_{\text{univ}}$ to represent the total change in entropy, both within the system being studied and its surroundings. According to the second law of thermodynamics, the entropy of the universe always increases in a spontaneous process. That means for any process that happens naturally without any external intervention, $\mathrm{\Delta }{S}_{\text{univ}}>0$.

This concept is crucial in determining whether or not a reaction can naturally occur. If we take an ice cube as an example, as it melts, the water molecules go from a highly ordered solid state to a less ordered liquid state. This change implies an increase in entropy, as the molecules are more disoriented and have greater freedom of movement.

Gibbs Free Energy

Gibbs free energy, symbolized by 'G', is a concept that intertwines entropy, enthalpy (a measure of total energy), and temperature to predict the favorability of a chemical process. It is defined as the maximum amount of work that can be extracted from a thermodynamic system during a process that takes place at constant temperature and pressure.

The change in Gibbs free energy $\mathrm{\Delta }G$ indicates the spontaneity of a reaction. A negative value of $\mathrm{\Delta }G$ suggests that a process is spontaneous, releasing free energy, while a positive value of $\mathrm{\Delta }G$ means that energy is needed for the process to proceed. The standard free energy of formation $\mathrm{\Delta }{G}_f^0$ specifically refers to the change in Gibbs free energy when one mole of a substance is formed from its elements in their standard states.

In a hypothetical scenario, if we were to form water vapor from hydrogen and oxygen gases, $\mathrm{\Delta }{G}_f^0$ would represent the energy change during the formation of one mole of water vapor under standard conditions. By understanding $\mathrm{\Delta }G$ and $\mathrm{\Delta }{G}_f^0$, we can predict whether a reaction is energetically feasible and if it will proceed without external energy input.

Equilibrium Constant

The equilibrium constant, represented by the symbol 'K', is a fundamental aspect of chemical thermodynamics that provides a quantitative measure of the composition of a reaction mixture when a reaction has reached a state of balance. In this equilibrium state, the rate of the forward reaction equals the rate of the reverse reaction, meaning there's no net change in the concentrations of reactants and products over time.

The value of 'K' is derived from the law of mass action, which states that for a balanced chemical reaction, the ratio of the product of concentrations of products to the product of concentrations of reactants, each raised to the power of their respective coefficients in the chemical equation, remains constant at equilibrium. A high value of $K$ indicates a reaction mix that favors products, while a low $K$ suggests a mix that favors reactants.

For example, in the synthesis of ammonia $(N_2+3H_2\leftrightarrow 2N{H}_3)$ the equilibrium constant $K$ would be expressed as $K=\frac{[N{H}_3{]}^2}{[N_2][H_2{]}^3}$ where $[X]$ denotes the concentration of X in moles per liter. Temperature affects the value of $K$ but not the concentrations of individual components unless temperature changes. Understanding $K$ helps chemists predict the concentration of substances at equilibrium and manipulate conditions to favor the formation of desired products.