Entropy

• Entropy ($S$) is defined as a measure of the number of possible ways that particles and their energy can be arranged in a given system. A system with more possible arrangements is considered more disordered and possesses a higher entropy value.

• The standard units for entropy are Joules per Kelvin per mole ($J K^{-1} mol^{-1}$), which is notably different from enthalpy units ($kJ mol^{-1}$). This unit difference is a critical factor when performing combined thermodynamic calculations.

• Unlike enthalpy of formation, the standard entropy ($S^\theta$) of an element in its standard state is not zero. Every substance has a positive entropy value because there is always some degree of disorder above absolute zero.

• An increase in entropy ($\Delta S > 0$) indicates that a system has become more disordered, which is energetically favourable according to the laws of thermodynamics.

• To calculate the standard entropy change of a system ($\Delta S_{system}^\theta$), use the sum of the standard entropies of the products minus the sum of the standard entropies of the reactants.

Calculation Formula

$\Delta S_{system}^\theta = \sum S_{products}^\theta - \sum S_{reactants}^\theta$

• Step 1: Identify the balanced chemical equation and the physical states of all species involved.

• Step 2: Look up the standard molar entropy values ($S^\theta$) for each substance in a data table, ensuring you use the correct state (e.g., $H_2O(l)$ vs $H_2O(g)$).

• Step 3: Multiply each $S^\theta$ value by its stoichiometric coefficient from the balanced equation.

• Step 4: Subtract the total entropy of reactants from the total entropy of products to find the final change.

• It is vital to distinguish between the system (the reacting chemicals) and the surroundings (everything else). Entropy changes can occur in both, but $\Delta S_{system}$ is what we typically calculate from molar entropy data.

• Feasibility vs. Rate: A reaction may be thermodynamically feasible (spontaneous) due to a large entropy increase, but it might occur so slowly that it is not observable. Thermodynamics tells us if a reaction can happen, not how fast it happens.

• Unit Consistency: This is the most common area for lost marks. When using $\Delta S$ in the Gibbs Free Energy equation ($\Delta G = \Delta H - T\Delta S$), you MUST divide the entropy value by 1000 to convert it from $J$ to $kJ$.

• State Symbols: Always check the state symbols in the equation. A change from $(s)$ to $(g)$ is a massive entropy increase, while a change from $(g)$ to $(l)$ is a massive decrease.

• Stoichiometry: Don't forget to multiply the molar entropy of each substance by the number of moles in the balanced equation. Even elements must be included in this calculation.

• Sanity Check: Before calculating, predict the sign. If a solid reacts to form a gas, your final answer for $\Delta S$ should be positive. If it isn't, re-check your subtraction order (Products - Reactants).