Question

How can you calculate the standard entropy change for a reaction from tables of standard entropies?

Short answer

The standard entropy change (\( \Delta S^\circ \) is calculated by subtracting the sum of the standard entropies of the reactants from the sum of the standard entropies of the products.

Step-by-step solution

Understand Standard Entropy Change

The standard entropy change for a reaction, denoted as \( \Delta S^\circ \), is calculated using the standard entropy values of the reactants and products. It is the difference between the sum of the standard entropies of the products and the sum of the standard entropies of the reactants.

Locate Standard Entropies

Find the standard entropy values \( (S^\circ) \) of all reactants and products involved in the reaction from standard entropy tables. These values are usually given in units of \( J/(mol\cdot K) \).

Calculate Entropy Change of Products

Multiply the standard entropy of each product by its coefficient in the balanced chemical equation. Add these values together to get the total entropy of the products \( (\Sigma S^\circ_{products}) \).

Calculate Entropy Change of Reactants

Similarly, multiply the standard entropy of each reactant by its coefficient in the balanced chemical equation. Add these values together to get the total entropy of the reactants \( (\Sigma S^\circ_{reactants}) \).

Determine the Standard Entropy Change

Subtract the total entropy of the reactants from the total entropy of the products to find the standard entropy change for the reaction: \[ \Delta S^\circ = \Sigma S^\circ_{products} - \Sigma S^\circ_{reactants} \]

Key concepts

Entropy in Thermodynamics

Entropy is a fundamental concept in thermodynamics, representing the degree of disorder or randomness in a system. It is a state function, meaning its value depends only on the current state of the system, not the path taken to reach that state. In simple terms, entropy can be viewed as a measure of the energy dispersal within a system. The second law of thermodynamics states that for any spontaneous process, the total entropy of the system and its surroundings always increases.

In the context of chemical reactions, the entropy change (denoted as \( \Delta S \)) provides insight into the energy distribution before and after the reaction. A positive \( \Delta S \) indicates that the products are more disordered than the reactants, suggesting that energy is more spread out in the system. Conversely, a negative \( \Delta S \) means that the products are more ordered.

Standard Entropy Tables

Standard entropy tables are indispensable tools in thermochemistry, providing the entropy values of substances at a common reference state, usually 1 atm pressure and 25°C (298 K). These tables list the standard molar entropy values \( (S^\circ) \) of thousands of compounds and elements in units of joules per mole kelvin \( (J/(mol\cdot K)) \).

When calculating the entropy change for a reaction, it's critical to use the correct values from these tables, taking into account the physical state (solid, liquid, gas) of the reactants and products. The accuracy of these values directly affects the reliability of the calculated standard entropy change \( (\Delta S^\circ) \).

Thermochemistry

Thermochemistry is the branch of chemistry that studies the heat energy involved in chemical reactions and physical transformations. One key concept is the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or transformed. Thermochemical calculations often involve enthalpies of reactions, heat capacities, and entropy changes to understand the energy balance of processes.

The standard entropy change \( (\Delta S^\circ) \) is a critical piece of the puzzle in thermochemistry, connecting the microscopic world of particle disorder to the macroscopic world of energy changes and providing a deeper understanding of the direction and feasibility of a chemical reaction.

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry deals with the quantitative relationship between reactants and products in a chemical reaction. It involves using the coefficients from the balanced chemical equation to determine the proportions in which substances react and form products. These coefficients are crucial when calculating the standard entropy change for a reaction.

In the context of entropy, stoichiometry helps determine the multiplicities of the various substances' entropy values. For each reactant and product, multiplying the standard molar entropy by the respective coefficient gives the total entropy for that substance. Summing these values for both reactants and products and then finding the difference, as explained in the steps provided, yields the overall entropy change for the reaction.