Standard Molar Entropy

In general, if a chemical reaction turns solids into liquids or liquids into gases, the entropy change will have a positive value.
In general, if a chemical reaction turns solids into liquids or liquids into gases, the entropy change will have a positive value. Geir Pettersen, Getty Images

You'll encounter standard molar entropy in general chemistry, physical chemistry, and thermodynamics courses, so it's important to understand what entropy is and what it means. Here are the basics regarding standard molar entropy and how to use it to make predictions about a chemical reaction.

What Is Standard Molar Entropy?

Entropy is a measure of the randomness, chaos, or freedom of movement of particles.

The capital letter S is used to denote entropy. However, you won't see calculations for simple "entropy" because the concept is fairly useless until you put it in a form that can be used to make comparisons to calculate change of entropy or ΔS. Entropy values are given as standard molar entropy, which is the entropy of one mole of a substance at standard state conditions. Standard molar entropy is denoted by the symbol S° and usually has the units joules per mole Kelvin (J/mol·K).

Positive and Negative Entropy

The Second Law of Thermodynamics states the entropy of an isolated system increases, so you might think entropy would always increase and that change in entropy over time would always be a positive value.

As it turns out, sometimes entropy of a system decreases. Is this a violation of the Second Law? No, because the law refers to an isolated system. When you calculate an entropy change in a lab setting, you decide on a system, but the environment outside your system is ready to compensate for any changes in entropy you might see.

While the universe as a whole (if you consider it a type of isolated system), might experience an overall increase in entropy over time, small pockets of the system can and do experience negative entropy. For example, you can clean your desk, moving from disorder to order. Chemical reactions, too, can move from randomness to order.

In general:

Sgas > Ssoln > Sliq > Ssolid

So a change in state of matter can result in either a positive or negative entropy change.

Predicting Entropy

In chemistry and physics, you'll often be asked to predict whether an action or reaction will result in a positive or negative change in entropy. The change in entropy is the difference between final entropy and initial entropy:

ΔS = Sf - Si

You can expect a positive ΔS or increase in entropy when:

  • solid reactants form liquid or gaseous products
  • liquid reactants form gases
  • many smaller particles coalesce into larger particles (typically indicated by fewer product moles than reactant moles)

A negative ΔS or decrease in entropy often occurs when:

  • gaseous or liquid reactants form solid products
  • gaseous reactants form liquid products
  • large molecules dissociate into smaller ones
  • there are more moles of gas in the products than there are in the reactants

Applying Information About Entropy

Using the guidelines, sometimes it's easy to predict whether the change in entropy for a chemical reaction will be positive or negative. For example, when table salt (sodium chloride) forms from its ions:

Na+(aq) + Cl-(aq) → NaCl(s)

The entropy of the solid salt is lower than the entropy of the aqueous ions, so the reaction results in a negative ΔS.

Sometimes you can predict whether the change in entropy will be positive or negative by inspection of the chemical equation. For example, in the reaction between carbon monoxide and water to produce carbon dioxide and hydrogen:

CO(g) + H2O(g) → CO2(g) + H2(g)

The number of reactant moles is the same as the number of product moles, all of the chemical species are gases, and the molecules appear to be of comparable complexity. In this case, you'd need to look up the standard molar entropy values of each of the chemical species and calculate the change in entropy.

See How To Calculate Change in Entropy