Thermodynamic Calculator: Delta S from Delta H

An expert tool to calculate the change in entropy (ΔS) from the change in enthalpy (ΔH) and temperature (T) for a reversible process at constant pressure.

Entropy Change (ΔS)

---

Calculation Breakdown

Formula: ΔS = ΔH / T

ΔH (Joules): — J/mol

T (Kelvin): — K

Reaction Spontaneity Reference

This table outlines how the signs of enthalpy and entropy changes determine the spontaneity of a reaction based on Gibbs Free Energy (ΔG).

ΔH Sign	ΔS Sign	Effect on Spontaneity (ΔG = ΔH – TΔS)
– (Exothermic)	+ (More Disorder)	Spontaneous at all temperatures (ΔG is always negative)
+ (Endothermic)	– (Less Disorder)	Non-spontaneous at all temperatures (ΔG is always positive)
– (Exothermic)	– (Less Disorder)	Spontaneous only at low temperatures (becomes non-spontaneous as T increases)
+ (Endothermic)	+ (More Disorder)	Spontaneous only at high temperatures (becomes spontaneous as T increases)

What does “calculate delta s using delta h” mean?

In thermodynamics, the phrase “calculate delta s using delta h” refers to determining the change in a system’s entropy (ΔS) based on its change in enthalpy (ΔH) at a specific absolute temperature (T). Entropy (S) is a measure of the randomness, disorder, or statistical probability of a system. Enthalpy (H) represents the total heat content of a system. For a process that occurs reversibly at constant temperature and pressure, like the melting of ice or boiling of water, there is a direct and simple relationship connecting these three fundamental properties. Understanding how to calculate delta s using delta h is crucial for predicting the direction and feasibility of chemical reactions and physical changes.

This calculation is most commonly applied to phase transitions, where a substance changes from one state (solid, liquid, gas) to another. During a phase change, the temperature remains constant while the substance absorbs or releases heat (enthalpy), leading to a significant change in its molecular disorder (entropy).

The Delta S from Delta H Formula and Explanation

The core relationship for a reversible process at constant temperature and pressure is given by the formula:

ΔS = ΔH / T

This equation states that the change in entropy is equal to the change in enthalpy divided by the absolute temperature in Kelvin. It is essential that the temperature is expressed in Kelvin because it is an absolute scale, where zero represents the complete absence of thermal motion.

Variables used in the entropy change calculation.

Variable	Meaning	Common Units	Typical Range
ΔS	Change in Entropy	Joules per Kelvin per mole (J/K·mol)	-200 to +400 J/K·mol
ΔH	Change in Enthalpy	Joules per mole (J/mol) or Kilojoules per mole (kJ/mol)	-1000 to +1000 kJ/mol
T	Absolute Temperature	Kelvin (K)	> 0 K (typically 273-400 K for common reactions)

Practical Examples

Example 1: Melting Ice

Let’s calculate the entropy change when one mole of ice melts into water at 0°C (273.15 K). The standard enthalpy of fusion (ΔH_fus) for water is +6.01 kJ/mol.

• Inputs:
  • ΔH = +6.01 kJ/mol = +6010 J/mol
  • T = 0°C = 273.15 K
• Calculation:
  • ΔS = 6010 J/mol / 273.15 K
• Result:
  • ΔS ≈ +22.0 J/K·mol

The positive sign indicates an increase in disorder, which makes sense as water molecules in a liquid state are more disordered than in a solid crystal lattice. Find out more with a Gibbs Free Energy Calculator.

Example 2: Vaporizing Benzene

Let’s calculate the entropy change for the vaporization of one mole of benzene (C₆H₆) at its boiling point, 80.1°C (353.25 K). The enthalpy of vaporization (ΔH_vap) is +30.8 kJ/mol.

• Inputs:
  • ΔH = +30.8 kJ/mol = +30800 J/mol
  • T = 80.1°C = 353.25 K
• Calculation:
  • ΔS = 30800 J/mol / 353.25 K
• Result:
  • ΔS ≈ +87.2 J/K·mol

Again, the positive value shows a large increase in entropy as the liquid turns into a much more disordered gas.

How to Use This Calculator

1. Enter Enthalpy Change (ΔH): Input the value for the change in enthalpy. Use a positive value for endothermic processes (heat absorbed) and a negative value for exothermic processes (heat released).
2. Select ΔH Units: Choose whether your input is in kilojoules per mole (kJ/mol) or joules per mole (J/mol). The calculator will handle the conversion.
3. Enter Temperature (T): Input the temperature at which the process occurs.
4. Select Temperature Units: Choose between Celsius (°C), Kelvin (K), or Fahrenheit (°F). The calculator will automatically convert the value to Kelvin for the calculation.
5. Interpret the Results: The primary result shows the calculated entropy change (ΔS) in J/K·mol. The breakdown section shows the converted values used in the formula, helping you understand how the final number was derived.

Key Factors That Affect the Calculation

• Temperature: As T is in the denominator, a higher temperature will result in a smaller entropy change for the same amount of enthalpy change.
• Direction of Heat Flow: An endothermic process (ΔH > 0) will always result in an increase in entropy (ΔS > 0), while an exothermic process (ΔH < 0) will result in a decrease in entropy (ΔS < 0).
• State of Matter: Phase transitions from more ordered to less ordered states (e.g., solid to liquid, liquid to gas) have positive ΔH values and therefore positive ΔS values. The reverse is true for transitions from gas to liquid or liquid to solid.
• Reversibility: This formula is strictly valid for reversible processes, where the system is always in equilibrium with its surroundings. For irreversible processes, the actual entropy change of the universe is always greater than what this formula predicts for the system.
• Pressure: The formula assumes the process occurs at constant pressure. Changes in pressure can affect enthalpy values and shift equilibrium temperatures.
• Accuracy of Inputs: The accuracy of the calculated ΔS depends directly on the accuracy of the input ΔH and T values. Using a reliable Thermodynamics Calculator is important.

Frequently Asked Questions (FAQ)

1. Why must temperature be in Kelvin?

The formula requires an absolute temperature scale. Kelvin is the standard absolute scale in science where 0 K represents absolute zero—the theoretical point of no thermal energy. Using Celsius or Fahrenheit directly would produce incorrect results because their zero points are arbitrary.

2. What does a positive ΔS mean?

A positive change in entropy (ΔS > 0) means the system has become more disordered or random. This is typical for processes like melting, boiling, or dissolving a solid.

3. What does a negative ΔS mean?

A negative change in entropy (ΔS < 0) means the system has become more ordered. This occurs during processes like freezing, condensation, or precipitation.

4. Can I use this formula for a chemical reaction that isn’t a phase change?

This specific formula (ΔS = ΔH/T) is primarily for reversible processes at a constant temperature, like phase transitions. For general chemical reactions where temperature changes or that are not at equilibrium, you typically calculate ΔS using standard molar entropy values from a table (ΔS°_rxn = ΣS°_products – ΣS°_reactants).

5. How does this relate to Gibbs Free Energy (ΔG)?

This calculation is a key component of the Gibbs Free Energy equation: ΔG = ΔH – TΔS. By finding ΔS, you can then calculate ΔG to determine if a process will be spontaneous at a given temperature. A negative ΔG indicates a spontaneous process.

6. What if my process occurs over a temperature range?

If temperature is not constant, you cannot use this simple formula. You would need to use integral calculus, integrating the heat capacity (Cp) over the temperature range: ΔS = ∫(Cp/T)dT.

7. Why is the entropy change for boiling so much larger than for melting?

The increase in disorder when a liquid turns into a gas is much greater than when a solid turns into a liquid. Gas particles move randomly in a large volume, representing a much higher state of entropy than the confined motion of particles in a liquid.

8. Can I calculate delta s using delta h for an irreversible process?

You can use the formula to find the entropy change of the *system*, but it won’t tell you the total entropy change of the *universe*. For any spontaneous (irreversible) process, the entropy of the universe (system + surroundings) must increase.