Chemical Thermodynamics: Definitions & Laws

Thermodynamics is the study of energy, heat, and work transitions within chemical systems. It allows us to predict the spontaneity of reactions and the maximum work obtainable from a process.

Internal Energy ($\Delta U$)

The total energy stored within a system. According to the First Law, $\Delta U = q + w$, where $q$ is heat exchanged and $w$ is work done on the system.

Gibbs Free Energy ($\Delta G$)

The criteria for spontaneity at constant temperature and pressure. If $\Delta G < 0$, the reaction is spontaneous (Exergonic).

Ultra Thermodynamics Solver

Internal Energy ($\Delta U$):
Work Done ($W$):
Enthalpy ($\Delta H$):
Entropy ($\Delta S$):
Gibbs Energy ($\Delta G$):

Guide: Entering Values

Our calculators use a smartParser to handle scientific notation.

^
Exponent: 10^5 means 105
*
Multiply: 10*1 means 10 multiplied by 1.
e
Scientific: 1.8e-5 means 1.8 × 10-5

Practical Examples:

  • Positive: Enter 10^2 for 100.
  • Negative: Enter -5 for acidic values.
  • Complex: Enter 10^-7 for neutral pH.

Fundamental Thermodynamic Equations

$\Delta H = \Delta U + P\Delta V$
$\Delta S = nC_v\ln(T_2/T_1) + nR\ln(V_2/V_1)$
$\Delta G = \Delta H - T\Delta S$

Thermochemistry: Heat & Energy

Enthalpy of Formation ($\Delta H_f^\circ$)

The heat change when **one mole** of a substance is formed from its elements in their most stable states under standard conditions. By convention, $\Delta H_f^\circ$ for pure elements is zero.

Enthalpy of Combustion ($\Delta H_c^\circ$)

The energy released when **one mole** of a substance is completely burned in excess oxygen. These values are always exothermic (negative).

Calculation Example (Gibbs Free Energy)

Problem: Determine if a reaction is spontaneous at $298\text{ K}$ if $\Delta H = -100\text{ kJ}$ and $\Delta S = -200\text{ J/K}$.

Formula: $\Delta G = \Delta H - T\Delta S$

Steps:
  • Convert $\Delta S$ to kJ: $-200 / 1000 = -0.2\text{ kJ/K}$
  • $\Delta G = -100 - (298 \times -0.2)$
  • $\Delta G = -100 + 59.6 = \mathbf{-40.4\text{ kJ}}$
  • Result: Spontaneous (since $\Delta G < 0$)

Entropy & Gibbs Energy Types

Entropy ($S$)

A measure of the thermal energy per unit temperature that is unavailable for doing useful work. It is often described as the degree of "disorder" or "randomness" in a system.

Standard vs. Non-Standard $G$

$\Delta G^\circ$: Change under standard states ($1\text{ atm}, 1\text{ M}$).
$\Delta G$: Real-time change calculated using $\Delta G = \Delta G^\circ + RT \ln Q$.

Research & Analytical Techniques

Isothermal Titration Calorimetry (ITC)

Used in drug discovery to measure the heat of binding between a drug and a protein, providing direct values for $\Delta H$, $\Delta S$, and $K_a$.

Differential Scanning Calorimetry (DSC)

Measures how a sample's heat capacity changes with temperature, essential for determining the melting points and stability of polymers and proteins.

Unique Thermodynamic Facts

The Third Law: As a system approaches absolute zero ($0\text{ K}$), the entropy of a perfect crystal becomes exactly zero. It is the only absolute thermodynamic value.

Heat Death: Some cosmologists suggest the universe will eventually reach a state of maximum entropy, where no more energy is available to sustain life or movement.

Biological Efficiency: Despite the 2nd Law, life maintains low internal entropy by constantly exporting high entropy (heat) to its surroundings.

Expert FAQ: Thermodynamics

What is the difference between $\Delta H$ and $\Delta U$?

$\Delta H$ is heat at constant pressure, while $\Delta U$ is heat at constant volume. Relationship: $\Delta H = \Delta U + \Delta n_g RT$.

Can a reaction be spontaneous if $\Delta H$ is positive?

Yes, if the entropy increase ($T\Delta S$) is large enough to outweigh the positive enthalpy (endothermic spontaneity).

What is Hess's Law?

The total enthalpy change of a reaction is the same regardless of the path taken, because enthalpy is a **state function**.

Why is $\Delta G = 0$ at equilibrium?

At equilibrium, the system is at its lowest possible energy state; there is no driving force to move in either direction.

How does $K_{eq}$ relate to $\Delta G^\circ$?

The connection is: $\Delta G^\circ = -RT \ln K_{eq}$. A large negative $\Delta G^\circ$ means a very large equilibrium constant.

What is Bond Enthalpy?

The energy required to break one mole of a specific bond in the gaseous state. It is used to estimate reaction $\Delta H$.

Is Entropy always increasing?

According to the 2nd Law, the entropy of the **entire universe** (system + surroundings) must increase for any spontaneous process.

What are Intensive vs. Extensive properties?

Temperature is intensive (doesn't depend on amount), while Enthalpy and Entropy are extensive (increase with mass).

What is the "Clausius Inequality"?

It states that for any real-world (irreversible) process, the entropy change is always greater than the heat exchanged divided by temperature.