This **Gibbs Free Energy Calculator** is a crucial tool for MCAT preparation, helping students quickly determine the spontaneity of a reaction ($\Delta G$), or solve for the required Enthalpy ($\Delta H$), Entropy ($\Delta S$), or Temperature ($T$) of a system using the fundamental thermodynamic relationship: $\Delta G = \Delta H – T\Delta S$.
Gibbs Free Energy Calculator (MCAT Prep)
Calculated Result:
Gibbs Free Energy Formula
The core relationship governing the spontaneity of a chemical reaction is given by the Gibbs Free Energy equation:
Formula Sources: LibreTexts Chemistry, Khan Academy
Variables Explained
The calculator utilizes four primary variables. Note that the $\Delta S$ input uses Joules (J) while the calculation converts it to kilojoules (kJ) for consistency with $\Delta G$ and $\Delta H$:
- $\Delta G$ (Gibbs Free Energy): Measures the total amount of useful energy available in a system. Determines spontaneity. Unit: kJ/mol.
- $\Delta H$ (Enthalpy Change): Measures the heat absorbed or released during a reaction. Unit: kJ/mol.
- $T$ (Temperature): The absolute temperature of the reaction. Must be in Kelvin. Unit: K.
- $\Delta S$ (Entropy Change): Measures the disorder or randomness of a system. Input Unit: J/(mol$\cdot$K).
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What is Gibbs Free Energy?
Gibbs Free Energy ($\Delta G$) is a thermodynamic potential that can be used to calculate the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but not matter). It is an essential concept on the MCAT, as its sign determines whether a reaction will occur spontaneously.
A negative $\Delta G$ (i.e., $\Delta G < 0$) indicates an **exergonic** reaction that will proceed spontaneously. A positive $\Delta G$ ($\Delta G > 0$) indicates an **endergonic** reaction that is non-spontaneous and requires an input of energy. If $\Delta G = 0$, the system is at chemical equilibrium.
How to Calculate $\Delta G$ (Example)
If a reaction has an Enthalpy Change ($\Delta H$) of -50 kJ/mol, an Entropy Change ($\Delta S$) of -150 J/(mol$\cdot$K), and occurs at 300 K, here is the step-by-step calculation for $\Delta G$:
- Convert Units: Convert $\Delta S$ from J to kJ: $\Delta S = -150 \text{ J/(mol}\cdot\text{K)} / 1000 = -0.15 \text{ kJ/(mol}\cdot\text{K)}$.
- Apply Formula: Substitute the values into the Gibbs Free Energy equation: $$\Delta G = \Delta H – T\Delta S$$
- Perform Calculation: $\Delta G = (-50 \text{ kJ/mol}) – (300 \text{ K} \times -0.15 \text{ kJ/(mol}\cdot\text{K)})$
- Solve: $\Delta G = -50 – (-45) = -50 + 45 = -5 \text{ kJ/mol}$.
- Conclusion: Since $\Delta G$ is negative, the reaction is spontaneous at 300 K.
Frequently Asked Questions (FAQ)
- What does a negative $\Delta G$ mean on the MCAT? A negative Gibbs Free Energy ($\Delta G < 0$) means the reaction is exergonic and spontaneous, or thermodynamically favorable.
- Why must Temperature ($T$) be in Kelvin? The Gibbs Free Energy equation relies on absolute temperature. Using Celsius or Fahrenheit would lead to incorrect thermodynamic values and potentially non-physical results.
- How do $\Delta H$ and $\Delta S$ affect spontaneity? If $\Delta H$ is negative (exothermic) and $\Delta S$ is positive (increased disorder), the reaction is always spontaneous. If both are negative, spontaneity depends on temperature (it must be low).
- What is the typical unit for $\Delta G$? The standard unit for Gibbs Free Energy ($\Delta G$) is Joules per mole (J/mol) or, more commonly in biological and chemical contexts involving larger numbers, kilojoules per mole (kJ/mol).