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Physical Chemistry : Gibbs Free Energy

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Example Question #1 : Physical Chemistry

For Constant Temperature, Gibbs Free Energy is defined as:

$\Delta G = \Delta H - T \Delta S \,$

Where , $\small \Delta G$ is the change in Gibbs Free Energy, $\small \Delta H$ is the change in enthalpy, $\small T$ is temperature, and $\small \Delta S$ is the change in entropy.

Which of the following scenarios is not possible?

Possible Answers:

$\Delta H>0, \Delta S<0, \Delta G<0$

$\Delta H>0, \Delta S<0, \Delta G>0$

$\Delta H>0, \Delta S>0, \Delta G>0$

$\Delta H < 0 , \Delta S < 0, \Delta G < 0$

$\Delta H >0, \Delta S>0, \Delta G<0$

Correct answer:

$\Delta H>0, \Delta S<0, \Delta G<0$

Explanation:

The following condition is not possible:

$\Delta H > 0 ,\Delta S < 0, \Delta G < 0$

This is because if enthalpy is positive, and entropy is negative, the negative sign in front of the temperature term in the formula becomes positive. Addition of 2 positive numbers can not be negative. Plugging in arbitrary numbers into the other conditions can show they are all possible.

Take the following condition:

$\Delta H>0, \Delta S>0$

Then Gibbs free energy $(\Delta G)$ can either be positive or negative, depending on the magnitude of enthalpy, entropy, and temperature. (If enthalpy is much larger than entropy and temperature, then the difference will be positive, but if entropy * is greater than the enthalpy, then the difference will be negative).

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Example Question #1 : Physical Chemistry

For constant temperature, Gibbs free energy is defined as:

$\Delta G = \Delta H - T \Delta S \,$

Where , $\small \Delta G$ is the change in Gibbs free energy, $\small \Delta H$ is the change in enthalpy, $\small T$ is temperature, and $\small \Delta S$ is the change in entropy.

Given that a system is spontaneous, which of the following states are possible?

I. $\Delta G<0, \Delta S>0, \Delta H<0$

II. $\Delta G<0, \Delta S<0, \Delta H>0$

III. $\Delta G<0, \Delta S>0, \Delta H>0$

IV. $\Delta G>0, \Delta S<0, \Delta H>0$

Possible Answers:

I, II, and III

IV only

II and III

I, II, III, and IV

I and III

Correct answer:

I and III

Explanation:

Condition I is always true. Condition II is never true, as Gibbs free energy cannot be negative if enthalpy is positive and entropy is negative. Condition III may be true if temperature is very high (this is the scenario when the $T*\Delta S$ term dominates the $\Delta H$ term. Condition IV is not possible because $\Delta G>0$ and we were given a system with a Gibbs free Energy that is $\Delta G<0$ (we were told the system was spontaneous).

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Example Question #1 : Thermochemistry And Thermodynamics

The enthalpy of a reaction is $35\frac{kJ}{mol}$ and the entropy of a reaction is $3\frac{J}{mol\cdot K}$ . Which of the following is the Gibbs free energy (in $\frac{kJ}{mol}$ ) of this reaction?

Possible Answers:

$32\frac{kJ}{mol}$

Cannot be determined from the given information

$72\frac{kJ}{mol}$

$34.9\frac{kJ}{mol}$

Correct answer:

Cannot be determined from the given information

Explanation:

Gibbs free energy of a system can be solved using the following equation.

$\bigtriangleup G = \bigtriangleup H + T\bigtriangleup S$

where $\bigtriangleup G$ is change in Gibbs free energy, $\bigtriangleup H$ is change in enthalpy, is temperature in Kelvins and $\bigtriangleup S$ is change in entropy. To solve for $\bigtriangleup G$ we need all three of the variables. We are not given the temperature; therefore, we cannot solve for Gibbs free energy.

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Example Question #1 : Thermochemistry And Thermodynamics

In an exergonic reaction, products will have __________ Gibbs free energy and the reaction is __________.

Possible Answers:

lower . . . spontaneous

higher . . . nonspontaneous

higher . . . spontaneous

lower . . . nonspontaneous

Correct answer:

lower . . . spontaneous

Explanation:

Exergonic reaction suggests that the Gibbs free energy is negative. Since the change in Gibbs free energy is defined as Gibbs free energy of products - Gibbs free energy of reactants, a negative change in Gibbs free energy suggests that the products have a lower Gibbs free energy than reactants. A reaction is spontaneous if it has negative Gibbs free energy; therefore, exergonic reactions are always spontaneous. This is because the reaction is producing a more stable product (lower energy) from a less stable reactant (higher energy).

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Physical Chemistry : Gibbs Free Energy

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