1. Home
  2. Chemistry
  3. Thermodynamics
  4. Free energy

16.4 Free energy  (Page 4/12)

<< Chapter < Page
  Chemistry     Page 4 / 12
Chapter >> Page >
Δ G = Δ H − T Δ S
y = b + m x

Such a plot is shown in [link] . A process whose enthalpy and entropy changes are of the same arithmetic sign will exhibit a temperature-dependent spontaneity as depicted by the two yellow lines in the plot. Each line crosses from one spontaneity domain (positive or negative Δ G ) to the other at a temperature that is characteristic of the process in question. This temperature is represented by the x -intercept of the line, that is, the value of T for which Δ G is zero:

Δ G = 0 = Δ H − T Δ S
T = Δ H Δ S

And so, saying a process is spontaneous at “high” or “low” temperatures means the temperature is above or below, respectively, that temperature at which Δ G for the process is zero. As noted earlier, this condition describes a system at equilibrium.

A graph is shown where the y-axis is labeled, “Free energy,” and the x-axis is labeled, “Increasing temperature ( K ).” The value of zero is written midway up the y-axis with the label, “delta G greater than 0,” written above this line and, “delta G less than 0,” written below it. The bottom half of the graph is labeled on the right as, “Spontaneous,” and the top half is labeled on the right as, “Nonspontaneous.” A green line labeled, “delta H less than 0, delta S greater than 0,” extends from a quarter of the way up the y-axis to the bottom right of the graph. A yellow line labeled, “delta H less than 0, delta S less than 0,” extends from a quarter of the way up the y-axis to the middle right of the graph. A second yellow line labeled, “delta H greater than 0, delta S greater than 0,” extends from three quarters of the way up the y-axis to the middle right of the graph. A red line labeled, “delta H greater than 0, delta S less than 0,” extends from three quarters of the way up the y-axis to the top right of the graph.
These plots show the variation in Δ G with temperature for the four possible combinations of arithmetic sign for Δ H and Δ S .

Equilibrium temperature for a phase transition

As defined in the chapter on liquids and solids, the boiling point of a liquid is the temperature at which its solid and liquid phases are in equilibrium (that is, when vaporization and condensation occur at equal rates). Use the information in Appendix G to estimate the boiling point of water.

Solution

The process of interest is the following phase change:

H 2 O ( l ) ⟶ H 2 O ( g )

When this process is at equilibrium, Δ G = 0, so the following is true:

0 = Δ H ° − T Δ S ° or T = Δ H ° Δ S °

Using the standard thermodynamic data from Appendix G ,

Δ H ° = Δ H f ° ( H 2 O ( g ) ) − Δ H f ° ( H 2 O ( l ) ) = − 241.82 kJ/mol − ( − 285.83 kJ/mol ) = 44.01 kJ/mol
Δ S ° = Δ S 298 ° ( H 2 O ( g ) ) − Δ S 298 ° ( H 2 O ( l ) ) = 188.8 J/K·mol − 70.0 J/K·mol = 118.8 J/K·mol
T = Δ H ° Δ S ° = 44.01 × 10 3 J/mol 118.8 J/K·mol = 370.5 K = 97.3 °C

The accepted value for water’s normal boiling point is 373.2 K (100.0 °C), and so this calculation is in reasonable agreement. Note that the values for enthalpy and entropy changes data used were derived from standard data at 298 K ( Appendix G ). If desired, you could obtain more accurate results by using enthalpy and entropy changes determined at (or at least closer to) the actual boiling point.

Check your learning

Use the information in Appendix G to estimate the boiling point of CS 2 .

Answer:

313 K (accepted value 319 K)

Got questions? Get instant answers now!

Free energy and equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for Δ G represents a finite driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When Δ G is zero, the forward and reverse driving forces are equal, and so the process occurs in both directions at the same rate (the system is at equilibrium).

In the chapter on equilibrium the reaction quotient , Q , was introduced as a convenient measure of the status of an equilibrium system. Recall that Q is the numerical value of the mass action expression for the system, and that you may use its value to identify the direction in which a reaction will proceed in order to achieve equilibrium. When Q is lesser than the equilibrium constant, K , the reaction will proceed in the forward direction until equilibrium is reached and Q = K . Conversely, if Q < K , the process will proceed in the reverse direction until equilibrium is achieved.

Questions & Answers

what's Thermochemistry
rhoda Reply
the study of the heat energy which is associated with chemical reactions
Kaddija
How was CH4 and o2 was able to produce (Co2)and (H2o
Edafe Reply
explain please
Victory
First twenty elements with their valences
Martine Reply
what is chemistry
asue Reply
what is atom
asue
what is the best way to define periodic table for jamb
Damilola Reply
what is the change of matter from one state to another
Elijah Reply
what is isolation of organic compounds
IKyernum Reply
what is atomic radius
ThankGod Reply
Read Chapter 6, section 5
Dr
Read Chapter 6, section 5
Kareem
Atomic radius is the radius of the atom and is also called the orbital radius
Kareem
atomic radius is the distance between the nucleus of an atom and its valence shell
Amos
Read Chapter 6, section 5
paulino
Bohr's model of the theory atom
Ayom Reply
is there a question?
Dr
when a gas is compressed why it becomes hot?
ATOMIC
It has no oxygen then
Goldyei
read the chapter on thermochemistry...the sections on "PV" work and the First Law of Thermodynamics should help..
Dr
Which element react with water
Mukthar Reply
Mgo
Ibeh
an increase in the pressure of a gas results in the decrease of its
Valentina Reply
definition of the periodic table
Cosmos Reply
What is the lkenes
Da Reply
what were atoms composed of?
Moses Reply
what is chemistry
Imoh Reply
what is chemistry
Damilola
<< Chapter < Page Page > Chapter >>
Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask