an introduction of chemical thermodynamics as it applies to water geochemistry
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An Introduction of Chemical Thermodynamics as it applies to Water Geochemistry. Law of Conservation of Energy The total energy of the universe is constant and can neither be created nor destroyed; it can only be transformed from one state to another.

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Law of Conservation of Energy

The total energy of the universe is constant and can neither be created nor destroyed; it can only be transformed from one state to another.

The internal energy, U, of a sample is the sum of all the kinetic and potential energies of all the atoms and molecules in a sample.

i.e. it is the total energy of all the atoms and molecules in a sample






Systems & Surroundings

In thermodynamics, the world is divided into a system and its surroundings

A system is the part of the Universe under study, separated from the rest of the Universe by a well-defined boundary.

The surroundings consist of everything else outside the system – rest of the universe.


Types of system



OPEN SYSTEM: can exchange both matter and energy with the surroundings (e.g. open reaction flask, rocket engine), across its boundaries

CLOSED SYSTEM: can exchange only energy with the surroundings (matter remains fixed) e.g. a sealed reaction flask. Closed systems have impermeable diathermal and moveable boundariesthat permit the transfer of heatand work between system and surroundings but prevent transfer of matter.

ISOLATED SYSTEM: can exchange neither energy nor matter with its surroundings (e.g. a thermos flask) …entirely removed from environmental influences

thermodynamic properties of a system matter
Thermodynamic properties of a System/Matter
  • Extensive : Additive, and depends on the total mass of the system.

Example: Volume

  • Intensive : Independent of the amount of matter present in the system.

Example: pressure, temperature, density

Change of state: when the properties of the system change it is called “change of state”. Example: when a quantity of gas in a cylinder is compressed by moving a frictionless piston, the system undergoes a “change of state”….State Variables


U = Ufinal - Uinitial

U change in the internal energy

INTERNAL ENERGY (U)-very imp concept

Internal energy changes when energy enters or leaves a system

Heat and work are 2 equivalent ways of changing

the internal energy of a system


Change in internal energy

Energy supplied to system as heat

Energy supplied to system as work



U like reserves of a bank: bank accepts deposits or withdrawals in two currencies (q & w) but stores them as common fund, U.






U = q (heat) + w (work)

work done by an expanding gas

Increase in volume, dV

+dV Positive Work (Work is

done by the gas)

-dV Negative Work (Work is

done on the gas)

Work Done by An Expanding Gas

Gas expands slowly enough to

maintain thermodynamic equilibrium.

Energy leaves the system

and goes to the environment.

Energy enters the system

from the environment.

pressure as a function of volume

Work depends on the path

taken in “PV space.”

Pressure as a Function of Volume

Work is the area under

the curve of a PV-diagram.

total work done
Total Work Done

To evaluate the integral, we must know how the pressure depends (functionally) on the volume.

Work is the transfer of energy that takes place when an object is moved against an opposing force


Work is defined as a quantity that flows across the boundary

of a system during a change in its state and is completely

convertible into the lifting of a weight in the surroundings.


The term Heat (Q) is properly used to describe energy in transit, thermal energy transferred into or out of a system from a thermal reservoir.



  • Q is not a “state” function --- the heat depends on the process, not just on the initial and final states of the system
  • Sign of Q : Q > 0 system gains thermal energy
    • Q < 0 system loses thermal energy

BUT, the quantity Q - W does not depend on the path taken; it depends only on the initial and final states.

Q - W internal energy.

the first law of thermodynamics
The First Law of Thermodynamics

statement of energy conservation for a thermodynamic system

Heat and work are forms of energy transfer and energy is conserved.

U = Q + Won

change in

total internal energy

work done

on the system

heat added

to system

State Function Path Functions


U = Q - Wby

Positive Q ->heat added to the system

Positive W -> work done by the system

the first law of thermodynamics1
The First Law of Thermodynamics

What this means: The internal energy of a system

tends to increase if energy is added via heat (Q)

and decrease via work (W) done by the system.

. . . and increase via work (W) done on the system.

enthalpy h
Enthalpy (H)

On integrating between the limits initial and final stages, we can write from 1st Law,


For constant pressure,



Replacing by Hi,

This H is called enthalpy


First Law of Thermodynamics: Energy is Conserved

ΔU = Ufinal - Uinital = q - w

q = heat absorbed by the system from the surroundings

w = work done by the system on the surroundings

heat is random molecular motion while work is force times distanced moved under its influence

Exothermic Processes release heat and have q<0

Endothermic Processes absorb heat and have q>0

Energy: The SI unit is joule (J) although we will frequently use calorie ;

1 cal = 4.2 J


The heat supplied is equal to the change in another thermodynamic property called enthalpy (H)

i.e. H = Qp

[only valid at constant pressure]

As most reactions in chemistry take place at constant pressure we can say that:

A change in enthalpy = heat supplied



Exothermic process: a change (e.g. a chemical reaction) that releases heat.

A release of heat corresponds to a decrease in enthalpy.

Exothermic process: H < 0 (at constant pressure).

Condensation, crystallization of liquids

Endothermic process: a change (e.g. a chemical reaction) that requires (or absorbs) heat.

Absorption of heat corresponds to an increase in enthalpy.

Endothermic process: H > 0 (at constant pressure).

Evaporation, fusion, melting of solids



  • Energy has to be supplied to a liquid to enable it to overcome forces that hold molecules together
  • endothermic process (H positive)
  • Melting
  • Energy is supplied to a solid to enable it to vibrate more vigorously until molecules can move past each other and flow as a liquid
  • endothermic process (H positive)
  • Freezing
  • Liquid releases energy and allows molecules to settle into a lower energy state and form a solid
  • exothermic process (H negative)
  • (we remove heat from water when making ice in freezer)

Heat of Reaction

Let us consider A and B (compounds or elements) react to form a product A2B3.

The change in enthalpy of the reaction in the standard state is:

Heat of the reaction

in the standard state

standard enthalpy of formation of A2B3 A and B

At equilibrium,


In general, is calculated by summing the standard enthalpies

of the products and by subtracting the enthalpies of the reactants:

n= molar coefficient of each reactant and product

taken from a balanced equation,

i= particular species involved in the reaction

Units: kcal/mole

Calorie: amount of heat required to raise the temperature

of 1 g of water from 14.5 to 15.5C.

Standard enthalpy of formation of ELEMENT is ZERO.


Heat Capacity

When heat is transferred to an object, the temperature of the object increases. When heat is removed from an object, the temperature of the object decreases. The relationship between the heat ( q ) that is transferred and the change in temperature ( ΔT ) is

The proportionality constant in this equation is called the heat capacity ( C ). The heat capacity is the amount of heat required to raise the temperature of an object or substance one degree. The temperature change is the difference between the final temperature ( Tf ) and the initial temperature ( Ti ).

Heat capacity can be measured experimentally.

Unit of T is Kelvin.


At constant pressure,

From the definition of Enthalpy,

So after rearranging,

On integration between the limits, T0 (standard temperature) to

T (any other temperature),

The equation enables us to calculate enthalpy of formation

of compound at temperature T.


Second Law of Thermodynamics

the disorder (or entropy) of a system tends to increase

  • Entropy is a measure of disorder
  • Low entropy (S) = low disorder
  • High entropy (S) = greater disorder

In any reversible process the change in the entropy of the system (dS) is equal to the heat received by the system (dQ) divided by the absolute temperature T.

dS=dQ/T for reversible process

dS>dQ/T for any spontaneous irreversible process

Entropy is a state function



disorder of solution

disorder of surroundings

Total entropy change

entropy change of system

entropy change of surroundings



  • must be an overall increase in disorder for dissolving to occur

1. If we freeze water, disorder of the water molecules decreases , entropy decreases

( -ve S , -ve H)

2. If we boil water, disorder of the water molecules increases , entropy increases (vapour is highly disordered state)

( +ve S , +ve H)


A spontaneous change is a change that has a tendency to occur without been driven by an external influence

e.g. the cooling of a hot metal block to the temperature of its surroundings

A non-spontaneous change is a change that occurs only when driven

e.g. forcing electric current through a metal block to heat it


A chemical reaction is spontaneous if it is accompanied by an increase in the total entropy of the system and the surroundings

  • Spontaneous exothermic reactions are common (e.g. hot metal block spontaneously cooling) because they release heat that increases the entropy of the surroundings.
  • Endothermic reactions are spontaneous only when the entropy of the system increases enough to overcome the decrease in entropy of the surroundings

Gibbs Free Energy (State function)

2nd law implies that the increase in the H of a system during a reversible

change in its state at constant T is diminished because a certain amount

of the H is consumed by an increase in the entropy of the system.

The relation between enthalpy & entropy can be defined as follows:


Gibbs free energy



In standard state,

Unit: kcal/mol

Standard Gibbs free energy of formation of a compound is the change

in the free energy of the reaction by which it forms from the elements

in the standard state.

forward reaction 0 >

>0 backward reaction

Driving force of a chemical reaction

For the reaction,

Is negative, the reaction proceeds from left to right.

if positive, the reaction proceeds from right to left.


Derivation of the Law of Mass action


or, G=U+PV-TS

or, dG=dU+PdV+VdP-TdS [at constant temp, dT=0]

or, dG=dQ-PdV+PdV+VdP-TdS [dU=dQ+PdV, 1st law]

Since, dS=dQ/T, dQ=TdS

Therefore, dG=VdP

According to Ideal Gas Law, V=RT/P

So, we can write,

On integration,

, gives

Since P0 =1 atm, ln P0 = 0,

Molar free energy of

ideal gas at pressure P

Molar free energy in

the standard state


Molar free energy is also called the chemical potential μ

The previous equation can be written as

For n mole of an ideal gas, we can write,



van’t Hoff Equation

After rearranging,

On differentiation,





Multiplying by dT,

On integration,


Chemical Equilibria:

G depends upon concentration (S changes with concentration)

GA = GA° + RT ln[A]; GA° is the standard free energy of A, R = 2.0 cal/deg-mole = 8.3 J / deg-mole.

For the reaction aA + bB == cC + dD ==>ΔG = ΔG° + RT ln ([C]c [D]d) / [A]a [B]b)

DG° is the standard free energy change for this reaction when reactants and products are in their standard states.

This principal is very important, because it shows that a reaction can be caused to go in either direction by changing the concentrations of products and reactants; this often occurs in living organisms.

At equilibrium, ΔG = 0 ==> ΔG° = - RT ln ([C]c [D]d) / [A]a [B]b) = -RT ln Keq

Note: ln Keq = -ΔH°/R (1/T) + ΔS°/R ==> a van\'t Hoff plot of LnKeq vs. 1/T allows one to calculate ΔH° and ΔS°, and, of course ΔG°

Note that a 10x change in Keq corresponds to a 5.7 kJ / mole (1.3 kcal/mole) change in ΔG° which is less than half the energy of a hydrogen bond.