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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An Introduction of Chemical Thermodynamicsas 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.
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
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)
Increase in volume, dV
+dV Positive Work (Work is
done by the gas)
-dV Negative Work (Work is
done on the 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.
Work depends on the path
taken in “PV space.”
Work is the area under
the curve of a PV-diagram.
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.
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.
statement of energy conservation for a thermodynamic system
Heat and work are forms of energy transfer and energy is conserved.
U = Q + Won
total internal energy
on the system
State Function Path Functions
U = Q - Wby
Positive Q ->heat added to the system
Positive W -> work done by the system
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.
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 & ENDOTHERMIC REACTIONS
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
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
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
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.
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
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
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
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,
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, 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
According to Ideal Gas Law, V=RT/P
So, we can write,
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
Multiplying by dT,
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.