Evaluation of solution order-disorder phenomena to determine the changes in entropy research proposal example

Funding is requested from the National Science Foundation in order to carry out proposed research based on the calorimetric study of enthalpy, Gibb’s energy, and entropy. The technique of calorimetric experimentation has changed a great deal from the early 1960s when studies of the heat ionization of water were conducted. The first adiabatic bomb calorimeters were very simple and controlling the difference in temperature between the inside and outside jackets was hard to control. The difference in temperature needs to be as small as possible, close to an infinitesimal amount. Technology has developed to sophisticated levels. The automatic capabilities of calorimeters are seem to be well designed and able to offer better data from laboratory studies of the physical chemistry of acid base reactions. This research proposes to add information about the design capabilities of a state-of the-art calorimeter with digital capabilities as well as researching the acid base mechanisms of weak acids and weak bases.

The purpose of the proposed research is to record the changes in entropy produced experimentally in order to better understand order-disorder kinetics in solutions. In general five main steps will be necessary to meet the objective of reporting the relationship between the change in entropy and the order-disorder reactions in a strong acid-weak acid reaction.
1) Conduct proton transfer reactions using a solution of sulphuric acid (H2SO3) and acetic acid (CH3CO2H) and record the change in Enthalpy (ΔH) observed
2) Organized and list the kinetic activity (Ka) values for each molecule/compound in solution
3) Calculate the change in Gibbs free energy (ΔG)
4) Determine the change in Entropy (ΔS)
5) Evaluate the relationship of ΔS with order-disorder phenomena of solutions

The intellectual merit of the proposed project

The proposed project uses modern state of the art calorimetric experimental instrumentation that is based on the foundational classis calorimetric principles. Therefore the traditional methodologies to determine the thermodynamic heat change in an unstable solution will be updated to meet the technology. The study of strong acid and weak acid solutions is one of the most challenging in physical chemistry because of the intermediate reactions taking place and because the reaction is reversible. The proposed research is particularly challenging because observations are focused on the reverse reactions involved with the salts that are produced upon the addition of a second strong acid. The data gathered will be important for progressing the understanding of order-disorder solutions and using a computer model to calculate the necessary values. (Garland, Nibler & Shoemaker, 2003)

The broader impact of the proposed project

Acid and base chemistry has important implications in understanding the biochemistry of the human body, disease and good health. The study of the thermodynamic implications of entropy in a solution is used in genetic research. Understanding as much as possible about pKa the mechanisms and equilibrium kinetics of solutions of acids and bases is essential to finding cures for cancer and other remedies. Even a quick review of research articles available at the PubMed digital library demonstrates the importance of this type of research. A sector of medical research is very involved in understand proteins and the metal ions that remain charged in particular situations, the thermodynamics of ions and ionizable functional groups on the human matrix metalloproteinase, and also the study of ATP-binding in genes. Many industrial applications also benefit from more study on the topic mainly for process stream quality control. The pharmaceutical industry uses the information generated to design drugs. (Osz & Benyei, 2007, pp. 11-15)

Background Information

Calorimetery is a method used to measure the enthalpy of combustion or heat which is equal to the change of enthalpy (ΔH). This is Heat Capacity has two types Molar Heat Capacity (heat capacity/molesubstance) and Specific Heat (heat capacity/gsubstance). Heat Capacity is always substance. Liquids have heat capacities less than solids but more than gasses. The heat is exothermic or endothermic unless it is dissipated. An adiabatic-jacket bomb calorimeter is used. (See fig. ) Pressure can be kept constant. Temperature can be measured before and after combustion of the solution which has been placed in the calorimeter. The temperature can be controlled at the inner and outer jacket. The object is to keep both the amount of energy constant. (No heat loss due to conduction or radiation.) The instrumentation is sophisticated. The materials used for the calorimeter cannot be destroyed by strong acids or strong bases which may be products in some of the reactions. The calorimetric experiment is based upon the First Law of Thermodynamics which is the conservation of energy. (Magder, S., n. d. p. 699)
(1) ΔH = q – w

H is the change in the system’s internal energy.

q is the energy transfer; (under adiabatic conditions q = 0)
w = work (done by the system)
(2)ΔS = dq revT
S is the entropy, rev is for reversible reactions because the integral is used to calculate the reversible process and T equals the temperature

Oxygen is the gas used for combustion

(3) E = 32 (nRT)
(Atkins & De Paulo, 2010, p. 57)

ΔE is zero because the reaction is isothermal

When ΔE then q = -q; so dq= -dw
PV represents the work performed; dwrev = – PextdV
Equation 2 can now be used written as dS = dq revT and the equation dwrev = – PextdVcan be substituted for the left side resulting in
dS = -dwrevT = PextdVT
We know that PV = nRT so another substitution results with
dS = -dwrevT = PextdVT = nRTdVVT = nRdVV

Now integrate the equation

ΔS = dS= V2VnRdVV
= nRln2V – nRlnV
ΔS = nRln2VV = nRln2
(4) ΔS = nRln2 (> 0)

We know

(Gibbs free energy) G = H= TS so from the First Law of Thermodynamics we can write
G = (U + PV) – TS and ΔG = ΔU = Δ(PV) – TΔS

And knowing that

ΔE – 0 and that PV = nRT (a constant) so Δ(PV) = 0
ΔG = -TΔS and ΔS = nRln2

Make one more substitution which results in the following equation

(Atkins & De Paulo, 2010, p. 128)
(5)ΔG = -nRT (< 0)


ΔS > 0 and ΔG < 0)(under conditions of spontaneity & irreversibility)

Second Law of Thermodynamics says that entropy cannot decrease in an isolated system

ΔStotal = 0 or ΔStotal = ΔSsys + ΔSsurr = 0
ΔSsys = dq revT = nRln2
ΔSsurr + -dq revT = -nRln2

For the two different states of

ΔS = S2 – S1
= klnW2 – klnW1
= kln(2No) – kln(1No)
= kln2no
= Nokln2
= nRkln2
Considering that k= R/No, we have another proof for
ΔS = nRln2
(Atkins & De Paulo, 2010, p. 97)
For the spreadsheet data analysis the following theoretical equations apply and are calculated by the computer on the calorimeter. A baseline shift from equilibrium is called a deflection and during the reaction a deflection froms during mixing and during deflection. (See fig. )
E = I2Rt and the electrical deflection recorded by the instrument are used to calculate the sensitivity factor (J/div)The sensitivity factor and ΔH (in Joules) divided by the [hydronium ions
(in moles) are used to calculate the ΔHmolar.
Figure. Deflection schematic

Source: Garland, Nibler & Shoemaker, 2003

An adiabatic combustion bomb calorimeter has a jacket (can) surrounding the solution and an outer jacket (see fig. ) The other jacket and the can each have a thermometer. Oxygen is used for combustion energy. There is a fuse wire inside the bomb element (See fig. ) that becomes hot and starts the combustion of the sample. When the circuit is open the fuse is oxidized.
Figure. Generic design for old fashioned calorimetric (adiabatic combustion bomb)

Source: Daniels, Williams, Bender, &Alberty, 1962.

Figure The bomb element of the adiabatic combustion bomb calorimeter

Source: Garland, Nibler & Shoemaker, 200, 3 p. 164

Figure . Ignition circuit

Source: Daniels, Williams, Bender, &Alberty, 1962.

Preliminary research demonstrates the complexities of acid base reactions for the determination of entropy. Generally speaking the reactions are difficult to characterize due to the fact that anions and cations are both in solution for all the systems containing the weak acids of strong acids and of course, the initial use of weak acids with the expectation of dynamic equilibrium. The entropies must be determined holistically with an evaluation of the acid base as a system not only a production reaction, for example.
Source: Everett & Wynne-Jones, 1939, p. 1384.
log Kobs – log Kcalc. x 104
Source: Everett & Wynne-Jones, 1939, p. 1386 & 1387.
Source: Osz & Benyei, 2007, p. 9 (1); Madgar, p. 701 (1& 2)

Source: Course packet, Chemistry 355: Physical Chemistry Lab, p. 40

Source: Course packet, Chemistry 355: Physical Chemistry Lab, p. 43-44
A new digital scanning calorimeter will be purchased for the experiment. The instrument will be networked with a computer in the lab so that the data can be immediately downloaded into the system to build the spreadsheet with the necessary calculations. (See fig. )Two solutions per run will be prepared. Practice runs will be done on the new instrument in order to perfect lab procedure. HCL and NaOH solutions will be used. The trials will also allow an estimation of how long to do the recording.
For each experimental run 10 mL of 1M HCl will be placed into the inner flask. (The measurement requires pipette accuracy.) 25 mL of 0. 45 m salt solution (dissolved in 95 ml of deionized water will be placed in the outer flask.

Heat dilution measurement: 10 mL HCL in the inner flask and 120 mL deionized water in the outer flask.

Figure . How the Experimental Set up will look. (approximate)

Source: Luhong Instruments, China, web catalogue

ΔHrxn is measured by the calorimeter
ΔGo is calculated from the Ka table
and then ΔS can be calculator
A spreadsheet will be created. The following information will be tabulated: H3O+ volume, the deflections from mixing and heating, heating time (seconds), and electrical current. Published Ka results will be tabulated. ΔGmolar = -RTlnKa is computed and used to calculate ΔG = ΔH – TΔS because it is needed to calculate the change in entropy in moles. The three properties of the solution ΔS, ΔG, ΔH will be tabulated in the order of the smallest to the largest values for ΔS. The theoretical change will be predicted for the qualitative change in ionic charge impacts ΔS and ΔH. The impact on ΔH of delocalized π bonding; theoretically it will be equal to zero in a zero order reaction. (We expect this to be a zero order reaction because 0-H bonds are equal and the only chemical replacements are O-H bonds replacing another O-H bond.) Compare observations to theoretical assumptions.


The use of the new instrument must be done after studying and practice so that systematic error will not enter the results. Reagents need to be prepared in the appropriately sized glassware. Lab procedure must be carefully and safely done or error will enter the experiment

Projected Budget

Personnel $9000
Labour (time) 3 months $3000 per month
Consumables $1000 for 3 months
(misc. Glassware and attachments for the calorimeter and the computer)


Sulphuric acid 38. 88 (BSP)
Hydrochloric acid 42. 01 (BSP)
Sodium carbonate 227. 76 (BSP)
Total $19, 500
Perkin Elmer Calorimeter $6000. 00 (USD)
Figure . Perkin Elmer DSC Calorimeter

Differential Scanning Calorimeter 4000/6000 Source: Perkin Elmer

Project Schedule
Order supplies
Order the instrument
Requisition a computer
Start literature review
Continue literature review
Extract useful data from scientific articles
Write out careful laboratory procedure and directions for using the calorimeter
Proceed with the experiment
Finish any work still not accomplished
Redo any part of the experiment if necessary
Evaluate the data
Write research paper based on the work


Atkins, P. and De Paula, J. Atkins’ Physical Chemistry 9th edition, Oxford: Oxford University Press. 2010.
Daniels, F., Williams, J. W., Bender, P. and Robert A. Alberty. Experimental Physical Chemistry. 6th Ed. New York: McGraw-Hill. 1962.
Everett, D. H. andWynne-Jones, W. F. K. The Thermodynamics of Acid-Base Equilibria. Trans. Faraday Soc. 35(9): 1380, 1938. Available from TransactionsFaradaySociety1939_35_1380. pdf
Engel, Thomas and Philip Reid. Physical Chemistry, International Edition, 3rd ed. Pearson Higher Education Publishers. 2010.
Garland, C. W., Nibler, J. W. and David P. Shoemaker. Experiments in Physical Chemistry. 8th Ed., Boston: McGraw Hill Higher Education. 2003.
Haynes, William M. CRC Handbook of Chemistry and Physics, 92nd ed, Boca Raton, FL: CRC Press. 2011.
Magder, S. Assessment of Acid-Base Balance: A Physical-Chemical Approach Chapt 61. Clinical Respiratory Physiology, pp. 700-
Osz, K. and Attila Benyei. Experiments in Physcial Chemistry. Univ. of Debrecen. 2007.
Perkin Elmer Waltham, Masachusetts, USA. www. perkinelmer. com
Fisher Scientific www. fishersci. com
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