Design and construction of an quasi-adiabatic dissolutioncalorimeter with a novel dosing apparatus and a low heat capacity

Gordan Horvat • Josip Pozar • Zvonimir Dojnovic •

Dragutin Grgec • Sasa Blazeka

Received: 27 November 2013 / Accepted: 14 April 2014

� Akademiai Kiado, Budapest, Hungary 2014

Abstract A quasi-adiabatic calorimeter for determining

the molar solution enthalpies (DsolH) of non-volatile solids

was constructed. The design of the instrument was adjusted

to allow the determination of solution enthalpies of small

amounts of solids. For that purpose, the novel apparatus for

sample dosage with virtually negligible ‘‘blank heat’’ was

built. The rather low heat capacity of the calorimeter was

achieved by reducing the volume of the reaction cell

(20 mL), the dosing unit, and electric elements (the

thermistor and the heater). Good thermal isolation of the

reaction cell from the surroundings was accomplished by

placing the cell into an evacuated polypropylene vessel. A

computer program for processing the calorimetric data

according to modified Regnault–Pfaundler method was

written. The performance of the calorimeter was tested by

determining the heats of the reactions serving as thermo-

chemical standards at 25 �C (the dissolution of KCl and

NaCl in water and the dissolution of tris(hydroxymethyl)-

aminomethane in 0.1 mol dm-3 HCl(aq)). The obtained

data were in very good agreement with the literature

values.

Keywords Calorimetry � Quasi-adiabatic calorimeter �Molar solution enthalpy

Introduction

The interest in obtaining the molar solution enthalpies of

solids (DsolH) has been considerable, since many experi-

mentally unavailable reaction enthalpies can be obtained

from the cycles including the DsolH values [1, 2]. The

molar solution enthalpies also provide a deeper insight into

the energetics of the solute solvent interactions. For

instance, the thermodynamics of the solute solvation in

different solvents [3, 4] or the influence of the solvent on

the thermodynamic reaction state functions [5] can be

rationalized in terms of the so-called transfer functions of

reactants and products. The standard enthalpy of transfer

from one solvent to another can be easily obtained as a

difference between the corresponding DsolH values.

The molar solution enthalpies of solids are of use to the

researchers in the field of solid-state chemistry, particularly

those dealing with polymorphism. Based on the DsolH of

polymorphs in a certain solvent, the differences in the

corresponding lattice enthalpies can be calculated [6].

These values, combined with the knowledge regarding the

crystal structure of the forms involved, enable a deeper

thermodynamic insight into the structure–stability relation,

at least in terms of energetics. It should be also noted that

the accurate determination of molar solution enthalpies is

of great practical importance, particularly in chemical

technology [7–9] and in pharmaceutical industry [10–13].

In the past, the solution enthalpies of solid compounds

were predominantly determined by using the so-called

‘‘macro solution calorimeters’’ [14–16]. These instruments

were basically Dewar’s vessels with a relatively large

reaction cell (up to 100 mL) accommodating the thermo-

metric sensor, the calibrating device, and the dosing unit.

The heat capacity of the calorimeter was large, and the

consumption of the sample in the experiment was

This paper is dedicated to late Mr. Zvonimir Dojnovic.

Electronic supplementary material The online version of thisarticle (doi:10.1007/s10973-014-3829-9) contains supplementarymaterial, which is available to authorized users.

G. Horvat (&) � J. Pozar � Z. Dojnovic � D. Grgec � S. Blazeka

Division of Physical Chemistry, Department of Chemistry,

Faculty of Science, University of Zagreb, Horvatovac 102a,

10000 Zagreb, Croatia

e-mail: ghorvat@chem.pmf.hr

123

J Therm Anal Calorim

DOI 10.1007/s10973-014-3829-9

substantial. The sample addition (most commonly achieved

by crushing a glass ampoule containing the solid) was

usually accompanied with a measurable ‘‘blank heat,’’

which had to be determined in a separate experiment. The

calorimetric determinations of DsolH were hence limited to

solids of high solubility with relatively large absolute

values of molar solution enthalpies.

Nowadays, the ever growing number of organic com-

pounds with interesting chemical properties (receptors of

neutral species, ionophores, or pharmaceutically active

compounds) puts new demands on the design of dissolution

calorimeters [17–22]. This is due to the fact that these solids

are commonly scarcely soluble (particularly in water and in

protic solvents), and the absolute values of their molar

solution enthalpies are in most cases relatively low. As a

consequence, the ‘‘blank heats’’ in the calorimeters used for

the determination of the corresponding DsolH values should

be as close to zero as possible. In addition, the heat capacity

of the instrument must be low. It is therefore not surprising

that sensitive isothermal microcalorimeters have been pro-

posed as the instruments of choice for determining the

DsolH of such compounds [23]. However, the commercially

available isothermal microcalorimeters are still quite

expensive, and their manufacture requires far more skill and

knowledge from a calorimetrist than needed for the con-

struction of a quasi-adiabatic calorimeter. In the present

paper, we report on the construction of a simple, yet quite

sensitive quasi-adiabatic calorimeter with a moderate heat

capacity. This instrument could be an affordable alternative

to commercial dissolution microcalorimeters.

Theory

The equation which describes the heat measuring principle

of the quasi-adiabatic calorimeter reads as follows [24]:

DrHdn ¼ �CpdT þ dq; ð1Þ

where DrH denotes the reaction enthalpy, Cp is the isobaric

heat capacity of the calorimeter, dT is the temperature

change within the reaction cell, whereas the last term

denotes the heat exchanged between the calorimeter and

the surroundings (thermostat). By the appropriate con-

struction of the quasi-adiabatic calorimeter, the heat flow

between the system and the thermostat is minimized.

In a typical quasi-adiabatic dissolution, experiment

temperature is measured before, during and after the

reaction (Fig. 1). A pre-reaction period (between points A

and B in Fig. 1) is used for determining the rate of tem-

perature change in the calorimeter caused by non-reaction

heat effects, i.e., heat exchange with the surroundings, heat

production by stirring the reaction mixture, and the work of

the electrical current on the thermistor. In the short time

interval during this period, temperature change is usually

linear with time. The central part of temperature–time

curve, between points B and C, is the period in which the

studied process takes place. In the post-reaction period

(from C to D), the temperature is monitored for the same

reason as during the period A to B.

The integral form of Eq. (1) during the reaction time

period equals:

Zn

0

DrHdn ¼ �ZTC

TB

CpdT þZtC

tB

Cp

dT

dt

� �dt ð2Þ

If the expression (2) is divided by the isobaric heat

capacity of the calorimeter, which is presumed to be tem-

perature independent, and then integrated, the following

relation is obtained:

DTR ¼ TC � TB � DTadd ¼ DTtot � DTadd: ð3Þ

In derivation of this expression, the left term in Eq. (2)

was substituted with:

Zn

0

DrHdn ¼ �CpDTR: ð4Þ

In the Eq. (3), DTR is the temperature change caused by

the heat effect of the reaction, DTtot denotes the total

temperature change during the examined process, and

DTadd is the temperature change due to non-reaction heat

effects. The DTtot can be easily determined from the tem-

perature–time curve by subtracting the last value of the

temperature that belongs to the linear AB period from the

first temperature value that belongs to the linear CD period.

On the other hand, the DTadd has to be calculated by esti-

mating the magnitude of non-reaction heat effects during

bCDTC

tB tC

A

B

DC

Time

Tem

pera

ture

TBbAB

Fig. 1 Temperature–time curve for the passive quasi-adiabatic

calorimeter

G. Horvat et al.

123

the reaction. This can be done by using one of the several

different approaches [25–30]. In general, a function

describing the time dependence of the temperature change

caused by the non-reaction heat effects is needed:

DTadd ¼ZtC

tB

dT

dt

� �dt: ð5Þ

In the present paper, the slopes of the linear temperature

changes during periods AB and CD, namely bAB and bCD,

were used to obtain the dT/dt dependence during the

reaction period (further denoted by bBC(T)) by means of the

following two-parameter linear equation:

bBCðTÞ ¼bCD � bAB

�TCD � �TAB

ðTBCðtÞ � �TABÞ þ bAB; ð6Þ

where �TAB and �TCD denote average temperatures in the AB

and CD periods, respectively.

Temperature time dependence during reaction period

(TBCðtÞ) can be obtained by fitting the collected data with

an empirically found function. By combining the Eqs. (5)

and (6), the expression for DTadd is obtained:

DTadd ¼bCD � bAB

�TCD � �TAB

ZtC

tB

TBCðtÞdt � �TABðtC � tBÞ

0@

1A

þ bABðtC � tBÞ: ð7Þ

The integral in the Eq. (7) can be divided in several

integrals in order to adequately describe the temperature

time dependence during reaction period. In our data ana-

lysis, the reaction period was divided in two segments, and

time dependence of temperature in each of these intervals

was fitted with a polynomial of sixth order.

It should be noted that as a result of non-instant heat

conduction through the shield enclosing the thermistor, the

temperature measured during an experiment slightly differs

from the temperature of the system studied. Temperature in

the reaction cell can be obtained from the (measured)

temperature of the thermistor, Tth:

TsysðtÞ ¼ TthðtÞ þ sth

dTthðtÞdt

� �: ð8Þ

where sth denotes the time constant of the thermistor which

is equal to Cp,th/kth. This constant is easily determined from

the integral form of the Eq. (8) by non-linear regression of

Tth(t) data measured by immersing the thermometric sensor

in the thermostated bath whose temperature differs from

the initial temperature of thermistor.

The expression for reaction enthalpy can be obtained by

integration of (4) where DrH is presumed to be independent

on the reaction extent:

qp ¼ DH ¼ DrHDn ¼ �CpDTR: ð9Þ

DrH is equal to the slope of the linear dependence of

enthalpy change caused by the reaction on Dn.

Experimental

Materials

The solids, KCl (Sigma-Aldrich, TRACESelect; C99.9995 %),

NaCl (Sigma-Aldrich, ACS; C99.95 %), and tris(hydroxy-

methyl)-aminomethane (Sigma-Aldrich, 99.9? %) (further

denoted as TRIS), were used without further purification.

The potassium chloride and TRIS were stored over calcium

chloride in a vacuum dessicator. Sodium chloride was dried

at 200 �C for 20 h and held in a vacuum dessicator after-

ward. Prior to dissolution or drying, NaCl and TRIS were

grounded to a fine powder in order to hasten the dissolution

process. The KCl and NaCl were dissolved in deionized

B

I

E D

FG

A

C

H

Fig. 2 Shematic drawing of the calorimeter. A reaction cell, B poly-

propylene shield, C polypropylene lid, D thermistor, E heater,

F stirrer, G dosing apparatus, H screw, I vacuum valve

Quasi-adiabatic dissolution calorimeter

123

water. For the dissolution of TRIS in 0.1 mol dm-3 HCl(aq),

a standard solution of HCl (Kemika, Titrival) was used.

Apparatus

The calorimeter (Figs. 2 and S1–S4, Supporting Informa-

tion) consisted of a cone-shaped stainless steel reaction cell

(V = 20 mL) (A), mounted onto a polypropylene vessel

(B, 5-cm thick), the polypropylene lid (C, 5-cm thick), the

thermistor (D), the heater (E), the stirrer (F), and the dosing

apparatus (G). The lid of vessel could be fitted to the

reaction cell by means of two screws (H) and two bolts.

The tubes accommodating the thermistor, heater, stirrer,

and the dosing apparatus (D–G) were welded to the inner

side of the lid. The connecting wires were cemented into

the lid by the two component epoxy resin glue. The

thermistor and the heater were coated with caps made of

gold-plated copper. The stirrer was made from stainless

steel.

The dosing apparatus (Figs. 3 and S4, Supporting

Information), also made from stainless steel, includes the

cylinder (a), the lid (b), and the piston (c). The piston and

the lid are connected by a rod (d), approximately 0.5-cm

thick. The tight fit of the lid to the cylinder is achieved by

means of spring with a large force constant (e) and a ring

made of synthetic rubber, mounted on the inner surface of

the lid (f). The spring is coiled around a second rod (g,

1-cm thick), filling the space between the rear of the piston

(h) and the cap of the apparatus (i). The operation principle

is quite similar to that of a spring ballpoint pen. At a

desired instant, the spring could be compressed by applying

the pressure on the cap, via a servo electromotor, thereby

causing the piston (c) and the lid (b) to move downward.

This, in turn, exposes the solid, placed in the space between

the piston and the lid (the sample compartment (j)), to the

solvent. The volume of the sample compartment inside the

dosing apparatus was 0.75 cm3. Blanks showed no

detectable heat effect due to this operation (Fig. S5).

The temperature sensor was a 5 kX thermistor (at

T & 298.15 K), whereas the heater consisted of coiled

copper wire (R = 15.2 X). The power of the heater could

be adjusted by varying the voltage across the feeding cir-

cuit. The resistance of the thermistor and the potential drop

across the heater were measured by means of the Agilent

34411A digital multimeter. The heating time was measured

by a stopwatch with a hundredth of a second precision. The

watch was coupled mechanically to the switch actuating

the heater. The stirrer (fitted with a propeller) was operated

by a synchronous motor driven by a 24 V power supply.

The calorimeter and the solvents used were thermostated

in an air thermostat made of Plexiglas. Temperature within

the thermostat was regulated up to a tenth of degree pre-

cision (Fig. S6, Supporting Information) by means of a

heater and thermocouples used for cooling. Contact mer-

cury thermometer was used for temperature control.

The addition of solid was made when a sufficiently low

change in temperature of the calorimetric cell content with

time was observed (approximately 10 min after the

experiment startup).

Methods

The thermistor was calibrated in the temperature range

278.15 B T/K B 323.15. For that purpose, a constant

temperature bath (PolyScience 9101) with a thermometer

of 0.01 K temperature resolution was used. The accuracy

of its temperature scale was assured by calibration that can

be traced to NIST temperature standards. The time constant

of the temperature sensor was obtained by monitoring the

time needed to accomplish the thermal equilibrium

between the sensor and the thermostat. These experiments

were done in triplicate. The obtained time constant was

used for the deconvolution of temperature–time curves

according to Eq. (8).

Prior to determination of the reaction enthalpies, the

performance of the calorimeter was tested by electrically

supplying the variable amount of heat (1 \ q/J \ 6) to the

reaction cell containing 20 mL of deionised water.

The solution enthalpies of KCl and NaCl in water and of

TRIS in 0.1 mol dm-3 HCl(aq) were determined by pro-

cessing the time dependence of the thermistor resistance.

The calorimeter was in all cases calibrated after the dis-

solution of compounds. The obtained data were processed

using the aforementioned, modified Regnault–Pfaundler

method implemented in a home-made software, written in

Wolfram Mathematica 7 (Fig. S7, Supporting Information).

Molar solution enthalpies were determined by linear

regression from the dependence of enthalpy changes on the

reaction extent given by Eq. (9). Linear and non-linear

curve fitting and data plotting were performed using the

Origin 7.5 software.

a

j

c

d

e

f

g

i

b

h

Fig. 3 Schematic drawing of

the dosing apparatus. a cylinder,

b lid, c piston, d steel rod,

e spring, f ring made of

synthetic rubber, g steel rod,

h piston rear, i cap, j sample

compartment

G. Horvat et al.

123

Results and discussion

Thermistor calibration and the performance

of the calorimeter

The response of the thermometric sensor was examined by

its abrupt immersion from air with the temperature of

298.55 K to a thermostated bath held at 295.15 K (Fig. S8,

Supporting Information). Time dependence of temperature

was fitted according to integral form of Eq. (8), and a time

constant of thermistor was obtained, sth = (1.34 ± 0.01) s.

The results of thermistor calibration are shown in Fig. 4.

As can be seen, the agreement between the experimental

data and the values calculated according to relation [31]

R Tð Þ ¼ Aexp �B=Tð Þ þ C ð10Þ

was excellent. The parameters A = (5.53 9 10-2 ± 5 9

10-4) X, B = (3,383 ± 2) K, and C = (–130 ± 3) X were

therefore used in processing the calorimetric data.

The sensitivity of the calorimeter was checked by a series

of electrical calibration experiments in which a variable

energy input to a calorimeter containing 20 mL of deionised

water was applied. The obtained heat capacities are given in

Table 1. The temperature–time curves recorded at the lowest

and the highest heats supplied are shown in Fig. 5a, b,

respectively.

The data presented in Table 1 suggest that the obtained

heat capacity is virtually independent on the calibration

heat. In addition, the standard deviations of the Cp values,

determined by repetitive calibrations with a similar energy

input from the heater (±1 %), were quite low. The

instrument is therefore sufficiently precise to allow the

determination of rather small enthalpy changes.

Determinations of molar solution enthalpies

The calorimeter accuracy was tested by performing three

reactions with a well-known reaction enthalpies at

&298.15 K, the dissolution of KCl [32, 33] and NaCl in

water [34–36] and of TRIS in HCl (aq, c = 0.1 mol dm-3)

[14, 21, 26, 37, 38]. For the reactions examined, multiple

experiments with variable sample mass and consequently

with variable solution enthalpy changes were carried out.

The addition of potassium chloride in water resulted in a

prolonged decrease of temperature of the calorimeter

content (approximately 50 s for higher amounts of solid

added, Figs. 6 and S10, Supporting Information), which

indicated that the dissolution of this solid was a relatively

slow process. Once the reaction came to a halt, a linear

change of temperature with time was again observed. The

calorimeter was then calibrated by means of electric heater.

From the temperature change in the reaction period and the

isobaric heat capacity of the calorimeter, heats associated

with the KCl dissolution in water were determined (Fig. 7;

Table S1).

As can be seen in Fig. 7, the obtained DH versus ndependence was linear. This result indicated that the

corresponding slope can be considered as the specific

dissolution enthalpy of potassium chloride in the examined

concentration range. The determined value DsolH =

(17.74 ± 0.11) kJ mol-1 is in very good agreement with

the values which can found in the literature, namely

17.584 kJ mol-1 determined by Kilday [32] and

17.587 kJ mol-1 measured by Gunn [33].

As in dissolution experiments with potassium chloride,

the addition of sodium chloride to water resulted with

relatively slow temperature change during the reaction

period (the decrease in temperature of the reaction mixture

once the solid was exposed to the solvent could be

observed for approximately 50 s, Figs. 6 and S11, Sup-

porting Information). The calorimeter was again calibrated

when a linear dependence of temperature with time was

observed (approximately 100 s after the sample addition).

Heats associated with the dissolution of NaCl are given in

Fig. 7 and in Table S2.

The obtained DH versus n dependence was linear

(Fig. 7). Owing to low concentrations of NaCl, the

obtained value should be close to the standard molar

enthalpy of solution of NaCl (DsolH8). The agreement

280 285 290 295 300 305 310 315 320 325

2

3

4

5

6

7

8

9

10

Res

ista

nce/

kΩ

Temperature/K

Fig. 4 Thermistor calibration. Filled square measured values, line

calculated values

Table 1 Isobaric heat capacity of the calorimeter obtained by elec-

trical calibration

�qp/J (Cp ± SE)/J K-1

0.98 112.0 ± 2.2

1.53 112.2 ± 1.2

3.04 113.6 ± 1.1

5.89 112.7 ± 0.7

SE standard error of the mean (N = 16–23)

Quasi-adiabatic dissolution calorimeter

123

between the determined value DsolH8 = (4.258 ± 0.022)

kJ mol-1 and those found in the literature, 4.213 kJ mol-1

measured by Archer and Kirklin [35], and 4.192 kJ mol-1

determined by Lehto et al. [22] is very good.

Contrary to the slow dissolution of sodium chloride,

the dissolution of TRIS in hydrochloric acid (c =

0.1 mol dm-3) was rather rapid (Figs. 6, S12, Supporting

Information). Hence, after the addition of TRIS sample, a

temperature rise lasting 10–30 s was observed. As in the

cases of KCl and NaCl, the DsolH was independent on the

amount of solid dissolved (Fig. 7; Table S3). The deter-

mined DsolH = (-29.72 ± 0.22) kJ mol-1 was again in

quite good agreement with the literature data, ranging from

-29.63 kJ mol-1 to -29.75 kJ mol-1 [14, 21, 26, 37, 38].

Conclusions

The constructed isoperibolic calorimeter possesses rela-

tively low thermal conductivity achieved by placing the steel

reaction cell in the vacuum jacket made of polypropylene.

The novel design of the sample dosing apparatus enabled the

addition of the solid accompanied with virtually zero ‘‘blank

heat’’. Moreover, the solid can be loaded into the sample

compartment as a fine powder, without a mechanical pre-

treatment (for instance pressing into a tablet), required in

certain types of instruments [19]. Because of the small size of

the reaction cell (20 mL), the heat capacity of the calorimeter

is rather low. The described instrument hence fulfills the

requirements needed for the determination of solution

enthalpies of small amounts of solids. Its main advantage, in

comparison with the instruments of similar performance, is

the simple and inexpensive construction (the value of the

parts needed does not exceed a sum of 200 Euros).

0 10 20 30 40 50 60

0

2

4

6

8

10

(a) (b)

ΔTem

pera

ture

/mK

Time/s0 10 20 30 40 50 60

0

10

20

30

40

50

Time/s

ΔTem

pera

ture

/mK

Fig. 5 Electrical calibration of the calorimeter filled with 20 mL of water. a �qp ¼ 0:99 J, T0 = 296.12 K. b �qp ¼ 5:87 J, T0 = 297.06 K.

DTemperature = (Tsys(t) - T0)

0 25 50 75 100 125 150

–60

–40

–20

0

20

40

60

80

100

120

KCl

NaCl

ΔTem

pera

ture

/mK

Time/s

TRIS

Fig. 6 Temperature–time curves for the dissolution of KCl

(m = 32.22 mg, T0 = 298.106 K) and NaCl (m = 37.43 mg,

T0 = 298.127 K) in water (V = 20 mL) and for the dissolution of

TRIS (m = 20.40 mg, T0 = 298.104 K) in hydrochloric acid

(V = 20 mL, c = 0.1 mol dm-3) and for the subsequent electrical

calibration of the calorimeter. DTemperature = (Tsys(t) - T0)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

–8

–6

–4

–2

0

2

4

6

8

10

KCl

NaCl

Hea

t/J

103 Δ /mol

TRIS

ξ

Fig. 7 Heat of dissolution of KCl, NaCl, and TRIS in water as a

function of the compound mass

G. Horvat et al.

123

Acknowledgements This work was supported by the Ministry of

Science, Education and Sports of the Republic of Croatia (Projects

119-1191342-2960 and 119-1191342-2961).

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