Page 100 - Physical chemistry eng

4.6 DIFFERENTIAL SCANNING CALORIMETRY 77

¢H° solution is defined per mole of the solution reaction, but because the reaction
includes exactly 1 mole of reactant, the factor m salt >M salt in Equation (4.21) is appro-
priate. Because ¢(PV) is negligibly small for the solution of a salt in a solvent,
¢U° solution =¢H° solution . The solution must be stirred to ensure that equilibrium is
attained before ¢T is measured.

EXAMPLE PROBLEM 4.4
The enthalpy of solution for the reaction
H O ( l )
2-
+
Na SO (s) 2 " 2 Na (aq) + SO (aq)
2
4
4
is determined in a constant pressure calorimeter. The calorimeter constant was deter-
-1
mined to be 342.5 J K . When 1.423 g of Na SO is dissolved in 100.34 g of H O(l),
2
4
2
¢T = 0.031 K. Calculate ¢H° solution for Na SO from these data. Compare your result
2
4
with that calculated using the standard enthalpies of formation in Table 4.1 (Appendix B,
Data Tables) and in Chapter 10 in Table 10.1.
Solution
M salt m H 2 O
¢H° solution =- a C P,m (H O)¢T + C calorimeter ¢Tb
2
m salt M H 2 O
100.34 g -1 -1
* 75.3 J K mol * 0.031 K
-1
142.04 gmol £ 18.02 g mol -1 ≥
=- *
1.423 g + 342.5 J K -1 * 0.031 K
3
=-2.4 * 10 Jmol -1
We next calculate ¢H° solution using the data tables.
+ 2-
¢H° solution = 2¢H°(Na ,aq) +¢H°(SO ,aq) -¢H°(Na SO ,s)
f
f
4
4
2
f
-1
= 2 * (-240.1kJmol ) - 909.3kJmol -1 + 1387.1 kJmol -1
=-2.4kJmol -1
The agreement between the calculated and experimental results is good.
SUPPLEMENT AL
4.6 Differential Scanning Calorimetry
Differential scanning calorimetry (DSC) is a form of constant pressure calorimetry that
is well suited to routine laboratory tests in pharmaceutical and material sciences. It is also
used to study chemical changes such as polymer cross-linking, melting, and unfolding of
protein molecules in which heat is absorbed or released in the transition. The experimen-
tal apparatus for such an experiment is shown schematically in Figure 4.5. The word
differential appears in the name of the technique because the uptake of heat is measured
relative to that for a reference material, and scanning refers to the fact that the tempera-
ture of the sample is varied, usually linearly with time.
The temperature of the enclosure T is increased linearly with time using a power
E
supply. Heat flows from the enclosure through the disk to the sample because of the tem-
perature gradient generated by the heater. Because the sample and reference are equidis-
tant from the enclosure, the heat flow to each sample is the same. The reference material
is chosen such that its melting point is not in the range of that of the samples.
We consider a simplified one-dimensional model of the heat flow in the DSC in
Figure 4.6 following the treatment of Höhne, Hemminger, and Flammersheim in
Differential Scanning Calorimetry, 2nd Edition, Berlin: Springer, 2003. The electrical
current through the resistive heater increases the temperature of the calorimeter
enclosure T to a value greater than that of the sample and reference, T , and T . The
R
S
E