The thermochromic system

How do we characterize a thermochromic system?
The central goal Lab Assignments 3 and 4 is to learn how to characterize the behavior of a chemical system that can
serve as the basis of a thermochromic thermometer. In this type of thermometer, temperature changes induce
processes in certain chemical substances that lead to structural forms differing in color.
Background
A chemical system exhibits thermochromic behavior when its color changes over a temperature range. You may
have observed this phenomenon in products such as mood rings, baby bottles that change color when the contents
are cool enough to drink, or actual thermometers used to measure water temperature in aquariums.
Most commercial thermochromic systems use chemical substances that exhibit liquid crystal behavior and reflect
light of different wavelengths as molecules adopt different arrangements when the temperature changes. Some
molecular dyes exhibit thermochromism. Such dyes have less accurate temperature responses than liquid crystals,
but are suitable asinexpensive, relatively simple temperature indicators for signaling when a particular temperature
threshold has been met or exceeded. One example is the use of thermochromic dyes to confirm when packaged
microwave-heated foods have been sufficiently heated. Another application is in the Duracell® battery test strips. A
layer of dye is applied on a resistive strip. The strip
is triangular in shape, so the resistance changes
along its length, thereby heating up a length in
proportion to the amount of current flowing
through it. The thermochromic dye indicates the
heating, thus gauging the amount of current the
battery is able to supply.
BDa and BDb (structures given on the right) are
two different, but related, synthetic
thermochromic dyes. When dissolved in ethanol,
both BDa and BDb exist in two forms that exhibit
distinctly different colors:
BDa1 ⇄ BDa2
Red Blue
BDb1 ⇄ BDb2
Red Blue
Here the two different forms of BDa and BDb are denoted with “1” and “2” subscripts. Equations (1) and (2) above
suggests one can control the color of a BDa or BDb ethanolic solution by controlling the extent of the chemical
reaction. Let us focus on BDa for the remainder of this this document (BDb is very similar). As written, BDa1 is the
“reactant” and BDa2 the “product.” The extent of reaction (1) depends on the system temperature. For example, if
the reaction is exothermic, increasing the temperature should favor formation of the reactant BDa1 and the chemical
system would become more red. Thus, in designing thermochromic thermometers, we need to explore how the
temperature affects the directionality and extent of the reaction.
(1)
(2)
BDa BDb
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When studying chemical equilibria of solutions, a good starting point is to determine the equilibrium constant (𝐾𝐶
).
The subscript “C” refers to molar Concentration. The equilibrium constant expression for (1) is written:
𝐾𝐶 =
[𝐵𝐷𝑎2
]
[𝐵𝐷𝑎1
]
Here the brackets signify molar concentrations of the reactant or product enclosed by the bracket. From (3), we see
that 𝐾𝐶
is the ratio of the product molar concentration over the reactant molar concentration. So clearly, if the BDa1
molar concentration is greater at equilibrium than the BDa2 molar concentration, (3) predicts 𝐾𝐶
should be smaller
than an equilibrium condition in which the BDa2 molar concentration is greater than the BDa1 molar concentration.
Evaluating Kc Experimentally
Using (3) the value of 𝐾𝐶
can be calculated if we know the equilibrium concentrations of all species in the system.
Unfortunately, it is very difficult, if not impossible, to measure concentration directly. To find [𝐵𝐷𝑎2
], recall BDa2
appears blue in color. This suggests we can use spectrophotometry to determine [𝐵𝐷𝑎2
]. In particular, BDa2 exhibits
a λmax at 628 nm with a molar absorptivity ε at this wavelength of 9.31 x 104
cm-1M-1
. So, once the absorbance at λmax
= 628 nm of the equilibrium solution is measured, [𝐵𝐷𝑎2
] can in theory be evaluated via Beer’s Law (𝐴 = 𝜀𝑏𝐶). In a
similar approach for [𝐵𝐷𝑎1
], we use a previously published observation that the red colored BDa1 has a λmax of 494
nm with ε = 3.11 x 105
cm-1M-1 at 494 nm. Hence, [𝐵𝐷𝑎1
] can be determined spectrophotometrically as well and 𝐾𝐶
may be calculated.
Kc as a Function of T
The equilibrium constant (𝐾𝐶
) should be independent of the initial concentration of the different species. However,
it is dependent on the temperature 𝑇 at which the reaction occurs. The relationship between 𝐾𝐶 and temperature
𝑇 follows
𝐾𝐶 = 𝑒
(−
∆𝐻𝑟𝑥𝑛
𝑅𝑇 +
∆𝑆𝑟𝑥𝑛
𝑅
)
In which ∆𝐻𝑟𝑥𝑛 is the enthalpy change of the reaction, ∆𝑆𝑟𝑥𝑛 the reaction entropy difference, and 𝑅 is the ideal gas
constant. ∆𝐻𝑟𝑥𝑛 and ∆𝑆𝑟𝑥𝑛 are signed values:
• ∆𝐻𝑟𝑥𝑛 > 0 ⇒ endothermic process, energetically disfavored
• ∆𝐻𝑟𝑥𝑛 < 0 ⇒ exothermic process, energetically favored • ∆𝑆𝑟𝑥𝑛 > 0 ⇒ entropically favored
• ∆𝑆𝑟𝑥𝑛 < 0 ⇒ entropically disfavored Kc as a Function of T: Graphical Relationships – Inferring the Signs of ∆𝑯𝒓𝒙𝒏 and ∆𝑺𝒓𝒙𝒏 Expression (4) implies the effect of temperature 𝑇 on 𝐾𝐶 is not the same for endothermic and exothermic reactions. In the case of endothermic reactions (∆𝐻𝑟𝑥𝑛 > 0), 𝐾𝐶
is always an increasing function of temperature with an
asymptotic value at high 𝑇 (𝐾𝐶 ∝ 𝑒
−(1⁄𝑇)
) that may rise above 𝐾𝐶 = 1 if ∆𝑆𝑟𝑥𝑛 > 0 or remain below 𝐾𝐶 = 1 if ∆𝑆𝑟𝑥𝑛
< 0 (as illustrated in the upper two graphs of Figure 1). For exothermic reactions (∆𝐻𝑟𝑥𝑛 < 0), 𝐾𝐶 is always a decreasing function of temperature with an asymptotic value at high 𝑇 (𝐾𝐶 ∝ 𝑒 (1⁄𝑇) ) that may remain above 𝐾𝐶 = 1 if ∆𝑆𝑟𝑥𝑛 > 0 or fall below 𝐾𝐶 = 1 if ∆𝑆𝑟𝑥𝑛 < 0 (the lower two
(3)
(4)
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graphs of Figure 1 illustrates these relationships).
Figure 1 𝐾𝐶 as a function of 𝑇 for different reaction types.
Figure 1 suggest that if 𝐾𝐶 is determine at two different temperatures 𝑇, then the sign of ∆𝐻𝑟𝑥𝑛 and ∆𝑆𝑟𝑥𝑛 may be
inferred by the relationship of the two data points to 𝐾𝐶 = 1, as Figure 2 below attempts to depict.
Figure 2 Possible relationship between 𝐾𝐶 = 1 and 𝐾𝐶 at two different
temperatures 𝑇 to the sign of ∆𝐻𝑟𝑥𝑛 and ∆𝑆𝑟𝑥𝑛.
The inferred signs of ∆𝐻𝑟𝑥𝑛 and ∆𝑆𝑟𝑥𝑛 should indicate the suitability of the system as a thermochromic thermometer.
Kc as a Function of T: Van’t Hoff Equation– Determining ∆𝐻𝑟𝑥𝑛 and ∆𝑆𝑟𝑥𝑛
To determine the value (as well as the sign) of ∆𝐻𝑟𝑥𝑛 and ∆𝑆𝑟𝑥𝑛, the relationship between 𝐾𝐶 and 𝑇 (in kelvins) given
by the Van’t Hoff equation finds use:
ln𝐾𝐶 = −
∆𝐻𝑟𝑥𝑛
𝑅
1
𝑇
+
∆𝑆𝑟𝑥𝑛
𝑅
𝑦 = 𝑚𝑥 + 𝑏
where 𝑅 is the ideal gas constant (𝑅 = 8.314 J/(K·mol)). This relationship suggests that the value of ∆𝐻𝑟𝑥𝑛 and ∆𝑆𝑟𝑥𝑛
may be derived experimentally using 𝐾𝐶 values at different temperatures 𝑇. This can be done by plotting 𝑙𝑛(𝐾𝐶
)
versus 1/𝑇 to prepare a Van’t Hoff plot which should result in a straight line with slope 𝑚 = −∆𝐻𝑟𝑥𝑛⁄𝑅 and yintercept 𝑏 = ∆𝑆𝑟𝑥𝑛⁄𝑅. (Side note: for this Van’t Hoff analysis, the temperatures must be expressed in kelvins (K).)