I recently conducted a coffee-cup calorimetry experiment in which we attempted to measure if the dissolution of inorganic crystals such as LiCl, NaCl, and SrCl were endothermic or exothermic based on a change in temperature over time plot, including measure the enthapy of solutions, but I'm not sure how to do that.
Methods:
We measured 7.9204 grams of SrCl2, 4.2143 grams of LiCl, and 2.9290 grams of NaCl and decanted these into separate coffee cups filled with 50 mL of deionized of water. (These were about 1 - 2 mole/liter solutions.). A temperature probe measured the temperature change over 600 seconds, recording a measurement twice a second. I've only displayed about 140 seconds of the measurement, because the temperature was just continually oscillating 0.1 degree Celsius after that point as it reached equilibrium.
We made plots for each of the chemicals, where an increasing curve shows an exothermic reaction, and an endothermic reaction displays a decreasing curve. Over time, these solutions (Temperature ~ Time) curves should equalize to equilibrium.
Theoretically, we predicted we could determine if the enthalpy of solution like so ...
Enthalpy of solution = Lattice Enthalpy + (Hydration Enthalpy of cation + Hydration Enthalpy of Anion),
where the Lattice Enthalpy is a measure of the stability of the compound crystal which is at least a function of the charges of the cation and anion, as well as their size, and the structure of the crystal body centered cubic vs face centered cubic, and the hydration enthalpy is the energy it takes to dissolve the gaseous ions after breaking the crystal lattice.
Schematically, the Lattice Enthalpies ( Δ H):
LiCl(s) ----> Li+ (g) + Cl- (g); ΔH = 852 kJ / mole
NaCl(s) ----> Na+ (g) + Cl- (g); Δ H = 787 kJ / mole
SrCl2(s) ---> Sr2+ (g) + 2 Cl- (g); ΔH = 2153
Source:
These Lattice Enthalpies were obtained from Table 18B.4 of my textbook:
Physical Chemistry Thermodynamics, Structure and Change, 10th Edition, VOlume 1, by Peter Atkins & Julio de Paula
Then the Enthalpies of Hydration are these:
Li^(+) (g) ---> Li^(+) (aq); ΔH = -519 kJ / mole
Cl^(-1) (g) ----> Cl^(-1) (aq) ; ΔH = -381 kJ / mole
Na^(+) (g) -------> Na^(+) (aq); ΔH = -409 kJ / mole
Sr^(2+) (g) -------> Sr^(2+) (aq); ΔH = -1443 kJ / mole
Source of Enthalpies of Hydration (Tables 1 - 2):
The Enthalpies of Hydration that I've used are experimental.
Smith, Derek W. "Ionic hydration enthalpies." Journal of Chemical Education 54.9 (1977): 540.
Therefore, the enthalpy of solution for LiCl, NaCl, SrCl2 is this:
For LiCl,
ΔHsolution, LiCl = (852 kJ / mole) + [(-519 kJ / mole) + (-381 kJ / mole)] = -48 kJ / mole < 0, so this reaction should be exothermic and it is as predicted.
For NaCl,
ΔHsolution, NaCl = (787 kJ / mole) + [(-409 kJ / mole) + (-381 kJ / mole)] = -3 kJ / mole < 0, so this reaction should be exothermic.
I've been searching the web about this reaction and most sources say it's endothermic which I my graph shows, but my calculations do not show that. What?
Doing the same kind of mathematics, the Enthalpy of solution for SrCl2 is this:
ΔHsolution, SrCl2 = [2153 + (-1443 - 2 * 381)](kJ / mole)
= -52 kJ / mole < 0, so this reaction should be exothermic.
BUT MY PLOT SHOWS that It's significantly endothermic!
What's going on? Is my mathematics faulty. Am I using too concentrated solutions? Is the SrCl2 that we are using impure or not really SrCl2? I suppose that's possible, but we didn't do any validation because this lab took quite some time. How is it possible that my experiments don't match theory mostly?
Thank you for you for your help.
Since you are talking about an adiabatic change under the constant pressure otherwise Enthalpy wouldn't be a proper characteristic thermodynamic function to be used for study the dissolution process. Then any drop in the temperature of the solution (salt plus water) indicates negative enthalpy variation of the aqua media which is exactly equal to the heat supplied to the salt to be dissolved. That is called endothermic reaction in practice. Since this heat is subtracted from the media insulated from the surroundings that causes its temperature will drop. Where Delta H (Water) = Cp(water) Delta T (negative); Delta H (Salt) = -Delta H(Water)
Note: This is a rough calculation: Here we have assumed that water has very (large mass) global heat capacity compared to the (mass) salt, furthermore the solution is very well stirred .
Note: The constant plateau on T vs t curve indicates stationary equilibrium state of the solution where forward and backward reactions take place in equal rates.
Beside enthalpies, the entropy changes are also important. The salts are in crystal forms. They are highly ordered. When dissolves in water, they becomes hydrated ions, which are highly disordered. The entropy changes are significant.
Entropy,
http://butane.chem.uiuc.edu/pshapley/GenChem1/L20/2.html
An example on how to calculate the free energy change of the solvation of CaCl2,
http://chemistry-reference.com/reaction.asp?rxnnum=170
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