Solubility and thermodynamics

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The purpose of this experiment is to measure the solubility of KNO3 at several temperatures, and from these measurements to determine ∆G°, ∆H°, and ∆S° for the reaction

KNO3 (s)  K1+ (aq) + NO31– (aq)

1. Set up a boiling water bath. Obtain a large (50 mL) graduated cylinder and remove the plastic base, so you can use it like a big test tube.
2. Weigh the cylinder, add about 20 g of KNO3, reweigh, and record the exact mass of KNO3 used. Add 15 mL deionized water (add it gradually, dripping it down the side so no KNO3 crystals stick to the inside of the cylinder) and heat the cylinder in the boiling water bath, stirring occasionally with a magnetic stir bar, until all of the KNO3 has dissolved. Leave the stir bar in the tube.
3. Remove the cylinder from the water bath. Allow it to cool, stirring constantly, and monitor the temperature. Record the temperature when crystals first appear. Record the solution volume (leave the stir bar in the liquid).
4. Add 5 mL of deionized water, stir, then re-warm the solution just until all solid has dissolved. Remove the cylinder from the bath and allow it to cool as before. Record the temperature and solution volume when crystals first appear.
5. Repeat step 4 several times until you have at least 5 data points. Lift the stir bar out of the solution and reread the volume of the last point without stir bar, so you can correct the data points for the volume of the stir bar. When you are finished pour the solution in the instructor’s beaker (so I can reclaim the KNO3), then rinse the cylinder, temperature probe, and stir bar thoroughly.
Write the chemical equation for the solubility equilibrium and the expression for its Ksp. Subtract the stir bar volume from each solution volume.
1. The system is at equilibrium when solid is in contact with saturated solution, a condition met when you first observe crystals in the solution. For each temperature, calculate the solubility of the KNO3 from the mass used and the corrected solution volume, then calculate the value of Ksp for the reaction.
2. Calculate ∆G° for the reaction at each temperature, using the relationship ∆G° = – RTlnKeq, where T is the absolute temperature and R is the gas constant in J/mol K.
3. The relationship between K and temperature has the same form as the Clausius-Clapeyron and Arrhenius equations:

That means a plot of ln K vs 1/T should yield a straight line with slope – H°/R. Construct this graph and use it to determine the value of ∆H° for the reaction. Remember to use the correct value for R. A straight line confirms that the value of ∆H° is constant over the temperature range of the experiment.

4. Calculate the value of ∆S° at each temperature using the relationship ∆G° = ∆H° – T∆S°.
1. Tabulate your results for Keq, ∆G°, ∆H°, and ∆S° at the various temperatures and show the average values for ∆H° and ∆S°. What do the signs tell you about this reaction? Are they what you expected?
2. Use the thermodynamic data tables at the back of your text to calculate values for ∆H° and ∆S° for this reaction. How do your values compare to the calculated values? Discuss.

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