DATA: CALCULATIONS: Because the potassium nitrate is a strong electrolyte, its solution reaction will be: KNO3(s) + H2O →K+ (aq) + NOз - (aq) The reaction is at equilibrium when the solid is in contact with a saturated solution, the condition we have when crystallization begins. The solubility, s, of the salt in moles per liter may be calculated from the amount of salt weighed out and the volume of the solution. The equilibrium constant, K, for the reaction will be: Ksp = [K][NO3] = (s)(s) = s² (1) The equilibrium constant Ksp may be used to calculate the AG for the reaction at each temperature using the thermodynamic relationship: AG = -RT In K (2) where T is the Kelvin temperature and R is the gas constant (8.314 J/mol-K). AGAHTAS (3) These two variables, AH and TAS, can be substituted for AG into Equation 3. With some rearrangement the mathematical relationship between Ksp, AH, and AS as a function of T is given in a useful form for graphing in Equation 5 below. The equation is written in In Ksp--AH/R*(1/T) + AS/R y = mx + b the form of a straight line, y = mx + b as shown above. The form of a straight line, y = mx + b as shown above. We may assume that AH and AS are constant over these small temperature ranges. The last equation relates the overall change in Gibbs free energy, AG, to the changes in Ksp as given in Equation 3. It also allows for the other two thermodynamic variables to be estimated. In this experiment you will obtain the thermodynamic values AG, AH, and AS, associated with the solubility of KNO3 One final note: Adding moderately large amounts of solids to moderately small amounts of water has a large effect on the final volume of the solution. When saturated solutions are prepared the volume of the resulting solution must be determined experimentally. Use The Excel Worksheet to do the calculations. 1. Using equation 1, calculate the K for each temperature, and 2. Using equation 2, calculate AG for each temperature. The variation of K with temperature is such that if a plot of In K (on the y axis) vs. 1/T is made, the result is a straight line with the slope -AH/R. 3. Using Excel construct a graph of In K vs 1/T and measure the slope of the line, and determine the value of AH for the reaction. At this point, K and AG for each temperature 2 Thermodynamics Mass of KNO3 20 g Moles of KNO3 0.1978 moles Total Volume Temperature Temperature (mL) °C K Molarity (Molarity)2 Trial 1 25.0 69.9 343.0 7.9 62.6 Trial 2 29.0 58.4 331.6 6.8 46.5 Trial 3 33.0 49.1 322.2 6.0 35.9 Trial 4 38.0 40.6 313.8 5.2 27.1 Trial 5 43.0 33.5 306.6 4.6 21.2 In Ksp 1/K AG Trial 1 4.1 0.00292 -12 Trial 2 3.8 0.00302 -11 Trial 3 3.6 0.00310 -10 Trial 4 3.3 0.00319 -9 Trial 5 3.1 0.00326 -8 Slope -14380 In Ksp vs 1/T AH (kJ/mole) 119.6 kJ/mole 4.5 4.0 y=-14380x + 48.044 R² = 0.9334 Intercept 48.0 3.5 AS (J/K Mole) 399 J/K mole 3.0 2.5 2.0 1.5. 1.0 0.5 0.0 0.00285 0.00290 0.00295 0.00300 0.00305 0.00310 0.00315 0.00320 0.00325 0.00330