Experiment 4 - Salicylic Acid Temperature Dependent Solubility

# Experiment 4 - Salicylic Acid Temperature Dependent Solubility

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Chem 257 Experiment 4 Thermodynamic Parameters from the Variation of an Equilibrium Constant with Temperature: The Solubility of Salicylic Acid This experiment will be done in pairs. A fundamental equation of thermodynamics chemistry is the Gibbs Equation : G = G° + RT ln Q (i) aA + bB ↔ cC +dD Q = [a C ] c [a D ] d /[a A ] a [a B ] b Q = [C] c [D] d /[A] a [B] b where the a refers to activity of a species and [C], [D] etc are the actual concentrations (activities) at some point in the reaction. The reaction quotient Q equals the activity of products raised to the power of their stoichiometric coefficients divided by the activities of the reactants raised to their stoichiometric coefficients, In this experiment, the activities are replaced by their concentrations since these solutions are dilute. Activities of solids are 1.000. A process is spontaneous , ie. goes toward more products, if the Gibbs Free Energy is negative. The process is at equilibrium, if G is zero. If G is positive, the reaction actually proceeds toward reactants, ie. backwards. At equilibrium, the reaction quotient, Q, has changed to the value of the equilibrium constant, K, and G is zero, resulting in equation (ii) G° = - RT ln K (ii) The change in Gibbs Free Energy in the standard state is related to temperature, enthalpy and entropy by equation (iii) G° = H° - T (iii) Equations (ii) and (iii) can be combined to give (iv): ln K = - H°/RT + S°/R (iv) Equation (iv) describes the variation of the equilibrium constant as a function of temperature. Given a number of measurements of K at different temperatures, and assuming H° and S° are independent of temperature, the thermodynamic parameter H°/R can be obtained from the slope respectively of a plot of ln K vs . T -1 and S° from the intercept. T is Kelvin and T=273.15 + t( 0 C). Note that this is the natural logarithm, not log base 10. In this way H° for a chemical reaction can be determined without calorimetric measurements. The assumption that H° and S° are temperature invariant is true if C p = 0, i.e. there is no change in heat capacity, C p , between reactants and products or if the temperature range is somewhat limited. Although it is seldom exactly zero, C p is often small. Experimentally one would expect to see non-linear plots of ln K vs . T -1 if C p 0. In this experiment we will measure the equilibrium constant of a solubility equilibrium, that of salicylic acid (I) in water, as a function of temperature and fit the results to equation (iv) in order to determine H° and S° for the dissolution process. At a temperature, T, I (s) dissolves until it reaches its equilibrium concentration.

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In order to determine K s at a particular temperature we need only measure the concentration of I in solution in equilibrium with the solid, i.e. the solubility of I since the pure solid is the standard state with an activity equal to 1.000.
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