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Thermodynamics of the Solubility of Borax Purpose: To determine the thermodynamic quantities Δ H ° and Δ S ° for the solvation reaction of borax in water, by measuring the solubility product constant over the temperature range from 55 to15 ° C. Na 2 B 4 O 7 10H 2 O( s ) qwe 2Na + ( aq ) + B 4 O 5 (OH) 4 2 - ( aq ) + 8H 2 O( l ) Introduction: As you have seen or will see in Thermochemistry (Chapter 18) the free energy change in a reaction, Δ G, is related to the equilibrium constant for the reaction by the equation Δ G ° = - RTln(K) (Chang Eqn. 18.14) Looking at this equation we see that if the reaction is thermodynamically favored, Δ G ° < 0, and we would expect K to be large, 1 K >> . If K is much greater than one, we will observe the reaction proceeding primarily to products. The free energy expresses the net effect of two thermodynamic quantities: the enthalpy, H, and the entropy, S. Under constant temperature conditions, this is expressed by the equation Δ G ° = Δ H ° - T Δ S ° (Chang Eqn. 18.10) The two physical contributions to the free energy are the heat absorbed or released during a reaction, Δ H, and the molecular disorder created during a reaction, Δ S. Because the above two equations are expressions of Δ G ° , the right hand side of each equation must be equivalent. - RTln(K) = Δ H ° - T Δ S ° Rearranging this expression yields R Δ S T 1 R Δ H - ln(K) o o + = . As long as we can determine the equilibrium constant at several temperatures, this equation is well-suited for determining Δ H ° and Δ S ° by linear regression. b x m y + = + = R Δ S T 1 R Δ H - ln(K) o o The above expression is valid only if Δ H ° and Δ S ° are not temperature dependent quantities. Over the small temperature range that we shall investigate, this assumption is valid for borax.
The method of determining the equilibrium constant in this experiment is worth discussing. The equilibrium for the reaction to be studied is actually a solubility product constant, K sp .

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