Borax, sodium tetraborate decahydrate, is an important mineral found in dry lakebeds in California. It is used to make soap and glass, and it is also used as a preservative. You can use the values of K_sp of borax at different temperatures to determine ΔH°, ΔS°, and ΔG° for the dissolution of borax:

has the form of a linear equation y = mx + b, where y is the ln Ksp and x is 1/T. The slope is equal to (-ΔH°/R) and the y-intercept is ΔS°/R, where R is the gas constant, 8.314 J /K mol.

If you measure K_sp at several different temperatures, you can plot the lnK versus 1/T (T in Kelvin), as shown here.

Knowing the values of ΔH° and ΔS° at a specific temperature allows the calculation of the change in Gibbs free energy for the reaction: ΔG° = ΔH° - T ΔS°.

The following table lists K_sp values for the dissolution of borax at several different temperatures (°C).

a. Plot a graph of lnK_sp versus 1/T (T in Kelvin) and find the best-fitting line.

b. Determine ΔH°. Is this process endothermic or exothermic?

c. Determine ΔS°.

d. Determine ΔG°.

e. Sketch a graph of lnK versus 1/T for an exothermic process.

Transcribed Image Text:

Na₂B4O5(OH)4 8 H₂O(s) (Borax) The relationship: In(Ksp) -AH° AS° + RT R 2 Na+ (aq) + B4O5(OH)42 (aq) + 8 H₂0 (1) (Borate)