Chemistry 1 6 3

The thermodynamics of the solubility of borax Purpose: To determine the thermodynamic quant it ies ΔH° and ΔS° for the solvat ion react ion of borax in water by measuring the solubility product constant over a temperature range. Introduction: Much of the derivat ions that follow may be found in the Thermo-dynamics chapter in the text . The standard free energy change of a react ion ΔG° is related to the equilibrium constant for the react ion by the equat ion ΔG° = – RT ln K. The react ion is thermodynamically favored if ΔG° < 0 ; this means that K > 1 . If K is significant ly larger than 1 , the react ion should proceed primarily to products. The free energy expresses the net effects of two thermodynamic quant it ies: the enthalpy H and the entropy S. Under constant temperature condit ions, the quant it ies are related by the equat ion ΔG° = ΔH° – TΔS°. ΔH° indicates that amount of heat absorbed or released during in the react ion and ΔS° represents the amount of molecular disorder created or removed during the react ion. Equat ing the two equat ions in the previous paragraphs, you get ΔH° – TΔS°= – RT ln K, which is rearranged to:

Let y = ln K and x = (1 /T) and the equat ion has the form of the linear relat ionship y = mx + b, where m is the slope of the line, given by – (ΔH°/R), and b is the y-intercept , given by (ΔS°/R). Thus, if the quant it ies ln K and 1 /T could be plot ted, you could measure the slope and intercept of a best-fit line you could draw through those data points and determine ΔH° and ΔS° for this react ion. The equat ion on the previous page is valid only if ΔH° and ΔS° are not temperature-dependent quant it ies. Over the small temperature range that you are invest igat ing, the assumpt ion is reasonably valid for borax.

So what is K, for this react ion? Note that the borax solvat ion react ion equilibrium constant is the solubility product Ksp for borax or Ksp = [Na+] 2 [B4O5(OH) 4

2–] . By the stoichiometry of the react ion [Na+] = 2 [B4O5(OH) 42–] , so Ksp

= 4 [B4O5(OH) 42–] 3.

The amount of B4O5(OH) 4

2– in solut ion is determined by t it rat ion with HCl solut ion using an indicator to mark the equivalence point . Skills: • Developing a temperature-series set of solubility measurements • Use of an indicator for qualitat ive determinat ion of the acidity/alkalinity of a solut ion • Use of a graph to determine a best -fit line • Use of a best -fit line equat ion to determine thermodynamic quant it ies Chemical equat ion: Na2B4O7•1 0 H2O (s) ↔ 2 Na+ (aq) + B4O5(OH) 4

2– (aq) + 8 H2O ( l) Chemicals needed:

• Borax (make sure it is not “cut” with other c leaning ingredients) • A precisely-known concentrat ion hydrochloric acid solut ion (about 0 .2 M) • A concentrated solut ion of sodium hydroxide (over 1 M) • Indicator solut ions (phenophthalein)

Equipment needed: • five c lean 2 5 0 mL beakers • one c lean 1 5 0 mL beaker • one c lean 1 0 0 mL beaker • thermometer • buret Procedure 1 . Pick an appropriate indicator: thymol blue (pKin = 1 .5 ) , methyl red (pKin = 5 .1 ) or phenolphthalein (pKin = 9 .4 ) . The pI of borax is about 4 .9 . After choosing the indicator, obtain about 1 0 mL of the HCl solut ion and add two drops of the indicator to that ; st ir. Then add drops of concentrated NaOH solut ion, st irring all the while, unt il the color change occurs. Note the color change (before and after) in your notebook for future reference.

2 . Obtain the five 2 5 0 mL beakers and label them #1 through #5 . 3 . In a 1 0 0 mL beaker, prepare a saturated solut ion of borax by adding roughly

7 g of borax to 5 0 mL of dist illed water. Obtain a hot plate and set the heat set t ing at about midpoint ; place the borax solut ion on the hot plate and st ir. You may use the thermometer as a st irring rod, but be gent le. Alongside that beaker, heat another beaker with about 1 0 0 mL of dist illed water.

4 . Take temperature readings constant ly while st irring; make sure the bulb of the thermometer is not touching the sides or bot tom of the beaker. When the temperature of the solut ion reaches 5 7 or 5 8 °C, remove the beaker from the hot plate. Heating over 60°C will decompose (not dissolve) the borax. Keep monitoring the temperature of the solut ion. 5. With the beaker sitting on the countertop, stir the solution until it has cooled to about

55°C. Let the beaker stand with the thermometer in it until the solid has settled out of solution. While the solution is settling, rinse a 10 mL graduated cylinder with the hot water from the hot plate. (If you pour the hot borax solution into a cold graduated cylinder, the borax will instantly precipitate against the cold glass. When the solid has settled out, read and record the temperature to the nearest 0.1°C, then immediately decant exactly 5.0 mL into the warmed 10 mL graduated cylinder. Then transfer the contents of the cylinder into beaker #1. Rinse the cylinder with hot water several times and pour these rinses into the beaker as well.

6 . Now allow the solut ion to cool to about 4 5 °C; make sure you are st irring the

solut ion frequent ly. When the solut ion is about 4 5 °C, let the solut ion stand (as above) unt il the solid set t les out and follow the sample collect ion process in step 5 for t ransferring 5 .0 mL of the solut ion to beaker #2 . Remember to record the temperature to the nearest 0 .1 °C. Do not forget to rinse the graduated cylinder and add the rinses to the beaker.

7 . Repeat this procedure near 3 5 °C, 2 5 °C and 1 5 °C (the last couple of

temperatures may require an ice water bath — be careful not to let the beaker t ip over in the bath) , t ransferring 5 .0 mL aliquots to beakers #3 , #4 and #5 , respect ively.

8 . Obtain about 1 0 0 mL of hydrochloric acid (note it s precise concentrat ion) in

a 1 5 0 mL beaker. Rinse and fill the buret with the acid.

9 . Add enough dist illed water to beakers #1 through #5 so they each have about 1 0 0 mL total ( the marking on the beaker is suffic ient precision) . Add five drops of your chosen indicator to each beaker. St ir the solut ions in the beakers to make sure all of the borax is redissolved; you may need to warm beakers #1 and #2 to redissolve the borax.

1 0 . Tit rate each beaker with hydrochloric acid from the buret . For beakers #1

and #2 , make sure the buret contains a full 5 0 mL of hydrochloric acid. Clearly, the amount of acid needed for t it rat ion should decrease from beaker #1 to beaker #5 . For this reason, you may wish to t it rate beaker #5 , then #4 , etc .

Waste disposal: Place all waste in the “aqueous waste” container in the hood. Data section: Remarks about the choice of indicator, given what t it rat ion was to be done later Remarks about the indicator’s color change — both endpoint colors as well as any t ransit ional color Mass of borax init ially added Table of beaker number, volume of borax solut ion collected and temperature of

collect ion Observat ions of how cloudy the collected solut ion was or how much material

crystallized on the inside of the graduated cylinder before the rinses Concentrat ion of hydrochloric acid solut ion (and units) Table of beaker number and endpoint (equivalence point ) volume Analysis 1 . Determine the concentrat ion of the dissolved B4O5(OH) 4

2– in each sample t it rated; show a complete calculat ion for beaker #1 . 2. Calculate Ksp for each borax solution.

3 . Prepare a graph of your results, plot t ing the two quant it ies x and y (as defined in the introduct ion) . Using EXCEL, determine the equation of the best-fit line through your data points. 4 . From the parameters of the best -fit line equat ion, calculate ΔH° and ΔS° for this react ion. Make sure to keep t rack of units, especially for R, so that the units of ΔH° and ΔS° work out sensibly. 5 . Obtain the rest of the c lass’s ΔH° and ΔS° values and calculate the mean and standard deviat ion of each for the c lass. Determine if there are any out liers, then recalculate the mean and standard deviat ion, if necessary. Pay at tent ion to the units and sig figs. Conclusion The literature values for enthalpy and entropy of the dissolut ion of borax in water are 1 1 0 kJ /mol and 3 8 0 J /mol K, respect ively. Determine the percent error in your experimentally determined values and the c lass’s mean values. Comment on the confidence you have about this procedure to determine ΔH° and ΔS° for this react ion accurately. Abstract First sentence: What are your results? (The process is called borax solvat ion) Second sentence: Enlarge to include c lass results (report mean and std. dev. in proper format with units) ; comment about your results compared to the c lass results Third sentence: In comparison to the literature values, how well did the procedure work? Appropriate to add comments about possible error sources, if significant