Molar Mass of a Solid

Experiment: Molar Mass of a Solid Abstract: The purposes of this experiment were to observe and measure the effect of a solute on the freezing point of a solvent and to determine the molar mass of the unknown nonvolatile nonelectrolyte solute labeled “Nematoad”. The colligative property of freezing point depression was the theory at work behind what was observed in the experiment trials. The unknown molar mass was calculated to be 166.278 g/mol. The freezing point of the solvent was lowered by the addition of the nonvolatile solute to the Cyclohexane solvent. The purpose of the lab was to calculate the effect of adding a nonvolatile, nonelectrolyte solute into a solvent had on that solvent’s freezing point. Also, to then calculate based on the equations for freezing point depression and molality the unknown solute Nematoad’s molar mass. The primary device utilized was a thermometer to measure the dependent variable temperature in degrees Celsius (℃ ). In the first part of the experiment, a sample of a pure solvent Cyclohexane measured in a test tube was placed in an ice-water bath and the temperature inside the test tube was taken every 15 seconds for two minutes and 15 seconds, a note made at the time the first signs of freezing appeared in the Cyclohexane solvent. The time at which freezing began represents the normal freezing point of the pure solvent, which served as a basis of comparison for later trials. In part B an unknown solute was added to the Cyclohexane in order to form a solution, which then assumes physical properties dependent on the amount of solute added. These properties are known as colligative properties, and in the case of this experiment, explain why the addition of the unknown solute in theory should lower the temperature at which the solution freezes—in comparison to the pure solvent. The degree of change Colligative properties are responsible for depends on the number of solute particles that have dissolved. The formula for calculating the change in freezing point (∆Tf) is; ∆Tf equals the freezing point constant (which depends on the solvent and was given as the value Kf = 20.0 ℃ ∙kg/mol) multiplied by the molality of the solution. After calculating the change in freezing point by taking the difference of the pure solvent’s freezing point and the unknown solution’s freezing point, the equation could be solved for molality and thus, the molar mass of the unknown was calculated. The hypothesis of the experiment was that if increasing amounts of an unknown solute was added to a sample of Cyclohexane and placed in an ice-water bath, then the freezing point of the solution will not change no matter how much solute was added. Materials and Methods Please refer to experiment 14 in the Laboratory Manual for Principles of General Chemistry by J.A. Beran on page 189. Results: Data Table one: Freezing Point of Cyclohexane Mass of beaker, test tube (g) 128.11 Freezing point, from cooling curve (℃ ) 6.0 Table one shows the data found from part A of the experiment using a sample of pure Cyclohexane solvent. Table two: Freezing Point of Cyclohexane + Unknown Solute Name of unknown solute Nematoad Mass of beaker, test tube, cyclohexane (g) 137.06 Mass of Cyclohexane (g) 8.95 Trial one Tared mass of solute (g) Freezing point, from cooling curve (℃ ) Trial two Trial three 0.140 0.200 0.140 2.0 1.0 2.0 Table two illustrates the different quantities of the unknown solute Nematoad added to the mass of the Cyclohexane in each of the performed trials. It also shows the temperature at which each sample began freezing in all three trials. Table three: Temperature Depression of Samples From Parts A and B A. Cyclohexane B. Cyclohexane and Unknown Solute Time (sec) Temp ℃ Trial one Trial two Trial three 0 21 Time (sec) Temp ℃ Time (sec) Temp ℃ Time (sec) 15 15 15 4.0 0 22 0 Temp ℃ 16 30 10 30 4.0 15 14 15 8.0 45 9.0 45 3.0 30 9.0 30 9.0 60 7.0 60 3.0 45 5.0 45 9.0 75 6.0 75 2.0 60 3.0 60 2.0 90 6.0 90 2.0 75 2.0 75 1.0 105 5.0 105 2.0 90 1.0 90 0.0 120 5.0 120 2.0 105 1.0 105 -0.50 135 4.0 135 1.0 120 1.0 120 -1.0 Table three shows the temperature decrease of the pure solvent Cyclohexane in part A and Cyclohexane plus unknown solute Nematoad in part B as a function of time. Temperatures were recorded at 15 second increments and the point at which freezing began was noted. Table four: Calculations Trial one Trial two Trial three 20.0 Kf for Cyclohexane (℃ ∙kg/mol) Freezing point change ∆Tf (℃ ) 4.0 5.0 4.0 Mass of Cyclohexane in solution (kg) 0.00895 0.00895 0.00895 Moles of solute (mol) 0.00179 0.00223 0.00179 Mass of solute in solution (g) 0.14 0.34 0.48 Molar mass of solute (g/mol) 78.212 152.46 268.15 Average molar mass of solute (g/mol) 166.278 Relative standard deviation of molar mass (%RSD) 57.56 Table four describes the results of the experiment based on the data produced and the equations used to generate results. The molar mass of unknown solute Nematoad was determined as well as the temperature depression change of the solution as a result of the added solute. Table five: Calculations (formulas) Trial one Kf for Cyclohexane (℃ ∙kg/mol) Freezing point change ∆Tf (℃ ) =H9-H10 Trial two 20.0 =H9-I10 Trial three =H9-J10 Mass of Cyclohexane in solution (kg) =H12*I12 =H12*I12 =H12*I12 Moles of solute (mol) =H13*I13 =H14*I13 =H13*I13 Mass of solute in solution (g) 0.14 =H15+I15 =H16+I16 Molar mass of solute (g/mol) 78.212 152.46 268.15 Average molar mass of solute (g/mol) =AVERAGE(C20,D20,E20) Relative standard deviation of molar mass (%RSD) =STDEV(C20,D20,E20) Table five shows the excel formulas utilized in determining the values of the above calculations. The information in this table is identical to that of table four, only this table shows how the value was calculated. Temperature ( ℃ ) Figure one: Freezing Point Depression in Parts A and B 25.0 23.0 21.0 19.0 17.0 15.0 13.0 11.0 9.0 7.0 5.0 3.0 1.0 -1.0 0 -3.0 Pure Solvent Trial 2 Solution Trial 3 Solution 15 30 45 60 75 90 105 120 Time (seconds) Figure one illustrates the cooling curves of the pure solvent cyclohexane (from part A) as well as all three trials of the solutions (from part B) containing the unknown solute Nematoad. The lines represent the temperature decrease over the period of time recorded. Calculations: 1. Freezing point of pure solvent – freezing point of solution (solvent + unknown solute) = Freezing Point Change = 6.0 ℃ – 2.0 ℃ = 4.0℃ 135 2. Mass of Cyclohexane (g) * 1 (kg) / 1000 (g) = Mass of Cyclohexane (kg = 8.95 g * 1 kg / 1000 g = 0.00895 kg Cyclohexane 3. ∆Tf = molality * Kf = Molality = .20 = 4 / 20 4. Moles of solute = molality (mol/kg) * Mass of Cyclohexane (kg) = 0.20 * 0.00895 = 0.00179 5. Mass of solute in solution = mass of solute added in trial one (g) + mass of solute added in trial two (g) + mass of solute added in trial three (g) = 0.14 + 0.20 + 0.14 = 0.48 6. Molar mass of the solute = mass of the solute in solution / moles of the solute = 0.14 (g) / 0.00179 = 78.21 7. Average molar mass of solute = molar mass from trial 1 + molar mass from trial 2 + molar mass from trial 3 / 3 = 78.212 + 152.46 + 268.15 / 3 = 166.278 8. Standard deviation of molar mass = = √(78.212- 166.278)2 + (152.46 – 166.278)2 + (268.15-166.278)2 / 2 = 95.719 9. Relative standard deviation = standard deviation / average mean * 100 = 95.719 / 166.278 * 100 = 57.56. Discussion The purpose of the experiment was to calculate the molar mass of an unknown solute though the information produced from the freezing point depression of the solution. The second was to observe and measure the effect of a solute on the freezing point of a solvent, which was done through the process of plotting the temperature changes in the experiment and comparing the line graphs of parts A and B. In part A of the experiment, the cooling curve of the sample of cyclohexane--a pure solvent—was plotted through the careful recording of the temperature of the solvent every 15 seconds for 2 minutes and 15 seconds. Just before recording began, the solvent was measured (see Table 1) and then placed into an ice-water bath with a thermometer in order to measure the change in temperature. The point at which the solvent showed signs of freezing was recorded as the freezing point of the pure solvent, and utilized as a comparison standard for the trials that took place in Part B. The freezing point of the pure solvent was found to be 6.0℃ because that was the temperature when the first evidence of frozen solvent was detected. This data was important in part B for the comparison of freezing points between pure solvent and the solution containing unknown Nematoad. In part B, three trials were done using increasing amounts of the unknown solute added to cyclohexane, each recording the temperature change of solution every 15 seconds over the same period of time. The point at which freezing began was noted for each trial and then used to calculate the freezing point change (∆Tf) between the pure solvent and the solution. This value illustrates the colligative property of freezing point depression which occurs when a solution contains a solute (in this case, Nematoad) and therefore requires a lower temperature than usual to initiate freezing. In figure one the lines on the graph represent the dropping temperatures of both the pure solvent from part A and the trials in part B with the solution containing Nematoad; it is clear from the graph that all three trials of the solution had lower reported temperatures than that of the pure solvent, confirming the theory that the addition of a solute does lower the freezing point of a solvent. The freezing points (see tables 4 and 5) of the solution in trials one, two, and three were 2℃ , 1℃ , and ℃ 2 , meaning at this temperature the solution of hexane and unknown solute began freezing. These values are lower than the freezing point of the pure solvent, and by calculating the difference between the freezing point of pure solvent and the freezing point of the solutions the change in temperature was determined. Thus, it was confirmed that the effect the addition of a solute had on the solvent was it brought the freezing point down for the solution. As for the second purpose of the experiment, calculating the unknown Nematoad’s molar mass, this was done through the equation relating freezing point change to molality then solving for the moles of solute by rearranging the equation for molality. Since the equation for change in freezing point is: ∆Tf =molality * freezing point constant, once the change in temperature was found and the freezing point constant was given (see table 4) the equation can be solved for molality. Then, given that in the experiment a measured amount of cyclohexane solvent is being mixed with a measured amount of Nematoad solute, the molality is equal to the moles of solute divided by kilograms of solvent, the moles of solute was calculated by multiplying the molality by the amount of cyclohexane solvent (in kg). From the equation for freezing point depression the molality of solution was calculated to be 0.20 mol/kg. This value was determined by the difference between freezing points of pure solvent and solution multiplied by the freezing point constant for cyclohexane, 20.0 ℃ ∙kg/mol. Then, by multiplying the amount of solvent in solution (8.95 g of cyclohaxane) by the molality calculated, the amount of moles of unknown solute was determined. Finally, dividing the amount of solute added (see table 4) by the moles of solute calculated, the molar mass of unknown solute Nematoad was found. This calculation was done because the units for molar mass are in grams per mole, and the amount of solute added was measured to be 0.14, 0.20, and 0.14 grams for each trial. The average for the three trials was the molar mass of Nematoad was found to be 166.278 grams per mole. Some factors that may have affected the accuracy of the data was that the LoggerPro equipment was not working so in it’s place a thermometer was used. Also, the time the cyclohexane solvent was left out of the ice-water bath to warm was not recorded, which could alter the amount of time it required to reach the freezing point. Post Lab Questions 4. Part B.2 Some of the cyclohexane solvent vaporized during the temperature versus time measurement. Will this loss of cyclohexane result in the freezing point of the solution being recorded as too high, too low, or unaffected? Explain. The temperature of the solution will be unaffected because the solvent is being lost not the solute. The amount of the unknown solute is what effects the freezing point temperature. 5. Part B 2. The solute dissociates slightly in the solvent. How will the slight dissociation affect the reported molar mass of the solute--too high, too low, or unaffected? Explain. The slight dissociation will cause the molar mass of the unknown solute to be reported as too high due to the solute not being completely dissolved in the solvent. 6. Part B.3. Figure 14.3. The temperature versus time data plot (Figure 14.3) shows no change in temperature at the freezing point for a pure solvent; however, the temperature at the freezing point for a solution steadily decreases until the solution has completely solidified. Account for this decreasing temperature. As the time the test tube has been submerged into the ice-water bath increases, the more the solution freezes leaving a higher concentration of solute in the solvent. This lowers the freezing point for the solution even more, resulting in the steadily decreasing temperature of the solution.