Experiment 14 Molar Mass of a Solid

Experiment 14: Molar Mass of a Solid On-Campus Lab General Chemistry II (DO3) 4 Feb 2022 Hypothesis The molar mass of a nonvolatile, nonelectrolyte solute can be determined using freezing-point change of a solvent. Abstract The purpose of this experiment was to measure the change in the freezing point of a solvent as a result of the number of solute particles dissolved in the solvent. This difference in freezing point and the freezing point constant of the solvent is then used to calculate the moles of an unknown solute in the solution. The freezing point constant of cyclohexane is noted to be 20 ˚C*kg/mol. The freezing point change obtained from the cooling curves in trial one and trail two were 1.75˚C and 4.35 ˚C, respectively. The moles of solute measured 7.498E-04 in trial one and 1.864E-03 in trial two. When combined with the measured mass of the solute, the molar mass of 1 the solute and thus the identity of the solute can be determined as well. The nonvolatile solute was calculated to have a molar mass of approximately 144 g/mol in trial one and 155 g/mol in trial two. Considering an 18.25% error in measured and accepted molar mass value of the nonvolatile solute (Naphthalene), this data does not optimally demonstrate the hypothesis that the molar mass of a nonvolatile, nonelectrolyte solute can be accurately determined using freezing-point change of a solvent. Introduction Pure liquids, such as cyclohexane used in this experiment have colligative properties, or physical properties that are changed in relation to the number of solute particles dissolved in them. Due to the Naphthalene particles’ lowering the vapor pressure of the cyclohexane, a freezing point depression is also observed. The molality of the solute in solution is multiplied by the freezing point constant to calculate the freezing-point change: ∆𝑇𝑓 = |𝑇𝑓,𝑠𝑜𝑙𝑣𝑒𝑛𝑡 − 𝑇𝑓,𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 | = 𝑘𝑓 𝑚 The 𝑘𝑓 value of the solvent was given and not determined mathematically. The molality is defined as: 𝑚𝑜𝑙𝑎𝑙𝑖𝑡𝑦, 𝑚 = 𝑚𝑎𝑠𝑠 𝑚𝑜𝑙 𝑠𝑜𝑙𝑢𝑡𝑒 (𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠) = 𝑘𝑔 𝑠𝑜𝑙𝑣𝑒𝑛𝑡 𝑘𝑔 𝑠𝑜𝑙𝑣𝑒𝑛𝑡 During the experiment, the solvent and solution freezing points are found from the cooling curve graphed. The freezing points are deduced once the cooling curve reaches a plateau, in the case of the solvent and at the intersection of lines drawn through the data points above and below the freezing point. (Beran, p. 191) After converting the mass of solvent to the necessary units, the 2 moles of solute were calculated against a freezing point constant of 20 degrees Celsius per kilogram per mole. Applying freezing-point change equation variation, the moles of solute were determined to be 7.498E-04 in trial one and 1.864E-03 in trial two. The molar mass of the nonvolatile solute can then be determined and subsequently this information may be used to identify the substance. Utilizing the number of moles and the mass of the solute added, the molar mass of the solute was determined to be approximately 144.0 g/mol in trial one and 155.1 g/mol in trial two. Between both trials, the sample solute was found to have an average molar mass of 149.6 g/mol. Materials and Methods Please refer to Experiment 14 on pages 189-194 of Laboratory Manual for Principles of General Chemistry by J. A. Beran (10th Ed.). Deviations from the published procedure are: 1. Two trials were conducted, rather than three. Data Molar Mass of a Solid Experiment A. Freezing Point of Cyclohexane (Solvent) Trial 1 101.8 6.05 1 Mass of beaker, test tube (g ) 2 Freezing point, from cooling curve (g ) 3 Instructor's approval of apparatus B. Freezing Poitn of Cyclohexane plus Unknown Solute 1 2 3 4 Mass of beaker, test tube, cyclohexane (g) Mass of cyclohexane (g) Tared mass of added solute (g) Freezing point, from cooling curve °C 0.108 4.3 110.369 8.569 0.289 1.7 Calculations 1 2 3 4 5 6 7 8 9 kf for cyclohexane (°C * kg/mol) Freezing-point change, Delta-Tƒ (°C) Mass of cyclohexane in solution (kg) Moles of solute, total (mol) Mass of solute in solution, total (g) Molar mass of solute (g/mol) Average molar mass of solute (g/mol) Standard deviation of molar mass Relative standard deviation of molar mass(%RSD ) 1.75 0.008569 7.498E-04 0.108 144.0 3 20.000 4.35 0.008569 1.864E-03 0.289 155.1 149.6 7.79 5.21% Table 1: Molar Mass of a Solid Trial 1 101.8 6.05 110.369 8.569 0.108 4.3 20.0 1.75 8.57E-03 7.498E-04 0.108 144.0 149.6 7.79 5.21% Mass of beaker, test tube (g) Freezing point, from cooling curve (˚C) Mass of beaker, test tube, cyclohexane(g) Mass of cyclohexane (g) Tared mass of added solute (g) Freezing point, from cooling curve (˚C) 𝑘𝑓 for cyclohexane (˚C*kg/mol) Freezing-point change, △Tf (˚C) Mass of cyclohexane in solution (g) Moles of solute, total (mol) Mass of solute in solution, total (g) Molar mass of solute in solution, total (g/mol) Average molar mass of solute (g/mol) Standard deviation of molar mass Relative standard deviation of molar mass (%RSD) Table 1: Molar Mass of a Solid (Formulas) Trial 1 101.8 6.05 110.369 =D12-D6 0.108 4.3 20.0 =D7-C15 =D13*10^-3 =(C20*C21)/D19 =C14 =C23/C22 =(C24+D24)/2 =STDEV(C24,D24) =D26/D25 Mass of beaker, test tube (g) Freezing point, from cooling curve (˚C) Mass of beaker, test tube, cyclohexane(g) Mass of cyclohexane (g) Tared mass of added solute (g) Freezing point, from cooling curve (˚C) 𝑘𝑓 for cyclohexane (˚C*kg/mol) Freezing-point change, △Tf (˚C) Mass of cyclohexane in solution (g) Moles of solute, total (mol) Mass of solute in solution, total (g) Molar mass of solute in solution, total (g/mol) Average molar mass of solute (g/mol) Standard deviation of molar mass Relative standard deviation of molar mass (%RSD) 4 Figure 1: Cooling Curve for Cyclohexane and Cyclohexane-Naphthalene Solution Temperrature (℃) 20 15 10 5 1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235 0 Time (sec) Trial 2 Solvent only Trial 1 Calculations B.2. Mass of cyclohexane (g) (Mass of beaker, test tube, cyclohexane)- (mass of beaker, test tube) 110.369-101.8= 8.569 g C.2. Freezing-point change, ∆𝑻𝒇 (˚C) Cyclohexane freezing point (from cooling curve)- Solution freezing point (from cooling curve) 6.05-4.3= 1.75 ˚C C.3. Mass of cyclohexane in solution (kg) 8.569*10^3= .008569 kg 5 C.4. Moles of solute, total (mol) (6.05 − 4.3) = (20 ˚C ∗ 𝑚𝑜𝑙 kg ) = 7.489𝐸 − 04 mol . 008569𝑘𝑔 C.6. Molar Mass of solute (g/mol) Molar mass of solute (g/mol) = Mass of solute (g)/ Moles of solute (mol) 0.108/7.489𝐸 − 04 ≈ 144.0 𝑔/𝑚𝑜𝑙 C.7. Average Molar Mass of solute (g/mol) Average molar mass (g/mol) = [Trial 1 molar mass + trial 2 molar mass] / 2 (144.0+155.1)/2=149.6 g/mol C.8. Standard deviation of molar mass (g) √(149.6(144.0 − 149.6)2 ∗ (155.1 − 149.6)2 )/2=7.79 C.9. Relative Standard Deviation (%) %𝑅𝑆𝐷 = (𝑠/𝑥  )100 (149.6*7.79) =5.21% Results and Discussion 6 In this experiment, approximately ten milliliters of cyclohexane were placed in a test tube. After subtracting the combined mass of the beaker and test tube (101.8 g) from the combined mass of the beaker, test tube and cyclohexane (110.369 g) this yields the mass of the cyclohexane (8.569 g). The test tube of cyclohexane was then placed in an ice-water bath prepared using 400-mL beaker of ice-water slurry placed inside a 600-mL beaker, separated by a paper towel. A thermometer probe was then used to record the temperature versus time data was then plotted to obtain the cooling curve for cyclohexane. From the cooling curve graph the freezing point of cyclohexane was determined to be 6.05˚C. Approximately .108 grams of an unknown nonvolatile solute was then transferred into the flask containing the cyclohexane and returned to the icewater bath to measure the freezing-point temperature of the solution. The freezing- point change was determined to be 4.3˚C in trial one. After adding approximately .181 additional grams of the unknown solute and repeating the thermometer probing process, a new freezing point was measured at 1.7˚C in trial 2. This data is then plotted against the cyclohexane-only freezing point data to determine the freezing-point change of 1.75˚C in trial one. and 4.35˚C in trial 2. The moles of solute were determined using the freezing-point change equation. The calculated ∆𝑻𝒇 (˚C) multiplied by kilograms of cyclohexane in the solution were then divided by the freezing point constant of 20 degrees Celsius per kilogram per mole to yield the moles present in the solution. The moles of solute were determined to be 7.498E-04 in trial one and 1.864E-03 in trial two. The molar mass of the nonvolatile solute can then be determined and subsequently this information may be used to identify the substance. Utilizing the number of moles and the mass of the solute added, the molar mass of the solute was determined to be approximately 144.0 g/mol in trial one and 155.1 g/mol in trial two. Between both trials, the sample solute was found to have an average molar mass of 149.6 g/mol. 7 The actual molar mass of the nonvolatile solute, Naphthalene, was stated to be approximately 126 g/mol. Given this information the percent error of the experiment data, particularly the calculated molar mass was 18.25 percent. This is a relatively high percent error considering a standard deviation of 7.79 and percent relative standard deviation of 5.21 percent. Conclusions The purpose of this experiment was to determine the molar mass of a nonvolatile, nonelectrolyte solute using freezing-point change of a solvent. Findings were a molar mass of 144.0 g/mol in trial 1 and 155.1 g/mol in trial two. Considering percent relative standard deviation of 5.21 percent between measured and accepted molar mass value of the nonvolatile solute (Naphthalene), this data may demonstrate the hypothesis that the molar mass of a nonvolatile, nonelectrolyte solute can be accurately determined using freezing-point change of a solvent. Some possible errors in these measurements could be caused by misreading of the cooling curve graph. Post-Lab Questions 1. Part A.3 Some of the cyclohexane solvent vaporized during the temperature versus time measurement. Will this loss of cyclohexane result in its freezing point being recorded as too high, too low, or unaffected? The freezing point will be too high as it is based on the molarity of the solution, which in this case would be calculated as too high. 8 2. Part A.3 The digital thermometer is mis-calibrated by +0.15˚C over its entire range. If the same thermometer is used in Part B.2, will the reported moles of solute in the solution be too high, too low or unaffected? The reported moles will be unaffected as the equation to determine them used the temperature difference which will still be correct if the same thermometer is used for both parts. 3. Part B.1. Some of the solid solute adheres to the side of the test tube during the freezing point determination of the solution in Part B.2. As a result of the oversight will the reported molar mass of the solute be too high, too low, or unaffected? Too low, as some of the solute will not be included in the solution. 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? Too high, due to the loss of some of the solvent. 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? Too high due to increase in van hoff factor. 6. Part B.3. Figure 14.3 The temperature versus time data plot shows no change in temperature at the freezing point for a pure solvent; however, the temperature at 9 the freezing point for a solution steadily decreases until the solution has completely solidified. Account for this decreasing temperature. The solute present in the solvent will cause a lowering of the freezing point. 7. Part C.1 Interpretation of the data plots consistently shows that the freezing points of three solutions are too high. As a result of this misreading the data, will the reported molar mass be too high, too low, or unaffected? Freezing point and molar mass are inversely proportional. This will cause the molar mass to be too low. 10