Freezing Point Depression Lab Manual - PDF

Here is the converted document in markdown format: # PROP 0344 ## Molar Mass Determination by Freezing Point Depression in t-Butyl Alcohol Prepared by M. Gillette and S. R. Johnson, Indiana University Kokomo ### PURPOSE OF THE EXPERIMENT Determine the freezing point of t-butyl alcohol, the molal f...

Here is the converted document in markdown format: # PROP 0344 ## Molar Mass Determination by Freezing Point Depression in t-Butyl Alcohol Prepared by M. Gillette and S. R. Johnson, Indiana University Kokomo ### PURPOSE OF THE EXPERIMENT Determine the freezing point of t-butyl alcohol, the molal freezing point constant for t-butyl alcohol, and the molar mass of an unknown. ## BACKGROUND INFORMATION ### I. The Concept of Physical States or Phases Pure molecular substances can exist in three physical states, often referred to as phases: solid, liquid, or gas. The extent to which the individual molecules are free to move independently of each other is different in each of these states. This freedom results from the extent to which one molecule has influence on, or is influenced by, other molecules in its immediate vicinity. The physical state of a substance depends upon two factors: 1. Intermolecular interactions resulting from hydrogen-bonding, dipole-dipole interactions, and/or London forces characteristic of the particular substance. 2. The amount of kinetic energy possessed by the molecules of the substance, which depends on temperature. ### II. The Melting Point of a Substance In the solid phase, the molecules of a substance have insufficient kinetic energy to overcome intermolecular attractions. Therefore, the substance has a rigid structure. When we heat a solid substance, the kinetic energy of the molecules increases. They begin to move with respect to one another. As we continue to heat the substance, the molecular motion becomes sufficient to cause the outer parts of the rigid structure to begin to break down, and we obtain a mixture of the solid and liquid. We call the breakdown process melting and the temperature at which the transition occurs, the melting point. Application of additional heat converts the entire sample from solid to liquid. In the liquid phase, intermolecular interactions are weaker than in the solid phase. ### III. The Freezing Point of a Substance We can reverse the melting process at any point simply by removing heat from a substance. For example, as a pure liquid cools, the molecules lose kinetic energy. At some temperature they have insufficient energy to overcome intermolecular forces, and the solid phase begins to form. We call the change from liquid to solid **freezing** and the temperature at which the transition occurs, the **freezing point**. The melting and freezing points of a substance should theoretically be the same. Because freezing and melting depend only on temperature and the particular intermolecular interactions characteristic of a substance, the freezing (or melting) point is a physical constant of the substance. ### IV. The Freezing Point of a Solution When we dissolve a nonvolatile solute in a liquid, we obtain a solution. The liquid in which the solute dissolves is the solvent. The presence of a solute affects the freezing behavior of the solvent. This is because the individual solute particles interfere with the intermolecular interactions that would establish the freezing behavior of the solvent if it were pure. Hence, the freezing point of the solvent is depressed, or lowered, by the presence of solute particles. The identity of the solute is not as important as is the number of solute particles in solution. If the solute and solvent react, new substances are formed, resulting in a complex system that is not as easily interpreted as the one we are discussing. For our purposes, we will assume no reaction between solute and solvent. The extent of freezing point depression caused by the presence of solute particles is different for each solvent but is always dependent on the molality of the solute. Molality is the number of moles of solute in one kilogram of solvent (Equation 1). $m_c = \frac{\text{number of moles of solute}}{\text{mass of solvent, kg}}$ (Eq. 1) The proportionality constant relating the change in freezing point ($\Delta T_f$) to the molality of solute particles ($m_c$) is the **molal freezing point depression constant**, $K_f$. The mathematical expression for this relationship is given in Equation 2. $\Delta T_f = T_f - T_f' = (K_f)(m_c)$ (Eq. 2) where $T_f$ is the freezing point of the pure solvent , and $T_f'$ is the freezing point of the solution. The molal freezing point depression constants for several solvents are listed in Table 1. ### V. Using Freezing Point Measurements Freezing point measurements are easy to make. We can use the relationship expressed in Equation 1 to determine the molar mass of an unknown. First, we determine the freezing point of a carefully weighed amount of solvent. Next, we add a carefully weighed amount of unknown solute to the solvent and repeat the freezing point determination. From these data, $\Delta T_f$ is calculated. By rearranging Equation 2 and solving for $m_c$, we obtain Equation 3. $m_c = \frac{\Delta T_f, \text{°C}}{K_f, \text{°C molal}^{-1}}$ (Eq. 3) ### Table 1 Some molal freezing point depression constants | Solvent | Freezing Point, °C | $K_f$, °C kg mol-1 | |---------------|--------------------|--------------------| | Water | 0.00 | 1.86 | | Acetic Acid | 16.6 | 3.90 | | Benzene | 5.50 | 5.10 | | Camphor | 179.8 | 40.0 | | Cyclohexanol | 25 | 39.3 | | Cyclohexane | 6.5 | 20.2 | | Nitrobenzene | 5.25 | 6.87 | Because Equation 1 and 3 are related to each other by the common $m_c$, we write Equation 4. $\frac{\Delta T_f}{K_f} = \frac{\text{number of moles of solute}}{\text{mass of solvent}}$ (Eq. 4) The number of moles of solute can also be found from Equation 5. $\text{number of moles of solute} = \frac{\text{mass of solute, g}}{\text{molar mass of solute, g mol}^{-1}}$ (Eq. 5) Because Equations 1 and 5 each have the term "number of moles of solute," we substitute Equation 5 into Equation 1 and obtain Equation 6. $m_c = \frac{\text{(mass of solute, g)}}{\text{(molar mass, g mol}^{-1}\text{)(mass of solvent, kg)}}$ (Eq. 6) Then we combine Equation 3 and 6, as a result of the common $m_c$, and obtain Equation 7. Now our experimental data provide the necessary information to determine the molar mass of an unknown compound, using Equation 7. $\text{gram molar mass of solute g mole}^{-1} = \frac{\text{(mass solute, g) }(K_f, \text{°C kg solvent per mole solute)}}{\text{(mass of solvent, kg) }(\Delta T_f, \text{°C})}$ (Eq. 7) Consider the following example. Suppose you dissolved 30.9 g of an unknown solute in 500 g of cyclohexane and found that the freezing point of the mixture was 8.17 °C lower than that of pure cyclohexane. What is the molar mass of the unknown? Substituting the experimental data into Equation 7, we have $\text{gram molar mass of unknown} = \frac{\text{(20.2 °C kg mol}^{-1}\text{)(30.9 g)}}{\text{(8.17 °C) (5.00 × 10}^{-1}\text{ kg)}} = 153 \text{ g mol}^{-1}$ ### VI. Colligative Properties The proper interpretation of results obtained using the above method of molar mass determination depends upon a clear understanding of the principles involved. The depression of the freezing point of a solvent depends on the number of solute particles in the solution which is indicated by the molality of particles in the solution. Often, we think of molecules as single particles, so we assume that 1 gram-molar mass of solute is equivalent to 1 mol or $6.022 \times 10^{23}$ particles of solute. This is not always the case, however. Some substances dissociate or associate in a solvent. In such cases, 1 mol of solute does not produce 1 mol of dissolved particles. Consider a $1.00 \times 10^{-3}$ molal aqueous solution of NaCl. What occurs when NaCl is dissolved in water? Equation 8 describes this process. $NaCl(s) \xrightarrow{H_2O} Na^+(aq) + Cl^-(aq)$ (Eq. 8) The molar mass of NaCl is 58.5 g mol-1. When we dissolve 0.0585 g NaCl in 1.00 kg H2O, we find that we have prepared a solution that acts like a $2.00 \times 10^{-3}$ molal solution in terms of its freezing point behavior, even though it is actually a $1.00 \times 10^{-3}$ molal solution in terms of the number of moles of NaCl present. This difference occurs because 1 mol of NaCl dissociates into 2 mol of ions in water. The necessity of considering the number of solute particles and not simply the molality of the solute is emphasized by the variable $m_c$ in Equation 1. The subscript c refers to the word colligative. **Colligative properties**, such as freezing point, are properties of solutions that are affected by the number of solute particles present, regardless of their identity. Thus, $Na^+$ and $Cl^-$ ions have identical effects on the freezing point of an NaCl solution. Some other colligative properties are boiling point elevation, vapor pressure lowering, and osmotic pressure. ### VII. Determining the Molar Mass of the Unknown in this Experiment In this experiment, you will cool a known mass of t-butyl alcohol and measure its temperature as it changes with time. Note that as with most organic materials, contact with liquid t-butyl alcohol or its vapors should be avoided since both are irritating and flammable. You will plot these data and prepare a graph similar to the one shown in Figure 1. In Figure 1, you can see that the temperature decreases as the liquid cools and then remains almost constant once freezing begins and both the liquid and solid phases are present. Frequently, there is a dip (see Figure 1) in the temperature curve at the freezing point. The dip is due to supercooling and should be ignored when determining the freezing point. Straight lines are fit to the liquid and liquid-solid portions of the curve and the latter is extrapolated to find the freezing point, $T_f'$. You will then add a known mass of water to the sample of t-butyl alcohol and collect temperature-time data for the cooling of this solution. From these data, you will determine the molal freezing point constant of t-butyl alcohol, using Equation 9. $K_f=\frac{\Delta T_f}{m_c}$(Eq. 9) #### The following is a description of Figure 1: A graph of temperature against Time, showing the supercooling effect. A downward line illustrates **temperature**, there is a **freezing point**, **super-cooling** has occured and there liquid has turned into the liquid and a solid. #### The following is a description of Figure 2: Finally, you will add a known mass or volume of your assigned unknown to a sample of t-butyl alcohol and cool the solution while collecting time-temperature data. You can measure the volume of liquid unknowns with a pipet or buret and then calculate the mass of the sample, using the density of the unknown and Equation 10. $mass \ of \ unkown, g = (volume \ of \ unknown, mL)(density \ of \ unkown, g \ mL^{-1}) \ (Eq. 10)$ #### Description of Figure 2: A graph of temperature against Time, illustrating liquid turned to a liquid and solid From these data, you will determine the molar mass of your unknown. Figure 2 shows a typical cooling curve for a solution. Care must be taken in analyzing this type of curve. Notice that the portion of the curve representing the liquid-solid mixture has a negative slope unlike the case of the pure solvent shown in Figure 1. This difference occurs because, as the solvent freezes from the solution, the molality of the solute in the remaining solution increases. This increase causes a decrease in the freezing point of the solution. A best straight line is drawn through the data points. This line is extended to the left until it intersects the portion of the curve representing the cooling of the liquid. The temperature corresponding to this point of intersection is the freezing point of the solution, $T_f'$. The determination of molar mass hinges on the accuracy with which you determine $\Delta T_f$. Because of the variation in temperature measured with different thermometers, you must use the same thermometer to measure the cooling temperatures of t-butyl alcohol, of your solution of water and t-butyl alcohol, and of your solution of t-butyl alcohol and unknown. ## PROCEDURE **Chemical Alert** t-butyl alcohol—flammable and irritant **Caution** Wear departmentally approved eye protection while doing this experiment. ### I. Determining the Freezing Temperature of t-Butyl Alcohol **Caution** Avoid inhaling fumes of t-butyl alcohol and ingesting the substance. Prevent eye and skin contact. **Caution** Use only an absolutely dry test tube for this experiment! Weigh a large test tube in a 250-mL Erlenmeyer flask to the nearest 0.1 g. Record this mass on Data Sheet 4. Measure 25 mL ± 1 mL of t-butyl alcohol in a graduated cylinder and transfer the alcohol to the test tube. Measure the mass of the alcohol, test tube, and flask. Record this mass on Data Sheet 4. Assemble the apparatus as shown in Figure 3. Place the thermometer so that the end of the thermometer bulb is at the midpoint of the t-butyl alcohol and so that the thermometer does not touch the side of the test tube. Adjust the stirrer so that it can be moved from the bottom of the test tube to almost the top of the liquid. Fill the 600-mL beaker two-thirds full of cold tap water. If the temperature of the tap water is greater than 20 °C add several small pieces #### Description of Figure 3: Diagram of apparatus: A beaker contains an ice-water bath. Inside the bath is a solution/solvent mix. The water bath thermometer is inside the solution/solvent. The glass is stoppered with a rubber stopper. A stirrer is inside the solution/solvent mix. of ice to the water to cool it below 20°C. Measure the temperature of the water and record the temperature on Data Sheet 1. Immerse the test tube assembly in the cold water. Position the test tube assembly in the ice-water so that the tube is in the center of the beaker. Make certain the level of the alcohol in the test tube is 5 mm below the water level in the beaker. Stir the alcohol continuously and steadily during the determination Record on Data Sheet 1 time-temperature data to the nearest 0.1 or 0.2°C every 15 s, beginning immediately after you place the test tube in the ice water bath. End the determination 3 min after the alcohol has become slushy. Remove the assembly from the water bath. Use your hands to warm the test tube and melt the alcohol. Raise the alcohol temperature to 25°C. Do another determination using the same 𝑡-butyl alcohol sample. Use the same sample for Part II. Note: Your laboratory instructor will inform you whether or not the class will do Part II of this experiment. If not, information will be given as to how to proceed to Part III. ### II. Determining Kf of t-Butyl Alcohol Add several pieces of ice to your water bath. Using a pipet, carefully add 0.20 mL (0.20 g) of distilled or deionized water to the sample of t-butyl alcohol used in Part I. Stir the 𝑡-butyl alcohol and water mixture until the water has completely dissolved and the solution appears homogeneous. Immerse the assembly in the ice-water bath. Make certain the liquid level in the test tube is 5 mm below the water level in the beaker. Constantly, but not vigorously, stir the solution and the ice-water bath. Record on Data Sheet 2 time-temperature data to the nearest 0.1 or 0.2 °C every 15 s, beginning immediately after you place the test tube in the ice-water bath. End the determination 3 min after the solution has become slushy. Remove the assembly from the water bath. Use your hands to warm the test tube and melt the solution. Raise the alcohol temperature to 25 °C. Do another determination using the same solution. Discard your t-butyl alcohol solution following the directions of your laboratory instructor. ### III. Determining the Gram Molar Mass of the Unknown Add several pieces of ice to your ice-water bath. Obtain an unknown from your laboratory instructor. Record the code number of your unknown on Data Sheet 4. Weigh a large test tube in a 250-mL Erlenmeyer flask to the nearest 0.1 g. Record this mass on Data Sheet 4. Measure 25 mL ± 1 mL of t-butyl alcohol in a graduated cylinder and transfer the alcohol to the test tube. Measure the mass of the alcohol, test tube, and flask. Record this mass on Data Sheet 4. Determine the mass of a sheet of weighing paper on an analytical balance to the nearest one thousandth of a gram (0.001 g). Weigh on this paper 2.0 g ± 0.1 g of the solid unknown to the nearest one thousandth of a gram (0.001 g). Record this mass on Data Sheet 4. Carefully transfer the solid to the test tube containing t-butyl alcohol. If your unknown is a liquid, pipet 2.0 mL of it into the test tube containing the alcohol. Record on Data Sheet 4 the volume and the density of the liquid unknown. NOTE: Carefully stir the t-butyl alcohol solution making certain the loop of the stirrer remains under surface of the liquid at all times. Carefully stir the 𝑡-butyl alcohol and unknown until the unknown compound has completely dissolved and the solution appears to be homogeneous. Check the temperature of your ice water bath. If the temperature is not between 14 °C and 16 °C add several pieces of ice to the bath. Immerse the assembly in the ice-water bath. Position the test tube as you did in Part II. Make certain the level of the solution in the test tube is 5 mm below the level of the ice-water in the beaker. Constantly stir the unknown solution and the ice-water bath. Record on Data Sheet 3 time-temperature data to the nearest 0.2 °C every 15 s, beginning immediately after you placed the test tube in the ice-water bath. End the determination 3 min after the solution has become slushy. Remove the assembly from the ice-water bath. Use your hands to warm the test tube and melt the solution. Raise the temperature to 25°C. Do another determination, using the same unknown solution. Discard the unknown solution following the directions of your laboratory instructor. **Caution** Wash your hands thoroughly with soap or detergent before leaving the laboratory! # Calulations (Do the following calculations for each determination and record the results on Data Sheet 4.) ## I. Determining the Freezing Temperature of 𝑡-Butyl Alcohol 1. For each set of time-temperature data obtained during the freezing point measurements of 𝑡-butyl alcohol, prepare a cooling curve by plotting temperature (ordinate) versus time (abscissa). 2. Determine the freezing point of 𝑡-butyl alcohol for each determination. 3. Determine the mean freezing point of 𝑡-butyl alcohol. ## II. Determining 𝐾f of 𝑡-Butyl Alcohol 1. For each set of time-temperature data obtained during the cooling of the 𝑡-butyl alcohol and water solution, prepare a cooling curve by plotting temperature (ordinate) versus time (abscissa). 2. Determine the freezing point of the solution. 3. Calculate the freezing point depression caused by the addition of water, using Equation 2. 4. Determine the mass, in grams, of water added (𝑑 = 1.00 g mL-1). 5. From the mass of water added and the gram molar mass of water, determine the number of moles of water added. 6. Calculate the molality of water in the solution, using Equation 6. 7. Determine 𝐾f of 𝑡-butyl alcohol, using Equation 9. 8. Calculate the mean 𝐾f of 𝑡-butyl alcohol. ## III. Determining the Gram Molar Mass of the Unknown 1. Prepare a cooling curve by plotting temperature (ordinate) versus time (abscissa). 2. Determine the freezing point of the mixture. 3. Calculate the depression in freezing point caused by the addition of your unknown, using Equation 2. 4. If your unknown is a liquid, calculate its mass, using Equation 10. 5. Calculate the molality of your unknown solution, using Equation 3. 6. Calculate the gram molar mass of your unknown, using Equation 7. 7. Calculate the mean gram molar mass of your unknown. ## Post-Laboratory Questions (Use the spaces provided for the answers and additional paper if necessary.) 1. Obtain from your laboratory instructor the gram molar mass of your unknown. Calculate the percent error for the gram molar mass of your unknown. 2. A student, following the procedure described in this module, used water as the solvent and encountered some interesting problems. Comment on the effect, if any, each of the following situations could have had on the experimental results. (1) The unknown, a white powder, failed to dissolve in the solvent. (2) The student returned to the laboratory instructor for a different solid unknown. This unknown dissolved, but bubbles were seen escaping from the solution almost immediately after the addition of the solid. (3) As the student was setting up the apparatus to measure the freezing point of the unknown solution, the thermometer assembly rolled off the laboratory bench, and the thermometer broke. The student obtained a new thermometer and performed the experiment as instructed. 3. A student determined the 𝐾f of 𝑡-butyl alcohol using tap water instead of distilled or deionized water. Describe the problems that might have been encountered. How would these problems affect the magnitude of 𝐾f? 4. As a research chemist, you are interested in studying the extent and types of interactions in aqueous salt solutions. As part of this study, you weigh three samples of NaCl and dissolve each in 1.000 kg H2O. You then measure the freezing temperature of each solution and compare these temperatures to the freezing point of water. The data you collect are tabulated below. Explain the observed results. Predict and briefly explain the result you would expect for a solution made up of 29.22 g NaCl dissolved in 1.000 kg H2O. | g NaCl per 1.000 kg H2O | ΔTf, °C | | :----------------------- | :------- | | 5.845 | 0.348 | | 0.585 | 0.0360 | | 0.293 | 0.0182 | ## Data Sheet 1 freezing point of 𝑡-butyl alcohol | | Determination | | :--------------------------------- | :--------------------------------- | | Temperature of water bath, °C | first ________ second ___________ | | Time, sec | Determination | | Time, sec | Determination | | | | First ________ | Second ________ | | First ________ | Second ________ | | :-------- | :------------ | :------------ | :-------- | :------------ | :------------ | | 0 | | |255 | | | |15 | | |270 | | | |30 | | |285 | | | |45 | | |300 | | | |60 | | |315 | | | |75 | | |330 | | | |90 | | |345 | | | |105 | | |360 | | | |120 | | |375 | | | |135 | | |390 | | | |150 | | |405 | | | |165 | | |420 | | | |180 | | |535 | | |195 | | || 450 | | | |210 | | || 465 | | | |225 | ｜ || 480 | | | |240 | | || | | | ## Data Sheet 2 freezing point of solution of 𝑡-butyl alcohol and water Temperature of water bath, °C | Determination | first___________second___________| | Time, sec | Determination | | Time, sec | Determination | | | | First ________ | Second ________ | | First ________ | Second ________ | | :-------- | :------------ | :------------ | :-------- | :------------ | :------------ | | 0 | | |255 | | | |15 | | |270 | | | |30 | | |285 | | | |45 | | |300 | | | |60 | | |315 | | | |75 | | |330 | | | |90 | | |345 | | | |105 | | |360 | | | |120 | | |375 | | | |135 | | |390 | | | |150 | | |405 | | | |165 | | |420 | | | |180 | | |535 | | |195 | | || 450 | | | |210 | | || 465 | | | |225 | ｜ || 480 | | | |240 | | || | | | ## Data Sheet 3 freezing point of solution of unknown and 𝑡-butyl alcohol Temperature of water bath, °C | Determination | first___________second___________| | Time, sec | Determination | | Time, sec | Determination | | | | First ________ | Second ________ | | First ________ | Second ________ | | :-------- | :------------ | :------------ | :-------- | :------------ | :------------ | | 0 | | |255 | | | |15 | | |270 | | | |30 | | |285 | | | |45 | | |300 | | | |60 | | |315 | | | |75 | | |330 | | | |90 | | |345 | | | |105 | | |360 | | | |120 | | |375 | | | |135 | | |390 | | | |150 | | |405 | | | |165 | | |420 | | | |180 | | |535 | | |195 | | || 450 | | | |210 | | || 465 | | | |225 | ｜ || 480 | | | |240 | | || | | | #### Data Sheet 4 |I. Determining the Freezing Temperature of t-Butyl Alcohol| |---| |mass of 𝑡-butyl alcohol, test tube, and flask, g ______ |mass of test tube and flask, g _____ |mass of 𝑡-butyl alcohol, g _______| | |determination| |---|---| |first_______second___________| #### freezing point of 𝑡-butyl alcohol, °C_______ #### mean freezing point of 𝑡-butyl alcohol, °C_____ #### II. Determining 𝐾f of 𝑡-Butyl Alcohol| #### mass of water, g _____| #### mass of 𝑡-butyl alcohol, g _____| #### |determination #### first______ second _______| #### freezing point of water and 𝑡-butyl alcohol solution, ° _____| #### freezing point depression, °C ______| #### number of mol of water added______ #### molality of water in solution, 𝑚_C ________| #### 𝐾_f of 𝑡-butyl alcohol, °C molal^(-1) _______ #### mean 𝐾_f of 𝑡-butyl alcohol, °C molal^(-1) _______ #### III. Determining the Gram Molar Mass of the Unknown #### mass of 𝑡-butyl alcohol, test tube, and flask, g _____| #### mass of test tube and flask, g _______| #### mass of 𝑡-butyl alcohol, g ________ #### solid unknown number________volume of liquid unknown, mL ______ #### mass of solid unknown and weighing paper, g _______ #### liquid unknown number _____ #### mass of weighing paper, g ________ #### density of liquid unknown, g mL^{-1 #### mass of solid unknown, g ______|_____mass of liquid unknown, g _____ #### |determination #### first _____|____second_____| #### freezing point of unknown solution, °C ________| #### freezing point depression, °C ________| #### molality of unknown solution, 𝑚_C _______ #### gram molar mass of unknown, g mol^(-1) _______ #### mean gram molar mass of unknown, g mol^(-1) _______ ## Pre-Laboratory Assignment 1. Read MISC 327, Graphical Representation of Data, in this series or another authoritative source that describes the principles of graphing. 2. A student beginning this experiment accidentally spilled some t-butyl alcohol on his hands and on the laboratory bench. Describe any potential danger this situation might cause and state the proper method of cleaning up from the accident. 3. The freezing point depression of a solution of nitrobenzene and a nonionic unknown was used to determine the molar mass of the unknown. Time–temperature data for the cooling of nitrobenzene and for the cooling of a solution.containing 50.0 g of nitrobenzene and 5.00 mL of a nonionic liquid unknown, are given below. The density of the unknown was 0.714 g mL-1. The Kf of nitrobenzene is 6.87 °C Kg mol-1. | nitrobenzene | | nitrobenzene + unknown | | | --- | --- | --- | --- | | time, min | temp, °C | time, min | temp, °C | | 0.0 | 12.50 | 0.0 | 9.00 | | 0.5 | 10.75 | 0.5 | 8.00 | | 1.0 | 8.75 | 1.0 | 7.00 | | 1.5 | 6.50 | 1.5 | 5.00 | | 2.0 | 4.80 | 2.0 | 3.75 | | 2.5 | 4.50 | 2.5 | 3.00 | | 3.0 | 4.25 | 3.0 | 1.25 | | 4.0 | 5.50 | 4.0 | -1.25 | | 5.0 | 5.00 | 5.0 | -2.25 | | 6.0 | 5.30 | 6.0 | -2.50 | | 7.0 | 5.30 | 7.0 | -2.25 | | 8.0 | 5.30 | 8.0 | -1.80 | | 9.0 | 5.30 | 9.0 | -1.50 | | 10.0 | 5.30 | 10.0 | -1.60 | | 11.0 | 5.20 | 11.0 | -1.75 | | 12.0 | 5.20 | 12.0 | -1.80 | | 13.0 | 5.20 | 13.0 | -1.90 | | 14.0 | 5.20 | 14.0 | -2.00 | | 15.0 | 5.20 | 15.0 | -2.10 | | 16.0 | 5.20 | 16.0 | -2.20 4. (1) Using the graph paper on the next page, draw the cooling curve for nitrobenzene. (2) Determine the freezing point of nitrobenzene from the curve. (3) On the same graph draw the cooling curve for the unknown solution composed of 50.0 g of nitrobenzene and 5.00 mL of the liquid unknown. (4) Determine the freezing point of the unknown solution. (5) Determine the freezing point depression, ΔTf. (6) Calculate the molality of the solution, mc. (7) Calculate the gram molar mass of the unknown. 5. Briefly explain why it is absolutely critical that the test tube containing the sample of nitrobenzene be absolutely dry when determining the freezing temperature of nitrobenzene.