Molar Mass Determination by Freezing Point Depression
Molar Mass Determination by Freezing Point Depression
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P R O P
344
m o d u l a r · l a b o r a t o r y · p r o g r a m · i n · c h e m i s t r y
program editor: H. A. Neidig
Molar Mass Determination by Freezing Point Depression
in t-Butyl Alcohol
prepared by M. Gillette and S. R. Johnson, Indiana University at Kokomo
Background Information
I. The Concept of Physical States or Phases
Pure molecular substances can exist in three physi- cal 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 differ- ent 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 vi- cinity. The physical state of a substance depends upon two factors:
- Intermolecular interactions resulting from hydro- gen-bonding, dipole-dipole interactions, and/or Lon- don forces characteristic of the particular
- The amount of kinetic energy possessed by the molecules of the substance, which depends on
II. The Melting Point of a Substance
In the solid phase, the molecules of a substance have insufficient kinetic energy to overcome intermolecu- lar attractions. Therefore, the substance has a rigid structure. When we heat a solid substance, the ki- netic energy of the molecules increases. They begin to move with respect to one another. As we continue to heat the substance, the molecular motion be- comes 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 interac- tions are weaker than in the solid phase.
III. The Freezing Point of a Substance
We can reverse the melting process at any point sim- ply by removing heat from a substance. For example,
Copyright © 1988 by Chemical Education Resources, Inc., P.O. Box 357, 220 S. Railroad, Palmyra, Pennsylvania 17078 No part of this laboratory program may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photo- copying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Printed in the United States of America
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as a pure liquid cools, the molecules lose kinetic en- ergy. At some temperature they have insufficient en- ergy 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 melt- ing and freezing points of a substance should theo- retically be the same. Because freezing and melting depend only on temperature and the particular intermolecular interactions characteristic of a sub- stance, 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 dis- solves is the solvent. The presence of a solute af- fects the freezing behavior of the solvent. This is be- cause 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 low- ered, by the presence of solute particles. The identity
of the solute is not as important as is the number of
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,
DTf is calculated. By rearranging Equation 2 and solv- ing for mc, we obtain Equation 3.
solute particles in solution.
If the solute and solvent react, new substances are formed, resulting in a complex system that is not
m c =
DTf , ° C
K f , ° C molal–1
(Eq. 3)
as easily interpreted as the one we are discussing. For our purposes, we will assume no reaction be-
Because Equations 1 and 3 are related to each other
by the common mc, we write Equation 4.
tween solute and solvent.
The extent of freezing point depression caused by the presence of solute particles is different for each
DTf
K f
= number of moles of solute mass of solvent
(Eq. 4)
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).
The number of moles of solute can also be found from Equation 5.
number of moles = mass of solute, g
m c =
number of moles of solute
(Eq. 1)
of solute
molar mass of solute, g mole –1
(Eq. 5)
mass of solvent, kg
The proportionality constant relating the change in
freezing point (DTf) to the molality of solute particles (mc) is the molal freezing point depression con-
Because Equations 1 and 5 each have the term “num- ber of moles of solute,” we substitute Equation 5 into Equation 1 and obtain Equation 6.
(mass of solute, g)
stant, Kf. The mathematical expression for this rela-
m c = æmolar mass,ö æ
mass of ö
(Eq. 6)
tionship is given in Equation 2.
DTf = Tf – Tf¢ = (Kf)(mc) (Eq. 2) where Tf is the freezing point of the pure solvent and
Tf¢ is the freezing point of the solution. The molal
freezing point depression constants for several sol- vents are listed in Table 1.
èô g mole –1 ôø ôèsolvent, kgôø
Then we combine Equations 3 and 6, as a result of the common mc, and obtain Equation 7. Now our experi- mental data provide the necessary information to de- termine the molar mass of an unknown compound, using Equation 7.
gram molar
(mass solute, g) æôK f , °C kg solventöô
Thus, Na+ and Cl– ions have identical effects on the freezing point of an NaCI solution. Some other
mass of solute =
g mole –1
ôæ mass of
öô(DTf , ° C)
colligative properties are boiling point elevation, va-
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èsolvent, kgø
(Eq. 7)
por pressure lowering, and osmotic pressure.
Consider the following example. Suppose you dis- solved 30.9 g of an unknown solute in 500 g of cyclo- hexane 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 ex- perimental data into Equation 7, we have
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
gram molar mass of unknown
= (20.2 ° C kg mol–1 ) (30.9 g)
(8.17 ° C) (5.00 ´ 10 –1 kg)
materials, contact with liquid t-butyl alcohol or its va-
pors should be avoided since both are irritating and flammable. You will plot these data and prepare a
= 153 g mol–1
VI. Colligative Properties
The proper interpretation of results obtained using the above method of molar mass determination de- pends upon a clear understanding of the principles in- volved. The depression of the freezing point of a sol- vent 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 ´ 1023 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 ´ 10–3 molal aqueous solution of NaCI. What occurs when NaCI is dissolved in water? Equation 8 describes this process.
graph similar to the one shown in Figure 1.
NaCl(s) ¾¾H2¾O¾®
Na+(aq) + Cl–(aq) (Eq. 8)
Figure 1 Cooling curve for a liquid solvent
The molar mass of NaCI is 58.5 g mol–1. When we dis- solve 0.0585 g NaCI in 1.00 kg H2O, we find that we have prepared a solution that acts like a 2.00 ´ 10–3 molal solution in terms of its freezing point behavior, even though it is actually a 1.00 ´ 10–3 molal solution in terms of the number of moles of NaCI present. This difference occurs because 1 mol of NaCI dissociates into 2 mol of ions in water.
The necessity of considering the number of sol- ute particles and not simply the molality of the solute is emphasized by the variable mc 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 sol- ute particles present, regardless of their identity.
In Figure 1, you can see that the temperature de- creases 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 freez- ing 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 por- tions of the curve and the latter is extrapolated to find the freezing point, Tf.
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 con- stant of t-butyl alcohol, using Equation 9.
K = DTf
f m c
(Eq. 9)
thermometers, you must use the same thermometer to measure the cooling temperatures of t-butyl alco- hol, of your solution of water and t-butyl alcohol, and
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–tempera- ture data. You can measure the volume of liquid un- knowns with a pipet or buret and then calculate the mass of the sample, using the density of the unknown and Equation 10.
of your solution of t-butyl alcohol and unknown.
Procedure
mass of
æ volume of ö æ
density of ö
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unknown, g = ôèunknown, mLôø èôunknown, g mL–1ôø
(Eq. 10)
From these data, you will determine the molar mass of your unknown.
Figure 2 shows a typical cooling curve for a solu- tion. Care must be taken in analyzing this type of curve. Notice that the portion of the curve represent- ing the liquid-solid mixture has a negative slope un- like 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 solu- tion. A best straight line is drawn through the data points. This line is extended to the left until it inter- sects the portion of the curve representing the cool- ing of the liquid. The temperature corresponding to this point of intersection is the freezing point of the so- lution, Tf.
Figure 2 Cooling curve for a typical solution
The determination of molar mass hinges on the
accuracy with which you determine DTf. Because of the variation in temperature measured with different
I. Determining the Freezing Temperature of t-Butyl Alcohol
Weigh a large test tube in a 250-mL Erlenmeyer flask to the nearest 0.1 g. Record this mass on Data Sheet
- Measure 25 mL ±1 mL of t-butyl alcohol in a gradu- ated 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 ther- mometer 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 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
Figure 3 Freezing point determination apparatus
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–tem- perature 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 this same sample for Part II.
II. Determining Kf of t-Butyl Alcohol
Stir the t-butyl alcohol and water mixture until the water has completely dissolved and the solution ap- pears 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 imme- diately 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 solu- tion. 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 instruc- tor. 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 thou- sandth 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.
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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.
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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 al- cohol used in Part I.
Carefully stir the t-butyl alcohol and unknown un- til 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. Po- sition 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 near- est 0.2 °C every 15 s, beginning immediately after you placed the test tube in the ice-water bath. End the de- termination 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 so- lution. Raise the temperature to 25 °C.
Do another determination, using the same un- known solution.
Discard the unknown solution following the direc- tions of your laboratory instructor.
Calculations
(Do the following calculations for each determination and record the results on Data Sheet 4.)
I. Determining the Freezing Temperature of t-Butyl Alcohol
- For each set of time–temperature data obtained during the freezing point measurements of t-butyl al- cohol, prepare a cooling curve by plotting tempera- ture (ordinate) versus time (abscissa).
- Determine the freezing point of t-butyl alcohol for each
- Determine the mean freezing point of t-butyl
II. Determining Kf of t-Butyl Alcohol
- For each set of time–temperature data obtained during the cooling of the t-butyl alcohol and water so- lution, prepare a cooling curve by plotting tem- perature (ordinate) versus time (abscissa).
- Determine the freezing point of the
- Calculate the freezing point depression caused by the addition of water, using Equation
- Determine the mass, in grams, of water added (d = 00 g mL–1).
- From the mass of water added and the gram molar mass of water, determine the number of moles of water
- Calculate the molality of water in the solution, using Equation
- Determine Kf of t-butyl alcohol, using Equation
- Calculate the mean Kf of t-butyl
III. Determining the Gram Molar Mass of the Unknown
- Prepare a cooling curve by plotting temperature (ordinate) versus time (abscissa).
- Determine the freezing point of the
- Calculate the depression in freezing point caused by the addition of your unknown, using Equation
- If your unknown is a liquid, calculate its mass, us- ing Equation
- Calculate the molality of your unknown solution, using Equation
- Calculate the gram molar mass of your unknown, using Equation
- Calculate the mean gram molar mass of your
Post-Laboratory Questions
(Use the spaces provided for the answers and additional paper if necessary.)
- Obtain from your laboratory instructor the gram molar mass of your unknown. Calculate the percent error for the gram molar mass of your
- A student, following the procedure described in this module, used water as the solvent and encoun- tered some interesting Comment on the ef- fect, if any, each of the following situations could have had on the experimental results.
- The unknown, a white powder, failed to dis- solve in the
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- The student returned to the laboratory in- structor for a different solid unknown. This unknown dissolved, but bubbles were seen escaping from the
- A student determined the Kf of t-butyl alcohol us- ing tap water instead of distilled or deionized water. Describe the problems that might have been encoun- How would these problems affect the magni- tude of Kf ?
- As a research chemist, you are interested in studying the extent and types of interactions in aque- ous salt solutions. As part of this study, you weigh three samples of NaCI and dissolve each in 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 NaCI dis- solved in 1.000 kg H2O.
(3) As the student was setting up the apparatus to measure the freezing point of the unknown solu- tion, the thermometer assembly rolled off the labora- tory bench, and the thermometer broke. The student obtained a new thermometer and performed the ex- periment as instructed.
name section date
Data Sheet 1
freezing point of
t-butyl alcohol
determination
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first |
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second |
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temperature of water bath, ° C |
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determination |
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determination |
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first second |
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first second |
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time, |
temp, ° C temp, ° C |
time, |
temp, ° C temp, ° C |
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sec |
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sec |
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0 |
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255 |
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15 |
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270 |
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30 |
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285 |
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45 |
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300 |
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60 |
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315 |
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75 |
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330 |
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90 |
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345 |
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105 |
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360 |
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120 |
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375 |
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135 |
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390 |
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150 |
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405 |
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165 |
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420 |
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180 |
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535 |
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195 |
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450 |
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210 |
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465 |
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225 |
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480 |
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240 |
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Data Sheet 2
freezing point
of solution of t-butyl alcohol and water
determination
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first |
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second |
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temperature of water bath, ° C |
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determination |
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determination |
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first second |
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first second |
|
time, |
temp, ° C temp, ° C |
time, |
temp, ° C temp, ° C |
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sec |
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sec |
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0 |
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255 |
|
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15 |
|
270 |
|
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30 |
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285 |
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45 |
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300 |
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60 |
|
315 |
|
|
75 |
|
330 |
|
|
90 |
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345 |
|
|
105 |
|
360 |
|
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120 |
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375 |
|
|
135 |
|
390 |
|
|
150 |
|
405 |
|
|
165 |
|
420 |
|
|
180 |
|
535 |
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195 |
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450 |
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210 |
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465 |
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225 |
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480 |
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240 |
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Data Sheet 3
freezing point
of solution of unknown and t-butyl alcohol
determination
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first |
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second |
|
|
temperature of water bath, ° C |
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|
|
|
determination |
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determination |
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first second |
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first second |
|
time, |
temp, ° C temp, ° C |
time, |
temp, ° C temp, ° C |
|
sec |
|
sec |
|
|
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 |
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240 |
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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
freezing point of t-butyl alcohol, ° C
determination
first second
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, ° C
freezing point depression, ° C
number of mol of water added
molality of water in solution, mc
Kf of t-butyl alcohol, ° C molal–1
mean Kf 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 liquid unknown number
mass of solid unknown and
weighing paper, g
volume of liquid unknown, mL
mass of weighing paper, g
density of liquid unknown, g mL–1
mass of solid unknown, g mass of liquid unknown, g
freezing point of unknown solution, ° C
determination
first second
freezing point depression, ° C
molality of unknown solution, mc
gram molar mass of unknown, g mol–1
mean gram molar mass of unknown, g mol–1
Pre-Laboratory Assignment
- Read MISC 327, Graphical Representation of Data, in this series or another authoritative source that describes the principles of
- 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
- Using the graph paper on the next page, draw the cooling curve for
- Determine the freezing point of nitroben- zene from the
answer
- On the same graph draw the cooling curve for the unknown solution composed of 0 g of nitrobenzene and 5.00 mL of the liquid unknown.
- Determine the freezing point of the un- known
- The freezing point depression of a solution of nitrobenzene and a nonionic unknown was used to determine the molar mass of the Time–temperature data for the cooling of nitroben- zene and for the cooling of a solution containing 50.0 g of nitrobenzene and 5.00 mL of a nonionic liquid un- known, 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 +
DTf.
answer
- Determine the freezing point depression,
answer
- Calculate the molality of the solution, mc.
answer
- Calculate the gram molar mass of the
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unknown
unknown.
answer
- Briefly explain why it is absolutely critical that the test tube containing the sample of nitrobenzene be absolutely dry when determining the freezing tem- perature of
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For assignments that need to be submitted to Lopes Write, please be sure you have received your report and Similarity Index (SI) percentage BEFORE you do a “final submit” to me. Once you have received your report, please review it. This report will show you grammatical, punctuation, and spelling errors that can easily be fixed. Take the extra few minutes to review instead of getting counted off for these mistakes. Review your similarities. Did you forget to cite something? Did you not paraphrase well enough? Is your paper made up of someone else’s thoughts more than your own? Visit the Writing Center in the Student Success Center, under the Resources tab in Loud-cloud for tips on improving your paper and SI score.
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The university’s policy on late assignments is a 10% penalty PER DAY LATE. This also applies to late DQ replies. Please communicate with me if you anticipate having to submit an assignment late. I am happy to be flexible, with advance notice. We may be able to work out an extension based on extenuating circumstances. If you do not communicate with me before submitting an assignment late, the GCU late policy will be in effect. I do not accept assignments that are two or more weeks late unless we have worked out an extension. As per policy, no assignments are accepted after the last day of class. Any assignment submitted after midnight on the last day of class will not be accepted for grading.
- Communication
Communication is so very important. There are multiple ways to communicate with me: Questions to Instructor Forum: This is a great place to ask course content or assignment questions. If you have a question, there is a good chance one of your peers does as well. This is a public forum for the class. Individual Forum: This is a private forum to ask me questions or send me messages. This will be checked at least once every 24 hours.
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