Background:
There  are  a  number  of  ways  of  determining  the  molar  mass  of  a  substance.  One  of  the  simplest   involves  finding  the  change  in  the  freezing  point  of  a  solvent  when  an  unknown  substance  is   dissolved  in  it.  The  change  in  freezing  point  is  directly  proportional  to  the  molality  of  the  solution.
This  change  in  freezing  point  is  one  of  several  “colligative”  properties  of  solutions  –  properties  that   depend  only  on  the  number  of  dissolved  particles  in  solution,  and  not  on  the  type  of  particle.  Other
colligative  properties  include  changes  in  boiling  point,  vapor  pressure  and  osmotic  pressure.
Measurements  of  these  properties  can  be  used  to  find  the  molar  mass  of  solutes.
The  molality  of  a  solution,   m ,  is  defined  as  the  moles  of  solute  divided  by  the  kilograms  of  solvent:   m"=" moles"(solute) kg"(solvent)
(1)
Since  the  moles  of  solute  is  the  same  as  the  grams  of  solute  divided  by  the  molar  mass  of  the
solution  the  following  is  true:
m"=" g"(solute) kg"(solvent) × molar"mass"(solute)
The  relationship  of  molality  to  change  in  freezing  point  is:
Δ T f
=$ik f
× m
(2)
(3)
where   Δ T f
is  the  change  in  freezing  point  of  the  pure  substance  versus  the  solution,  i  is  the  van’t
Hoff  factor  for  the  solvent,  k f
is  the  freezing  point  depression  constant  for  the  solvent  and   m  is  the   molality  of  the  solution.  The  value  of  k f
must  be  determined  for  each  solvent.
Equations  2  and  3  can  be  combined  to  solve  for  the  molar  mass  of  the  solute:
MM solute
(=( ik f
× g((solute) kg((solvent) × Δ T f
(4)
The  solvent  used  in  this  experiment  is  a  nonpolar,  nonvolatile,  nonelectrolytic  solvent  with  the   common  name  butylated  hydroxytoluene.  This  compound  is  abbreviated  BHT  and  is  frequently   used  as  an  antioxidant  in  foods.  The  IUPAC  name  for  the  compound  is  2,6-­‐di-­‐tert-­‐butyl-­‐4-­‐
methylphenol.
Molar  mass  by  freezing  point  depression
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The  freezing  point  of  BHT  is  approximately  70 ° C.  If  the  freezing  points  are  determined  for  both  the   solvent  and  the  solution  using  a  thermometer  with  minor  scale  divisions  marked  every  0.1
° C,  the
freezing  points  can  be  estimated  in  the  range:   ± 0.02
° C.
Figure  1  shows  cooling  curves  obtained  for  both  a  pure  solvent  and  for  a  solution.  Note  that   supercooling  occurs  in  both  the  solvent  and  the  solution.  When  supercooling  occurs,  the   temperature  falls  below  the  freezing  point  until  the  first  crystal  forms.  The  temperature  then  rises
up  and  either  stays  at  the  freezing  point,  in  the  case  of  the  pure  substance,  or  slowly  falls  as  the   solution  freezes.  The  freezing  point  temperature  T f
of  the  solution  is  extrapolated  from  the  graph.
Figure  1
Experimental  overview:
The  purpose  of  this  experiment  is  to  determine  the  molar  mass  of  an  unknown  substance  by   measuring  the  freezing  point  depression  of  a  solution  of  the  unknown  substance  and  BHT.  First,  the   freezing  point  of  BHT  is  determined * .  In  a  second  procedure,  a  known  amount  of  cetyl  alcohol  is   added  to  a  measured  quantity  of  BHT.  The  freezing  point  depression  of  this  solution  is  found  and   the  freezing  point  depression  constant  (k f
)  is  calculated.  The  unknown  is  added  to  BHT,  the  freezing   point  of  this  solution  is  measured,  and  the  molar  mass  of  the  unknown  is  then  determined.
*Even  though  the  freezing  point  of  BHT  is  known,  it  is  necessary  to  determine  it  with  the  thermometer  that  is  used  in   the  experiment.  Thermometers  can  give  temperature  readings  that  are  slightly  different  from  true  values.  It  is   important  that  the  same  thermometer  is  used  to  determine  both  the  freezing  point  temperature  of  the  solution  and  that
of  the  solvent.
Safety  precautions:  Goggles  must  be  worn  at  all  times.  BHT  is  moderately  toxic  by  ingestion  and   inhalation  and  is  a  body  tissue  irritant.  Cetyl  alcohol  and  the  unknown  substance  are  slightly  toxic   by  ingestion  and  are  body  tissue  irritants.  Wash  hands  thoroughly  with  soap  and  water  before   leaving  the  laboratory.
Molar  mass  by  freezing  point  depression
Page  2  of  6

Procedure:
1.
Obtain  and  wear  safety  goggles.
2.
Log  into  your  computer  and  open  Logger  Pro  from  your  desktop.
3.
In  Logger  Pro,  select  File   →  Open   →  Advanced  Chemistry  With  Vernier   →  04  Freezing  Point
4.
Assemble  the  apparatus  as  diagrammed  in  Figure  2,  below.   Do  not  add  water  to  the  beaker.
Clamp  the  thermometer  using  a  rubber  stopper.   Do  not  seal  the  test  tube  with  the  stopper  –   its  only  purpose  is  to  support  the  thermometer.  In  all  likelihood,  a  stainless  steel  probe   temperature  probe  interfaced  to  your  computer  will  be  used  as  your  thermometer.  Make  a   stirrer  out  of  wire  bent  with  a  circle  at  the  bottom.  The  test  tube  is  clamped  in  the  beaker  so
that  the  solid  it  contains  will  be   below  the  level  of  the  water  in  the  beaker.  The  beaker  sits  on   a  hot  plate.
Figure  2
5.
Disassemble  the  apparatus  by  sliding  both  the  thermometer  and  stirring  wire  assembly  and   the  test  tube  clamp  off  the  ring  stand.  Weigh  and  record  the  mass  of  the  test  tube  on  an   analytical  balance.
6.
Accurately  measure  about  8  g  of  BHT  into  the  test  tube.  Record  the  combined  mass  of  the   test  tube  and  the  BHT.
7.
Clamp  the  test  tube  in  the  beaker  and  insert  the  thermometer  and  stirring  wire  assembly   into  the  test  tube  and  clamp  the  assembly.   Do  not  force  the  thermometer  into  the  solid  –   allow  it  to  sit  on  top  of  the  solid.  Add  water  to  the  beaker  so  that  the  solid  in  the  test  tube  is   well  below  the  level  of  the  water.
8.
Turn  on  the  hot  plate  and  heat  the  water  bath  to  about  90 ° C.
9.
Allow  the  BHT  in  the  test  tube  to  melt.
10.
When  the  BHT  is  completely  melted  remove  the  entire  apparatus   from  the  water  bath  beaker.  See  Figure  3,  at  right.  Confirm  that   the  thermometer  is  still  positioned  in  the  BHT.  Press  COLLECT   on  your  computer  and  continuously  stir  the  BHT  to  maintain   even  cooling.  Stirring  also  helps  prevent  supercooling.  Stir  until
BHT  solidifies.  Make  a  note  of  the  temperature  at  which  crystals   begin  to  form.
11.
Press  STOP  on  your  computer  when  all  of  the  BHT  has  solidified.
Select  Experiment   →  Store  Latest  Run  (your  graph  will  remain
Figure  3
Molar  mass  by  freezing  point  depression
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on  the  screen,  the  next  experiment  data  will  appear  on  top  of  it).  Record  the  melting  point  of
BHT.
12.
Mass  out  approximately  1  g  of  cetyl  alcohol  onto  a  piece  of  weighing  paper  and  record  its   exact  mass.
13.
Place  the  cetyl  alcohol  in  the  test  tube  containing  BHT.
14.
Clamp  the  test  tube  in  the  water  bath  and  insert  the  thermometer  and  stirring  wire  assembly   into  the  test  tube  (Figure  2).
15.
Heat  the  mixture  in  the  hot  water  bath  until  the  substances  are  all  melted.  Stir  well  to  ensure   the  solution  is  homogeneous.
16.
When  the  solution  is  melted  remove  the  test  tube  from  the  hot  water  bath  (Figure  3).
Confirm  that  the  thermometer  is  still  positioned  in  the  solution.  Press  COLLECT  on  your   computer  and  continuously  stir  the  solution  to  maintain  even  cooling.  Stirring  also  helps   prevent  supercooling.  Stir  until  the  solution  solidifies.  Make  a  note  of  the  temperature  at   which  crystals  begin  to  form.
17.
Press  STOP  on  your  computer  when  all  of  the  solution  has  solidified.  Select  Experiment   →
Store  Latest  Run  (your  graph  will  remain  on  the  screen,  the  next  experiment  data  will  appear   on  top  of  it).  Record  the  melting  point  of  the  BHT/cetyl  alcohol  solution.  Set  this  test  tube   aside.
18.
Clean  your  stirrer  and  temperature  probe.
19.
Obtain  a  clean  test  tube.  Record  the  mass  of  the  test  tube.  Mass  out  approximately  8  grams  of   fresh  BHT.  Record  the  mass  of  the  test  tube  and  fresh  BHT.  Accurately  mass  out  1  gram  of   the  unknown  compound  and  add  it  to  the  test  tube  and  fresh  BHT.
20.
Repeat  steps  14-­‐19.  Record  the  melting  point  of  the  BHT/unknown  solution.
21.
Save  your  Logger  Pro  graph  (which  should  now  have  three  graphs  on  it)  to  Stushare   →
Students   →  Barry   →  AP  Chem   →  Freezing  point  depression.  Include  your  name  on  the   document.
Molar  mass  by  freezing  point  depression
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Calculations:
Copy  the  following  table  into  your  lab  notebook.  Leave  enough  space  for  you  to  put  in  answers.
BHT   BHT  +  cetyl  alcohol   BHT  +  unknown
Freezing  point,   ° C
Δ T f
,   ° C
k f
,   ° C/ m
Molar  mass,  g/mol
%  error,  molar  mass
Calculations:
1.
Determine  the  molality  of  the  BHT  +  cetyl  alcohol  mixture.  The  formula  for  cetyl  alcohol  is
CH
3
(CH
2
)
15
OH.
2.
Determine   Δ T f
for  the  BHT  +  cetyl  alcohol  mixture.
3.
Determine  k f
for  BHT.
4.
Determine   Δ T f
for  the  BHT  +  unknown  mixture.
5.
Determine  the  molality  of  the  BHT  +  unknown  mixture.
6.
Determine  the  molar  mass  of  the  unknown.
7.
The  molar  mass  of  the  unknown  is  284.49  g/mol.  Determine  your  percent  error.
Conclusion:
Addresses  the  purpose  of  the  experiment  in  a  simple,  concise  statement.  What  was  the  outcome  or   trends  developed?  Use  numbers  or  formulas  where  appropriate!  Were  any  new  techniques  or   instrumentation  utilized?
Molar  mass  by  freezing  point  depression
Page  5  of  6

Post  lab  questions:
1.
(Error  analysis)  The  following  errors  occurred  when  the  experiment  was  carried  out.  How   would  each  affect  the  calculated  molar  mass  of  the  solute  (too  high,  too  low,  no  effect)?
Explain  your  answer.     a.
The  thermometer  used  actually  read  1.4
° C  too  high  during  the  entire  experiment.     b.
Some  of  the  solvent  was  spilled  before  the  solute  was  added.   c.
Some  of  the  solute  was  spilled  after  it  was  weighed  and  before  it  was  added  to  the   solvent.   d.
Some  of  the  solution  was  spilled  after  the  solute  and  solvent  were  melted  but  before   the  freezing  point  was  determined.     e.
A  significant  but  unknown  amount  of  solvent  evaporates  ( i.e.
it  is  volatile)  from  the
test  tube.
2.
The  accepted  molal  freezing  point  depression  constant  (k fp
)  for  BHT  is  9.2
° C/ m .  This  means   that  a  1   m  BHT  solution  shows  a  freezing  point  depression  of  9.2
° C.  Why  is  it  advantageous   to  choose  a  solvent  that  has  a  large  value  for  k fp
for  this  lab?
3.
One  solute  used  in  this  experiment  was  cetyl  alcohol,  CH
3
(CH
2
)
15
OH.  Would  liquid  cetyl
alcohol  to  be  miscible  or  immiscible  in  water?  Explain.
Molar  mass  by  freezing  point  depression
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