Chem  26.1  Midterms  Reviewer     /steffigatdula/  1  

CHEM  26.1  –  MIDTERMS  REVIEWER    Experiment   1:   Application   of   Statistical   Concepts   in   the  Determination  of  Weight  Variation  in  Samples    Sample  and  Population  • population  –  collection  of  all  measurements  of  interest    

o parameter   –   quantity   that   describes   a  property  of  the  population    

• sample   –   refers   to   the   subset   of   a   population   that   is  representative   of   the   population   from   which   it   was  collected    

o statistic   –   quantity   that   describes   a   property  of   the  sample;   in   the  absence  of  determinate  errors,   it   is   considered   as   a   good   estimate   of  the   parameter;   reliability   increases   with   the  number  of  measurements  taken  

 Measures  of  Central  Tendency  • mean   –   average   of   the   values   measured   from   the  

sample;  use  a  calculator  to  get  this  (x)    

x =  (x! +  x! +  x!+  . . . x!)

n  

 • median   –  middle   value   in   a   set   of   data   that   has   been  

arranged  in  increasing  or  decreasing  order;  if  the  set  of  values   is   even,   the   median   is   the   average   of   the   2  midpoints  

 Measures  of  Accuracy  • absolute   error,   E   –   difference   between   the  

experimental  value  and  true  value    

E = x! −  x!    • relative   error,   Er   –   absolute   error   divided   by   the   true  

value;  expressed  in  percent    

E! =  x! − x!x!

 x  100  

 Measures  of  Precision    • variance,  s2  -­‐  measure  of  how  far  each  value  in  the  data  

set  is  from  the  mean;  use  a  calculator  to  get  this  (xσn-­‐1);  unit2  

 

s! =    (x! −  x)!!

!!!

n − 1    

   • standard   deviation,   s   –   square   root   of   variance   use   a  

calculator  to  get  this  (square  of  xσn-­‐1);  same  unit    

s =    (x! −  x)!!

!!!n − 1  

!  

 • relative  standard  deviation,  RSD  -­‐  absolute  value  of  the  

coefficient  of  variation;  unit  is  ppt    

RSD =  sx  x  1000  

• coefficient  of  variation,  CV  –  RSD  expressed  in  percent;  unit  is  %  

 

CV =  sx  x  100  

 • pooled   standard   deviation,   spooled   –   used   when   there  

are  several  data  sets  (n!);  same  unit      

s!""#$%   =    (x! −  x!)!

!!!!! +    (x! −  x!)!

!!!!!

n! +  n!+    . . .    −  n!

!

 

               =  s!! n! − 1 + s!! n! − 1

n! +  n!+    . . .    −  n!

!  

 • range,   R   –   difference   between   highest   and   lowest  

values  in  a  set  of  measurements;  same  unit    

R =   x!"#!$%& −  x!"#$%&    • relative  range,  RR  –  range  expressed   in  relative  terms;  

unit  is  ppt    

RR =  Rx  x  1000  

 Confidence  Interval    • provides  a  range  of  values  within  which  the  population  

mean  is  expected  to  lie  at  a  specified  confidence  level  • uses  n − 1  in  the  table  for  values  of  t    

CI = x  ±  tsn  

 Grubbs  Test    • used   to   detect   outliers;   can   only   detect   1   outlier   per  

data  set  • arrange  data  set  from  lowest  to  highest  then  calculate  

|x! −  x|  for  both  extremes,  calculate  gexp   for  the  value  with  a  higher  |x! −  x|  

• if   gtab  >   gexp   then   the  value   is   accepted,  otherwise   it   is  rejected    

o if  gexp  is  rejected,  calculate  the  new  s  and  x  for  the  data  set  with  the  outlier  removed  

• uses  n  in  the  table  of  critical  values    

g =  max!!!..!

|x! −  x|

s  

 3  Types  of  Errors  • gross  errors  

o outliers  →  Grubbs  test  o e.g.  

§ arithmetic  mistake  § reading  a  scale  backward  § using  a  wrong  scale  § spilling  a  solution    

• systematic/determinate  Errors  o have  a  definite  value  o assignable  cause  o affects  accuracy    

Chem  26.1  Midterms  Reviewer     /steffigatdula/  2  

1. instrumental  § faulty  calibration    § instrument   used   is   under  

inappropriate  condition    2. method  

§ non-­‐ideal   chemical/physical   behavior  of  the  chemicals  

• side  reactions  • impurities  in  the  product  • slight   solubility   of   the  

precipitate  • incomplete  reaction      

§ minimize  by:  • blank  determination    • standard  reference  material  • independent  analysis  

3. personal  § prejudice  in  estimation    

• random/indeterminate  o affects  precision    o sources:  cannot  be  determined    

 Experiment  2:  Solution  Preparation  and  Standardization      Expressions  of  Concentration        

Molarity   M =  moles  soluteL  solution

 

 

Molality   m =  moles  solutekg  solvent

 

 

Mole  Fraction, X =  moles  solutemoles  solution

 

 Dilution      

𝑀!𝑉! = 𝑀!𝑉!    

Dilution  Factor,DF =  total  volume  of  solution

volume  of  aliquot  

→M!"#!$#%&'%$( = M!"#$%&!  x  DF    

Aliquot  Factor,AF =  volume  of  aliquot

total  volume  of  solution=  

1DF

 

→M!"#$%&! = M!"#!$#%&'%$(  x  AF      Experiment   3:   Chemical   Kinetics   –   The   Iodine   Clock  Reaction      Chemical  Kinetics  • how  fast  or  slow  a  reaction  occurs    Factors      • nature  of  reactants  • concentration    • temperature  • presence  of  a  catalyst    • surface  area    

Rate  Law  A  +  B  →  C  +  D  

rate  =  k[A]m[B]n     where:     k  =    rate  constant       m  &  n  =  rate  orders       m  +  n  =  overall  reaction  order    Graphical  Method  of  Determining  Rate  Law    

    Zero   First   Second  

Rate  Law    

R = k    

 R = k[A]  

 

 R = k[A]!  

 

Int.  Rate  Law  

 [A]! = −kt + [A]!  

 

 ln[A]! = −kt + ln[A]!  

 

 1[A]!

= kt +  1[A]!

 

 

Units  of  k  

 Ms  

 

1s  

1M ∙ s

 

Linear  Plot   [A]t  vs.  t     ln[A]t  vs.  t    

![!]!

 vs.  t  

 Slope   -­‐k   -­‐k   k  

Half-­‐life  

 

𝑡!!=[A]!2k

 

 

 

𝑡!!=ln  (2)k

 

 

 

𝑡!!=

1k[A]!

 

 

 Initial  Rate  Method    

rate  1rate  2

=  k[A!]![B!]!

k[A!]![B!]!  

 Elementary  Steps  Method  • include  only  the  slow  reaction  and  the  steps  before  it    

ex.     A  +  B  →  C   fast     C  +  B  →  D   slow                D  →  E     fast    

    rate  =  k[A][B]2  

 Arrhenius  Equation    E! = Activation  Energy  A = Arrhenius  Constant    ln k =  !!!

!∙ !!+ ln  (A)  [in  the  form  y = mx + b]  

  where:  R = 8.3124   !!"#

 &  T  is  in  Kelvin    linear  regression  on  a  calculator  (Casio)    • STAT  →  A+BX  →  enter  x  &  y  values  

o x =   !!  (!"#$%&)

 

o y =  ln  (k)  • press  SHIFT  +  STAT  →  go  to  Reg  

o A = y − intercept = b = ln A  →  A = e!  o B = slope =  m = !!!

!    →  E! = mR    

o r! = linearity = approaching  1  

Chem  26.1  Midterms  Reviewer     /steffigatdula/  3  

Experiment    starch  and  iodine  create  a  blue  complex:  • S!O!

!! + 2I!  → 2SO!!! + I!  

• persulfate  +  iodide  →  sulfate  +  iodine    addition  of  thiosulfate  creates  a  clock  reaction:    • 2S!O!

!! + I!  → S!O!!! +  2I!  

• thiosulfate  +  iodine  →  tetrathionate  +  iodide    maintaining  a  constant  ionic  strength  for  all  set-­‐ups:  • addition  of  KCl  and  K!SO!    Experiment  4:  Common  Ion  Effect  and  Buffers    Acid-­‐Base  Indicators    

Indicator   pH  values   Color    

Methyl  Orange  pH  <  3.1   Red  

3.1  <  pH  <  4.5   Salmon  Pink  pH  >  4.5   Yellow  

 Phenolphthalein  

pH  <  8.3   Colorless  8.3  <  pH  <  10.0   Very  Light  Pink  

pH  >  10.0   Red    Buffers  • resists   appreciable   change   in  pH  upon   the   addition  of  

small  amounts  of  strong  acid  or  strong  base  • composed  of  weak  acid/base  +  conjugate  ion    

o HA  &  A-­‐  or  BH+  &  B  • buffer  capacity  –  amount  of  acid  or  base  the  buffer  can  

neutralize   before   pH   begins   to   change   to   an  appreciable  level  

o  𝑝𝐻 = 𝑝𝐾! ± 1  or  𝑝𝑂𝐻 = 𝑝𝐾! ± 1      Determining  the  pH/pOH  of  Weak  Acids/Bases  • remember  that:  

o 𝐻𝐴   → 𝐻! + 𝐴!  o 𝐵   +  𝐻!𝑂   → 𝐵𝐻! + 𝑂𝐻!  

• use  ICE  table  to  determine  equilibrium  concentrations  o when  𝐾!  ≤ 10!! ,   x   is   negligible   in   addition  

and  subtraction  operations  o change   values   if   strong  acid/base   is   added   to  

weak   acid/base   (addition   of   initial   amount  present   or   calculation   of   limiting/excess  reactant  when  salt  is  formed)  

 

𝐾!  𝑜𝑟  𝐾! =  [𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠][𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠]

 

 pK! =  − logK!  &  pK! =  − logK!  → K!K! =  K! = 1.00  x  10!!"  

 pH =  − log H!  &  pOH = −log  [OH!]  

→ 14 = pH + pOH                

Henderson-­‐Hasselbalch  Equation    

pH = pK! + log[base][acid]

 

 

addition  of  SA:  pH = pK! + log!!"#  !"#$!!!"#  !!  !"".!!"#  !"#$!!!"#  !!  !"".

   addition  of  SB:  pH = pK! + log

!!"#  !"#$!!!"#  !"!  !"".!!"#  !"#$!!!"#  !!!  !"".

   

pOH = pK! + log[acid][base]

 

 addition  of  SB:  pOH = pK! + log

!!"#  !"#$  !!!"#  !"!  !"".!!"#  !"#$!!!"#  !!!  !"".

   

addition  of  SA:  pOH = pK! + log!!"#  !"#$!!!"#  !!  !"".!!"#  !"#$!!!"#  !!  !"".

   Titration  (For  E5  &  E6)    titrimetric  analysis    • quantitative  • aims  to  determine  concentration  of  analyte  • uses  a  titrant  of  known  concentration    requirements  ü fast  ü complete  ü known  reaction  ü has  a  way  to  detect  equivalence  point    2  parts  • standardization   of   titrant   concentration   using   a  

primary  standard  with    o high  %  purity    o high  molecular  weight  o high  stability    o known  reaction    

• sample  analysis  o known  titrant  concentration  and  volume  o known  analyte  volume    o determine:  analyte  concentration  

 Experiment   5:   Determination   of   the   Solubility   Product  Constant  of  Calcium  Hydroxide    Solubility  Product  Constant      

for  a  reaction:  A!B!(!) → xA!! + yB!!  → K!" = [A!!]![B!!]!  

 • K!"  is  the  product  solubility  constant  • [A!!]![B!!]!  is   the   ion-­‐product,   IP,   or   reaction  

quotient,   Q,   when   the   concentration   used   are   initial  concentrations  

• solids   do   not   appear   as   a   denominator   in   the  K!"  expression  because  the  activity  of  any  solid  is  1  

• K!"  is  temperature  dependent    When  A!!  ions  were  added  to  a  solution  with  B!!  ions:  

Chem  26.1  Midterms  Reviewer     /steffigatdula/  4  

• resultant  solution  is  unsaturated  if  IP < K!"  • reaction  mixture  is  saturated  if  IP =  K!"  • precipitation  is  observed  if  IP > K!"    Other  Factors  Affecting  𝐊𝐬𝐩  • common  ion  –  identical  ion  is  added  to  solution  

o lowers  s  -­‐   based   on   Le   Chatelier’s   principle,  the  CI  will  shift  the  reaction  backward  

• diverse-­‐ion   /   ionic   strength   –   ion   from   a   substance  containing  no  common  ion  is  added  to  a  solution    

o 𝑠  increases  with  ionic  strength  (shielding)  

µμ =  12

𝐶!(𝑍!)!  where:  C! = concentration  of  ion    

                                                   Z! = charge  of  the  ion      Calculations    

Ca(OH)!   !  ⇋ Ca!! + 2OH!  K!" = Ca!! [OH!]!  

 • [OH!]  is  calculated  from  HCl  titration    • Ca!!  is   OH!  /  2  • compute  𝑠  using  an  ICE  table  • use  1:1  ratio  for  HCl  standardization    (only  PH  is  used)  

   Experiment   6:   Quantitative   Determination   of   Soda   Ash  Composition  by  Double  Indicator  Titration      Soda  Ash  Components  ü 𝑁𝑎!𝐶𝑂!  -­‐  sodium  carbonate  ü 𝑁𝑎𝐻𝐶𝑂!  -­‐  sodium  bicarbonate  ü 𝑁𝑎𝑂𝐻  -­‐  sodium  hydroxide    

 Indicators  • NaOH  –  phenolphthalein    • NaHCO!  –  methyl  orange  • Na!CO!  –  phenolphthalein  +  methyl  orange    Relationship  of  VPH  and  VMO  

Substance  Present  

mmol  of  Substance  

VMO  =  0   NaOH   M!"#V!"  VPH  =  0   NaHCO!   M!"#V!"  VPH  =  VMO   Na!CO!   M!"#V!"  

M!"#V!"  VPH  >  VMO   Na!CO!   M!"#V!"  

NaOH   M!"#(V!" − V!")  VPH  <  VMO   Na!CO!   M!"#V!"  

NaHCO!   M!"#(V!" − V!")    

Factors  in  the  Experiment  • use  of  boiled  𝑑H!O    

o removes  CO!  that  can  lead  to  carbonate  error  (only  present  in  sample  with  NaOH)  

o CO! + 2OH!  → CO!!! +  H!O  

§ instead   of   needing   2   moles  H!  to  neutralize   2   moles  OH! ,   you   only  need  1  mole  H!  to  neutralize  1  mole  CO!

!!  § carbonate  error  leads  to  a  lower  VPH  

• boiling  near  MO  endpoint    o to  obtain  a  sharper  endpoint  o to  disrupt    

   • NaHCO! + NaOH   →    Na!CO! +  H!O  

o impossible  to  determine  original  composition    o NaHCO!  as  the  LR:  Na!CO! +  H!O + NaOH    o NaOH  as  the  LR:  Na!CO! +  H!O +  NaHCO!  

 Calculations    

%Na!CO! =  mg  Na!CO!sample

 x  100  

 

%NaHCO! =  mg  NaHCO!sample

 x  100  

 

%NaOH =  mg  NaOHsample

 x  100  

 %inert =  100 −  %Na!CO! −  %NaHCO! −  %NaOH      *use  AF  or  DF  as  needed    Error  Propagation      Addition  and  Subtraction    • R = A + B − C  • r =   a! + b! + c!  • final  result:  R   ± r  

o R  follows  the  decimal  place  of  r  o r  should  only  have  1  significant  figure  

 Multiplication  and  Division    • R =  AB C  

• r = R !!

!+ !

!

!+ !

!

!  

• final  result:  R   ± r  o R  follows  the  decimal  place  of  r  o r  should  only  have  1  significant  figure  

 Multiple  Operations  • ex.   1.5 ± 0.1 + 2.6 ± 0.2    /  (1.4 ± 0.3)    

o addition:  R = 4.1  and  r =  0.2236067977  

o division:  r =   !.!!.!

!!

!+ !.!

!.!

!  

o final  result:  2.9   ± 0.6    

CO!!! + 𝐻!  → 𝐻𝐶𝑂!!    

𝐻𝐶𝑂!! + 𝐻!  → 𝐻!𝐶𝑂!    

 𝐻!  𝑂 + 𝐶𝑂!(𝑔)    

⇋  

8.3  

3.9  

𝐕𝐌𝐎  𝐕𝐏𝐇  

𝐻𝐶𝑂!! + 𝐻!  → 𝐻!𝐶𝑂!    

 𝐻!  𝑂 + 𝐶𝑂!(!)  

 

⇋