328  Quantitative  Estimation  of  Phosphates.  \Am'j^v;I&&Ym' 
tion  of  alkali  and  acid  may  be  employed,  but  under  exceptional 
circumstances,  where  the  phosphates  are  known  to  be  present  in 
very  small  quantities,  very  satisfactory  results  may  be  obtained  by 
using  one-fiftieth  normal  solutions.  Ten  cubic  centimeters  of  the 
solution  obtained  above,  containing  phosphates,  is  exactly  neutral- 
ized with  one-tenth  normal  alkali  to  the  phenolphthalein  end  point. 
Alizarin  is  then  added  and  the  mixture  is  titrated  back  with  one- 
tenth  normal  sulphuric  until  the  alizarin  end  point  is  reached.  This 
figure  represents  the  equivalent  of  one  of  the  acid  groups  of  the 
phosphoric  acid.  (2)  Ten  cubic  centimeters  are  neutralized  in  the 
same  way  as  the  previous  experiment,  using  phenolphthalein  as  an 
indicator,  an  excess  of  2  or  3  c.c.  alkali  is  then  added  and  the  mix- 
ture boiled.  It  is  then  retitrated  with  sulphuric  acid  to  see  if  any 
appreciable  loss  of  alkali  has  taken  place.  If  the  difference  is  more 
than  o-i  of  a  c.c.  a  further  excess  of  alkali  is  added,  once  more 
boiled  and  retitrated  to  the  neutral  point  with  sulphuric  until  fairly 
constant.  Then  a  definite  excess  of  alkali,  5  c.c.  for  example,  is 
added  to  the  mixture,  and  5  c.c.  of  an  absolutely  neutral  and  phos- 
phate-free barium  chloride  solution,  the  whole  is  boiled  vigorously 
for  a  minute,  allowed  to  cool  for  a  minute,  and  titrated  with  one-tenth 
normal  acid  until  the  phenolphthalein  end  point  is  reached.  If 
phosphates  are  present  it  will  be  found  that  the  full  amount  of  acid 
is  not  required.  The  difference  between  the  amount  of  alkali 
added  and  the  amount  of  acid  required  to  titrate  back  represents 
another  acid  group  of  the  phosphoric  acid.  This  figure  should  exactly 
coincide  with  that  obtained  above  in  the  first  experiment,  since  each 
one  of  them  represents  one  of  the  three  acid  affinities  of  the  total 
amount  of  phosphates  present  in  the  mixture.  As  a  matter  of  fact, 
the  phenolphthalein  alizarin  end  point  is  more  nearly  correct,  the 
other  result  being  usually  slightly  high.  If  any  great  discrepancy 
exists  it  is  necessary  to  look  for  some  source  of  error  and  repeat  the 
experiments.  Having  obtained  these  results  it  is  comparatively  easy 
to  calculate  the  exact  effect  which  would  have  been  produced  by 
the  phosphates  present  in  the  mixture  upon  the  alizarin  end  point 
and  the  phenolphthalein  end  point,  allowance  being  made  accord- 
ingly. It  is  obvious  that  the  effect  upon  the  alizarin  end  point 
would  be  exactly  half  that  upon  the  phenolphthalein  end  point,  since 
one  hydrogen  was  saturated  at  the  alizarin  end  point  and  a  second 
at  the  phenolphthalein  end  point. 
