When  15  c.c.  are  required,  the  acid  is  £f  or  f  N.  If  the  actual  weight
of  the  acid  in  the  latter  case  has  to  be  calculated,  we  remember  that
there  are  36.45  g.  of  hydrogen  chloride  in  1  1.  of  a  normal  solution,
and  therefore  36.45  X  f  X  T§jhf  g-  =  -5467  g.  in  25  c.c.  of  a  solution
which  is  f-normal.
Methods  of  quantitative  analysis  in  which  standard  solutions  are
employed  are  known  as  volumetric  methods,  and  are  much  used  by
analysts  and  investigators.  They  occupy  much  less  time  than  gravi-
metric operations,  in  which  numerous  weighings  have  to  be  made,
and  are  often  just  as  accurate.  The  substances,  like  litmus,  by  whose
change  of  color  the  completeness  of  the  action  is  made  known,  are
called  indicators  (see  below).
Indicators.  —  Indicators  are  substances  which,  in  presence  of
certain  other  substances,  assume  a  very  deep  color,  or  change  sharply
from  one  deep  color  to  another.  Thus,  phenolphthale'in  is  colorless
in  presence  of  acids  (i.e.,  hydrogen-ion),  and  red  (when  dilute,  pink)
in  presence  of  alkalies  (i.e.,  hydroxide-ion).  Litmus,  again,  is  red
with  acids,  and  blue  with  alkalies.  The  change  of  color  depends
upon  a  chemical  interaction  in  each  case,  but  since  indicators  are
chosen  for  their  strong  coloration,  the  quantity  of  the  acids  or  base
used  up  in  changing  the  tint  of  the  trace  of  the  indicator  is  so  small
as  to  be  negligible.  The  common  indicators  are:

Phenolphthaleih,  C14H10O4,  a  colorless  substance  and  very  feeble
acid.  It  is  not  perceptibly  dissociated  into  its  ions:

C14H10O4  (colorless)  ±=>C14H9O4'  (red)  +  H',


IONIC   SUBSTANCES  243

and  in  neutral  or  acid  solutions  is,  therefore,  without  visible  color.
