0.848 g aqueous solution of a mixture containing `Na_(2)CO_(3)` NaOH, and an inert matter is titrated with `(M)/(2)` HCl. The colour of phenolphthalein disappears when 20 " mL of " the acid has been added. Methyl orange is then added and 8.0 mL more of the acid is requried to give a red colour to the solution. The percentage of `Na_(2)CO_(3)` is

Options

A. 25
B. 12.5
C. 75
D. 50

Answer

D

Explanation

Let `x` and `y` are m" Eq of "`NaOH` and `Na_(2)O_(3)`,
Phenolphthalein as indicator:
`m" Eq of "NaOH=(1)/(2)m" Eq of "Na_(2)O_(3)=m" Eq of "HCl`
`x+(y)/(2)=(1)/(2)xx1xx20=10` …(i)
Methyl orange as indicator:
`(mEq Na_(2)CO_(3)("left"))/(2)=m" Eq of "HCl`
`(y)/(2)=(1)/(2)xx8=4` ..(ii)
`y=8,x=6`
Weight of `Na_(2)CO_(3)=8xx10^(-3)xx(106)/(2)=0.424g`
`% of Na_(2)SO_(3)=(0.424)/(0.848)xx100=5%`