50 " mL of " a solution containing 1 g each of `Na_2CO_3`, `NaHCO_3` and `NaOH` was titrated with N HCl. What will be the titre value if:
(a). Only phenolphthalein is used as an indicator? ltbr. (b). Only methyl orange is used as an indicator from the very begining?
(c). Methyl orange is added after the first end point with phenolphthalein?

Explanation

Let a,b, and c be the m" Eq of "`Na_(2)CO_(3),NaHCL_(3)`, and `NaOH`,
Respectively.
(a). With phenolphthalein:
`m" Eq of "NaOH+(1)/(2)m" Eq of "Na_(2)CO_(3)=m" Eq of "HCl`
`(1)/(40)xx10^(3)+(1)/(2)xx(1)/(53)xx10^(3)=1xxV_(1)`
`thereforeV_(1)=34.4mL`
(b). Withy methyl orange from the begining:
`m" Eq of "NaOH+m" Eq of "Na_(2)CO_(3)+m" Eq of "NaHCO_(3)`
`=m" Eq of "HCl`
`(1)/(40)xx10^(3)+(1)/(53)xx10^(3)+(1)/(84)xx10^(3)=1xxV_(2)`
(c). With methyl orange when first end point using phenolphthalein is used:
`(1)/(2)m" Eq of "Na_(2)CO_(3)+m" Eq of "NaHCO_(3)=m" Eq of "HCl`
`(1)/(2)xx(1)/(53)xx10^(3)+(1)/(84)xx10^(3)=1xxV_(3)`
`thereforeV_(3)=21.3mL`