A 100 ml mixture of Na_(2)CO_(3) and NaHCO_(3) is tittrated against 1 M HCl. If v_(1)L and v_(2)L are consumed when phenolphthalein and methyl orange are used as indicators respectively in two separate titrations, which of the following is true form molarities in the original solution.

A 100 ml mixture of Na_(2)CO_(3) and NaHCO_(3) is tittrated against 1

1.	A 100 ml mixture of Na_(2)CO_(3) and NaHCO_(3) is tittrated against 1 M HCl. If v_(1)L and v_(2)L are consumed when phenolphthalein and methyl orange are used as indicators respectively in two separate titrations, which of the following is true form molarities in the original solution.
Answer» molarity of `Na_(2)CO_(3)=20v_(1)` molarity of `NaHCO_(3)=10(v_(2)-2v_(1))` molarity of `Na_(2)CO_(3)=10(v_(2)+v_(1))` molarity of `NaHCO_(3)=10(v_(2)-v_(1))` Solution :When HPh USED `(1)/(2)xx` Eqts of `Na_(2)CO_(3)` = Eq of HCl `(1)/(2)xx(100)/(1000)xxM_(Na_(2)CO_(3))xx2=V_(1)xx1` `M_(NC_(2)CO_(3))=10V_(1)......(1)` When meOH used Eqts of `NC_(2)CO_(3)+` Eqts of `NaHCO_(3)` = Eq of HCl `((100)/(1000)xxM_(Na_(2)CO_(3))xx2)+((100)/(1000)xxM_(NCHCO_(3))xx1)=V_(2)xx1....(2)` On solving (1), (2) `M_(NaHCO_(3))=10(V_(2)-2V_(1))`