A solution contains only NaOH and $Na X_{2} CO X_{3}$ . Titrated with HCl, phenolphthalein is decolourised after 20.0 mL; methyl orange is then added and a further 7.5 mL is needed. The mole ratio $NaOH : Na X_{2} CO X_{3}$ in the solution is:

Answer: A

The further volume V2 = 7.5 mL converts

HCO X_{3} X^{-}

CO X_{2}

, and equals the volume that converted

CO X_{3} X^{2 -}

HCO X_{3} X^{-}

. So

Na X_{2} CO X_{3}

\propto

7.5, and NaOH

\propto

V1 - V2 = 20.0 - 7.5 = 12.5. Ratio = 12.5 : 7.5 = 5 : 3.