A solid mixture contains exactly equal masses of and . If this mixture is titrated with a standard s — Redox Reactions and Volumetric Analysis Chemistry Question
Question
A solid mixture contains exactly equal masses of $Na_2CO_3$ and $NaOH$ . If this mixture is titrated with a standard $HCl$ solution, let $V_1$ be the volume of $HCl$ required to reach the phenolphthalein end point, and let $V_2$ be the total volume of $HCl$ required from the start to reach the methyl orange end point. Which mathematical relationship is correct?
💡 Solution & Explanation
Let the mass of each component be $m$ . Moles of $NaOH = m/40$ , Moles of $Na_2CO_3 = m/106$ . $V_1$ (Phenolphthalein endpoint) measures the complete neutralization of $NaOH$ plus exactly half the neutralization of $Na_2CO_3$ (conversion to $NaHCO_3$ ). So, $V_1 \propto (m/40) + (1/2)(m/106)$ . $V_2$ (Methyl orange total endpoint) measures complete neutralization of both: $V_2 \propto (m/40) + (m/106)$ . Testing $2V_1$ : $2V_1 \propto (2m/40) + (m/106) = m/20 + m/106$ . Since $m/20 > m/40$ , it algebraically follows that $2V_1 > V_2$ , or $V_2 < 2V_1$ .