$2.5 g$ of a mixture containing ${CaCO}_{3}, Ca {({HCO}_{3})}_{2}$ and $NaCl$ was dissolved in $100 m L$ water and its $10 m L$ portion required $10 m L 0.05 M$ $H_{2} {SO}_{4}$ solution to reach the phenolphthalein end Point Another $10 m L$ portion of the same stock solution required $32.35 m L$ of the same acid solution reach the methyl orange end point. Determine mass percentage ratio of ${CaCO}_{3}$ and $Ca ({HCO}_{3})_{2}$ in the original mixture.

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Detailed Solution

Here,

For phenolphthalein end point,

$\begin{array}{l} \underset{1}{2 {CaCO}_{3}} + \underset{\underset{= 0.5}{10 \times 0.05}}{H_{2} {SO}_{4}} ⟶ Ca {({HCO}_{3})}_{2} + {CaSO}_{4} \end{array}$

For methyl orange end point

$\underset{1}{{CaCO}_{3}} + \underset{1 m m o l}{H_{2} {SO}_{4}} ⟶ {CaSO}_{4} + H_{2} O + {CO}_{2}$

$Ca {({HCO}_{3})}_{2} \underset{\begin{matrix} (32.35 \times 0.05 - 1) \\ = 6.175 \times 10^{- 1} \end{matrix}}{+ H_{2} {SO}_{4}} ⟶ {CaSO}_{4} + 2 H_{2} O + 2 {CO}_{2}$ $Ratio = \frac{1 \times 100}{6.175 \times 10^{- 1} \times 162} = 1$