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Q.

A 100 ml mixture of $N a_{2} C O_{3}$ and $N a H C O_{3}$ is titrated 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 for molarities in the original solution?

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a

Molarity of $N a_{2} C O_{3} = 10 (V_{2} + V_{1})$

b

Molarity of $N a H C O_{3} = 10 (V_{2} - 2 V_{1})$

c

Molarity of $N a_{2} C O_{3} = 20 V_{1}$

d

Molarity of $N a H C O_{3} = 10 (V_{2} - V_{1})$

answer is B.

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Detailed Solution

Let molarities of $N a_{2} C O_{3}$ and $N a H C O_{3}$ be xM and yM, respectively.
Phenolphthalein :
$\frac{100 \times x}{1000} \times 1 = V_{1} \times 1 \times 1 \Rightarrow x = 10 V_{1}$
Methyl orange :
$\frac{100 \times x}{1000} \times 2 + \frac{100 \times y}{1000} \times 1 = (V_{2} \times 1) \times 1 \Rightarrow y = 10 (V_{2} - 2 V_{1})$

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A 100 ml mixture of Na2CO3 and NaHCO3 is titrated against 1 M-HCl. If V1 L and V2 L are consumed when phenolphthalein and methyl orange are used as indicators, respectively, in two separate titrations, which of the following is true for molarities in the original solution?