In the study of titration of NaOH and `Na_(2)CO_(3)`. NaOH and `NaHCO_(3)`, `Na_(2)CO_(3)` and `NaHCO_(3)`, phenophthalein and methyl orange are used as indicators.
(a). When phenolphthalein is used as an indicator for the above mixture:
(i). It indicates complete neutralisation of NaOH or KOH
(ii). It indicates half neutralisation of `Na_(2)CO_(3)` because `NaHCO_(3)` is formed at the end point.
(b). When methyl orange is used as an indicator for the above mixture
(i). It indicates complete neutralisation of `NaOH` or KOH
(ii). It indicates half neutralisation of `Na_(2)CO_(3)` because `NaCl` is formed at the end point.
Q. A 10 g moxture of `NaHCO_(3)` and `KOH` is dissolved in water to make 1000 mL solution. 100 " mL of " this solution required 50 " mL of " 0.2 M HCl for complete neutralisation in the presence of phenolphthalein as indicator What is the percentage of `NaHCO_(3)` in the mixture?

Options

A. `50%`
B. `56%`
C. `44%`
D. `60%`

Explanation

To solve the problem step-by-step, we will analyze the titration of a mixture of sodium bicarbonate (NaHCO₃) and potassium hydroxide (KOH) with hydrochloric acid (HCl) using phenolphthalein as an indicator.

### Step 1: Understand the Reaction
In the presence of phenolphthalein, only KOH will react with HCl, while NaHCO₃ will not react until it is fully neutralized. The reaction for KOH with HCl is:
\[ \text{KOH} + \text{HCl} \rightarrow \text{KCl} + \text{H}_2\text{O} \]

### Step 2: Calculate the Milliequivalents of HCl
Given:
- Volume of HCl = 50 mL
- Molarity of HCl = 0.2 M

The number of milliequivalents of HCl can be calculated using the formula:
\[ \text{Milliequivalents} = \text{Volume (mL)} \times \text{Molarity} \]
\[ \text{Milliequivalents of HCl} = 50 \, \text{mL} \times 0.2 \, \text{M} = 10 \, \text{meq} \]

### Step 3: Relate Milliequivalents of KOH to HCl
Since the reaction between KOH and HCl is a 1:1 ratio, the milliequivalents of KOH will also be 10 meq.

### Step 4: Calculate the Mass of KOH
To find the mass of KOH, we can use the relationship between milliequivalents and grams. The equivalent weight of KOH is its molar mass, which is approximately 56 g/mol. Therefore:
\[ \text{Mass of KOH} = \text{Milliequivalents} \times \text{Equivalent weight} \]
\[ \text{Mass of KOH} = 10 \, \text{meq} \times \frac{56 \, \text{g}}{1000 \, \text{meq}} = 5.6 \, \text{g} \]

### Step 5: Calculate the Mass of NaHCO₃
The total mass of the mixture is 10 g. Therefore, the mass of NaHCO₃ can be calculated as follows:
\[ \text{Mass of NaHCO₃} = \text{Total mass} - \text{Mass of KOH} \]
\[ \text{Mass of NaHCO₃} = 10 \, \text{g} - 5.6 \, \text{g} = 4.4 \, \text{g} \]

### Step 6: Calculate the Percentage of NaHCO₃ in the Mixture
The percentage of NaHCO₃ in the mixture can be calculated using the formula:
\[ \text{Percentage of NaHCO₃} = \left( \frac{\text{Mass of NaHCO₃}}{\text{Total mass}} \right) \times 100 \]
\[ \text{Percentage of NaHCO₃} = \left( \frac{4.4 \, \text{g}}{10 \, \text{g}} \right) \times 100 = 44\% \]

### Final Answer
The percentage of NaHCO₃ in the mixture is **44%**.

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