The overall equation for the reaction between sodium carbonate solution and dilute hydrochloric acid is
`Na_(2)CO_(3)(aq.)+2HCl(aq.)rarrNaCl(aq)+CO_(2)(g)H_(2)O(l)`
If you had the two solutions of the same concentration, you would have to use double volume of HCl to reach the equivalence point.
Indicators change their colours at the end point of the reaction and hence we are able to know the end points (equivalence points of reactions).
How many ml of 1N HCl are required for X milimoles of NaOH + Y milimoles of `Na_(2)CO_(3)+Z` milimoles of `NaHCO_(3)`with methyl orange indicator

Options

A. (2X+Y+Z)ml
B. (X+2Y+2Z)ml
C. (X+2Y+3Z)ml
D. (X+2y+Z) ml

Explanation

To determine how many milliliters of 1N HCl are required for a mixture of X millimoles of NaOH, Y millimoles of Na₂CO₃, and Z millimoles of NaHCO₃, we can follow these steps:

### Step 1: Understand the Reaction
The overall reaction between sodium carbonate (Na₂CO₃) and hydrochloric acid (HCl) is given as:
\[ \text{Na}_2\text{CO}_3 (aq) + 2 \text{HCl} (aq) \rightarrow 2 \text{NaCl} (aq) + \text{CO}_2 (g) + \text{H}_2\text{O} (l) \]

For sodium bicarbonate (NaHCO₃), the reaction is:
\[ \text{NaHCO}_3 (aq) + \text{HCl} (aq) \rightarrow \text{NaCl} (aq) + \text{CO}_2 (g) + \text{H}_2\text{O} (l) \]

### Step 2: Determine the Equivalents
- **NaOH**: Each mole of NaOH reacts with 1 mole of HCl. Therefore, the equivalents of NaOH are equal to the number of millimoles of NaOH, which is \(X\).

- **Na₂CO₃**: Each mole of Na₂CO₃ reacts with 2 moles of HCl. Therefore, the equivalents of Na₂CO₃ are \(2Y\) (since Y is in millimoles).

- **NaHCO₃**: Each mole of NaHCO₃ reacts with 1 mole of HCl. Therefore, the equivalents of NaHCO₃ are equal to the number of millimoles of NaHCO₃, which is \(Z\).

### Step 3: Sum the Equivalents
The total equivalents of HCl required will be the sum of the equivalents from each component:
\[ \text{Total equivalents of HCl} = \text{equivalents of NaOH} + \text{equivalents of Na}_2\text{CO}_3 + \text{equivalents of NaHCO}_3 \]
\[ = X + 2Y + Z \]

### Step 4: Calculate the Volume of HCl Required
Since we are using 1N HCl, the volume in milliliters (mL) can be calculated using the formula:
\[ \text{Volume of HCl (mL)} = \frac{\text{Total equivalents of HCl}}{\text{Normality of HCl}} \times 1000 \]
Given that the normality of HCl is 1N:
\[ \text{Volume of HCl (mL)} = X + 2Y + Z \]

### Final Answer
Thus, the total volume of 1N HCl required for \(X\) millimoles of NaOH, \(Y\) millimoles of Na₂CO₃, and \(Z\) millimoles of NaHCO₃ is:
\[ \text{Volume of HCl (mL)} = X + 2Y + Z \]