How many milliliter of conc. HCI of specific gravity 1.19 and which contains 37% by mass HCI will be required to prepare 2 litre of decinormal solution?

Options

A. 13.22 ml
B. 23.41 ml
C. 16.58 ml
D. 28.26 ml

Answer

To solve the problem of how many milliliters of concentrated HCl are needed to prepare 2 liters of a decinormal solution, follow these steps:

### Step 1: Understand the Given Data
- Specific gravity of concentrated HCl = 1.19
- Concentration of HCl = 37% by mass
- Volume of solution required = 2 liters
- Decinormal solution = 0.1 N (which is equivalent to 0.1 M for HCl since its n-factor is 1)

### Step 2: Calculate the Density of Concentrated HCl
Specific gravity is defined as the ratio of the density of a substance to the density of water. Since the density of water is approximately 1 g/mL, the density of concentrated HCl can be calculated as follows:
\[ \text{Density of HCl} = \text{Specific Gravity} \times \text{Density of Water} = 1.19 \times 1 \text{ g/mL} = 1.19 \text{ g/mL} \]

### Step 3: Calculate the Molarity of Concentrated HCl
To find the molarity, we need to determine the number of moles of HCl in 1 liter of the concentrated solution. First, we calculate the mass of HCl in 1 mL of the solution:
\[ \text{Mass of HCl in 1 mL} = \text{Density} \times \text{Volume} = 1.19 \text{ g/mL} \times 1 \text{ mL} = 1.19 \text{ g} \]
Since the solution is 37% HCl by mass, the mass of HCl in 1 mL is:
\[ \text{Mass of HCl} = 0.37 \times 1.19 \text{ g} = 0.4403 \text{ g} \]

Next, we convert this mass to moles using the molar mass of HCl (approximately 36.5 g/mol):
\[ \text{Moles of HCl in 1 mL} = \frac{0.4403 \text{ g}}{36.5 \text{ g/mol}} \approx 0.01206 \text{ moles} \]

To find the molarity (moles per liter), we multiply by 1000 (since there are 1000 mL in a liter):
\[ \text{Molarity} = 0.01206 \text{ moles/mL} \times 1000 \text{ mL} = 12.06 \text{ M} \]

### Step 4: Calculate the Number of Moles Required for the Decinormal Solution
For a decinormal (0.1 N) solution, the number of moles needed for 2 liters is:
\[ \text{Moles required} = \text{Normality} \times \text{Volume} = 0.1 \text{ N} \times 2 \text{ L} = 0.2 \text{ moles} \]

### Step 5: Calculate the Volume of Concentrated HCl Required
Using the molarity of the concentrated HCl, we can find the volume needed to obtain 0.2 moles:
\[ \text{Volume} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.2 \text{ moles}}{12.06 \text{ M}} \approx 0.01658 \text{ L} \]
Convert this volume to milliliters:
\[ \text{Volume in mL} = 0.01658 \text{ L} \times 1000 \text{ mL/L} = 16.58 \text{ mL} \]

### Final Answer
The volume of concentrated HCl required is approximately **16.58 mL**.

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