To solve the problem of how many milliliters of concentrated HCl are required to prepare 2 liters of a decinormal solution, we will follow these steps:
### Step 1: Calculate the Density of Concentrated HCl
Given the specific gravity of concentrated HCl is 1.19, we can find its density. The density of water is approximately 1 g/mL. Therefore, the density of the 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 2: Calculate the Molarity of Concentrated HCl
The concentrated HCl solution contains 37% HCl by mass. To find the molarity, we first need to calculate the mass of HCl in 1 liter of solution:
1. **Mass of 1 liter of solution**:
\[
\text{Mass} = \text{Density} \times \text{Volume} = 1.19 \, \text{g/mL} \times 1000 \, \text{mL} = 1190 \, \text{g}
\]
2. **Mass of HCl in the solution**:
\[
\text{Mass of HCl} = 0.37 \times 1190 \, \text{g} = 440.3 \, \text{g}
\]
3. **Moles of HCl**:
The molar mass of HCl is approximately 36.5 g/mol.
\[
\text{Moles of HCl} = \frac{440.3 \, \text{g}}{36.5 \, \text{g/mol}} \approx 12.06 \, \text{mol}
\]
4. **Molarity of HCl**:
Since this is for 1 liter of solution, the molarity is:
\[
\text{Molarity} = 12.06 \, \text{mol/L}
\]
### Step 3: Determine Moles Required for Decinormal Solution
A decinormal solution (0.1 N) means we need 0.1 moles of HCl per liter. For 2 liters:
\[
\text{Moles required} = 0.1 \, \text{mol/L} \times 2 \, \text{L} = 0.2 \, \text{mol}
\]
### Step 4: 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:
\[
\text{Volume} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.2 \, \text{mol}}{12.06 \, \text{mol/L}} \approx 0.01658 \, \text{L}
\]
Converting this to milliliters:
\[
\text{Volume in mL} = 0.01658 \, \text{L} \times 1000 \, \text{mL/L} \approx 16.58 \, \text{mL}
\]
### Final Answer
To prepare 2 liters of a decinormal solution, approximately **16.58 mL** of concentrated HCl is required.
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