100 g of a solution of hydrochloric acid (sp.gr. 1.18) contains 36.5 g of the acid. The normality of the solution is:

Options

A. `1.18`
B. `11,8`
C. 118
D. 10

Explanation

To find the normality of the hydrochloric acid (HCl) solution, we will follow these steps:

### Step 1: Calculate the density of the solution
Given that the specific gravity (sp.gr.) of the solution is 1.18, we can calculate the density of the solution using the formula:
\[ \text{Density of solution} = \text{Specific Gravity} \times \text{Density of water} \]
Since the density of water is approximately 1 g/mL, we have:
\[ \text{Density of solution} = 1.18 \times 1 = 1.18 \text{ g/mL} \]

### Step 2: Calculate the volume of the solution
Using the mass of the solution (100 g) and the density calculated in Step 1, we can find the volume of the solution:
\[ \text{Volume of solution} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \text{ g}}{1.18 \text{ g/mL}} \]
Calculating this gives:
\[ \text{Volume of solution} \approx 84.745 \text{ mL} \]

### Step 3: Calculate the number of moles of HCl
We know that the mass of HCl in the solution is 36.5 g. To find the number of moles, we use the molecular weight of HCl, which is:
\[ \text{Molecular weight of HCl} = 1 \text{ (H)} + 35.5 \text{ (Cl)} = 36.5 \text{ g/mol} \]
Now, we can calculate the number of moles of HCl:
\[ \text{Number of moles of HCl} = \frac{\text{Mass of HCl}}{\text{Molecular weight of HCl}} = \frac{36.5 \text{ g}}{36.5 \text{ g/mol}} = 1 \text{ mol} \]

### Step 4: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution. We need to convert the volume from mL to L:
\[ \text{Volume in L} = \frac{84.745 \text{ mL}}{1000} \approx 0.084745 \text{ L} \]
Now, we can calculate the molarity:
\[ \text{Molarity} = \frac{\text{Number of moles of HCl}}{\text{Volume in L}} = \frac{1 \text{ mol}}{0.084745 \text{ L}} \approx 11.8 \text{ M} \]

### Step 5: Calculate the normality of the solution
Normality (N) is related to molarity (M) by the formula:
\[ \text{Normality} = \text{Molarity} \times n \]
Where \( n \) is the number of hydrogen ions that can be donated by the acid. For HCl, \( n = 1 \):
\[ \text{Normality} = 11.8 \text{ M} \times 1 = 11.8 \text{ N} \]

### Final Answer
The normality of the hydrochloric acid solution is **11.8 N**.

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