When excess of `CaCO_3` is treated with 100 ml. of HCI solution, the `CO_2` gas obtained was found to be `1.12` litre (at N.T.P.). What is the normality of HCI?

Options

A. 0.2 N
B. 1 N
C. 0.1 N
D. 2 N

Answer

To find the normality of the HCl solution when treated with excess CaCO₃, we can follow these steps:

### Step 1: Write the balanced chemical equation
When calcium carbonate (CaCO₃) reacts with hydrochloric acid (HCl), the products are calcium chloride (CaCl₂), carbon dioxide (CO₂), and water (H₂O). The balanced reaction is:

\[ \text{CaCO}_3 + 2 \text{HCl} \rightarrow \text{CaCl}_2 + \text{CO}_2 + \text{H}_2\text{O} \]

### Step 2: Calculate the number of moles of CO₂ produced
At NTP (Normal Temperature and Pressure), 1 mole of gas occupies 22.4 liters. Given that 1.12 liters of CO₂ was produced, we can calculate the number of moles of CO₂:

\[ \text{Number of moles of CO}_2 = \frac{\text{Volume of CO}_2}{\text{Molar volume at NTP}} = \frac{1.12 \, \text{L}}{22.4 \, \text{L/mol}} = 0.05 \, \text{moles} \]

### Step 3: Relate moles of HCl to moles of CO₂
From the balanced equation, we see that 2 moles of HCl produce 1 mole of CO₂. Therefore, the number of moles of HCl can be calculated as follows:

\[ \text{Number of moles of HCl} = 2 \times \text{Number of moles of CO}_2 = 2 \times 0.05 = 0.1 \, \text{moles} \]

### Step 4: Calculate the molarity of HCl
The molarity (M) of a solution is defined as the number of moles of solute per liter of solution. Given that the volume of HCl solution is 100 mL (which is 0.1 L), we can calculate the molarity:

\[ \text{Molarity of HCl} = \frac{\text{Number of moles of HCl}}{\text{Volume of solution in liters}} = \frac{0.1 \, \text{moles}}{0.1 \, \text{L}} = 1 \, \text{M} \]

### Step 5: Calculate the normality of HCl
For HCl, which is a strong acid and dissociates completely, the normality (N) is equal to the molarity (M) because the n-factor (the number of H⁺ ions produced per molecule of HCl) is 1.

\[ \text{Normality of HCl} = \text{Molarity of HCl} \times \text{n-factor} = 1 \, \text{M} \times 1 = 1 \, \text{N} \]

### Final Answer
The normality of the HCl solution is **1 N**.

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