What is the molality of 1M HCl.

Explanation

To find the molality of a 1M HCl solution, we can follow these steps:

### Step 1: Understand the Definitions
- **Molarity (M)** is defined as the number of moles of solute per liter of solution.
- **Molality (m)** is defined as the number of moles of solute per kilogram of solvent.

### Step 2: Identify the Given Information
- We have a 1M HCl solution, which means there is 1 mole of HCl in 1 liter of solution.
- The density of the solution is assumed to be approximately 1 g/mL (similar to water) since no specific density is provided.

### Step 3: Calculate the Mass of the Solution
- Since the density is 1 g/mL, the mass of 1 liter (1000 mL) of the solution is:
\[ \text{Mass of solution} = 1000 \, \text{mL} \times 1 \, \text{g/mL} = 1000 \, \text{g} \]

### Step 4: Calculate the Mass of HCl
- The molar mass of HCl is approximately 36.5 g/mol. Therefore, the mass of 1 mole of HCl is:
\[ \text{Mass of HCl} = 36.5 \, \text{g} \]

### Step 5: Calculate the Mass of the Solvent (Water)
- The mass of the solvent (water) can be calculated by subtracting the mass of HCl from the total mass of the solution:
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of HCl} = 1000 \, \text{g} - 36.5 \, \text{g} = 963.5 \, \text{g} \]

### Step 6: Convert the Mass of Solvent to Kilograms
- To convert grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{963.5 \, \text{g}}{1000} = 0.9635 \, \text{kg} \]

### Step 7: Calculate the Molality
- Now we can calculate the molality using the formula:
\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{1 \, \text{mol}}{0.9635 \, \text{kg}} \approx 1.038 \, \text{mol/kg} \]

### Final Answer
The molality of the 1M HCl solution is approximately **1.038 mol/kg**.

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