The density of `1 M` solution of `NaCl` is `1.0585 g mL^(-1)`. The molality of the solution is

Options

A. 1.0585
B. `1.00`
C. `0.10`
D. 0.0585

Explanation

To find the molality of a 1 M solution of NaCl with a density of 1.0585 g/mL, 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: Calculate the Mass of the Solution
Since we have a 1 M solution, this means there is 1 mole of NaCl in 1 liter of solution.

Using the density of the solution:
\[ \text{Density} = 1.0585 \, \text{g/mL} = 1.0585 \times 1000 \, \text{g/L} = 1058.5 \, \text{g/L} \]
Thus, the mass of 1 liter of the solution is 1058.5 grams.

### Step 3: Calculate the Mass of the Solute (NaCl)
The molar mass of NaCl (sodium chloride) is:
- Sodium (Na) = 23 g/mol
- Chlorine (Cl) = 35.5 g/mol
\[ \text{Molar mass of NaCl} = 23 + 35.5 = 58.5 \, \text{g/mol} \]
Since we have 1 mole of NaCl in the solution, the mass of NaCl is:
\[ \text{Mass of NaCl} = 1 \, \text{mol} \times 58.5 \, \text{g/mol} = 58.5 \, \text{g} \]

### Step 4: Calculate the Mass of the Solvent
To find the mass of the solvent, we subtract the mass of the solute from the total mass of the solution:
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of NaCl} \]
\[ \text{Mass of solvent} = 1058.5 \, \text{g} - 58.5 \, \text{g} = 1000 \, \text{g} \]
Convert this mass into kilograms:
\[ \text{Mass of solvent} = 1000 \, \text{g} = 1 \, \text{kg} \]

### Step 5: Calculate the Molality
Now we can calculate the molality using the formula:
\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
Substituting the values:
\[ \text{Molality} = \frac{1 \, \text{mol}}{1 \, \text{kg}} = 1 \, \text{mol/kg} \]

### Final Answer
The molality of the solution is:
\[ \text{Molality} = 1 \, \text{m} \]

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