A solution of sodium sulfate contains 92g of `Na^(+)` ions per kilogram of water. The molality of `Na^(+)` ions in the solution in mol `kg^(-1)` is

Options

A. 16
B. 8
C. 4
D. 12

Answer

To find the molality of sodium ions (Na⁺) in the solution, we can follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula for molality is:
\[ m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]

### Step 2: Identify the mass of the solvent
In this case, we are given that there is 1 kg of water (solvent) in the solution. Therefore, the mass of the solvent is:
\[ \text{Mass of solvent} = 1 \text{ kg} \]

### Step 3: Calculate the number of moles of sodium ions
To find the number of moles of sodium ions, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

We are given that the mass of sodium ions (Na⁺) is 92 g. The molar mass of sodium (Na) is approximately 23 g/mol. Therefore, we can calculate the number of moles as follows:
\[ \text{Number of moles} = \frac{92 \text{ g}}{23 \text{ g/mol}} \]

### Step 4: Perform the calculation
Calculating the number of moles:
\[ \text{Number of moles} = \frac{92}{23} = 4 \text{ moles} \]

### Step 5: Calculate the molality
Now that we have the number of moles of sodium ions and the mass of the solvent, we can calculate the molality:
\[ m = \frac{4 \text{ moles}}{1 \text{ kg}} = 4 \text{ mol/kg} \]

### Final Answer
The molality of Na⁺ ions in the solution is:
\[ \text{Molality} = 4 \text{ mol/kg} \]

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