If the density of some lake water is 1.25 g/L and contains 92 g of Na⁺ ions per kilogram of water, calculate the molality of Na⁺ ions in the lake.

To find the molality of Na⁺ ions in the lake water, we first need to understand the definitions involved. Molality (m) is defined as the number of moles of solute per kilogram of solvent.

Step 1: Calculate Moles of Na⁺

We start by calculating the number of moles of sodium ions (Na⁺). The molar mass of Na⁺ is approximately 23 g/mol. Given that there are 92 g of Na⁺ ions:

Moles of Na⁺ = Mass of Na⁺ / Molar Mass of Na⁺

Moles of Na⁺ = 92 g / 23 g/mol = 4 moles

Step 2: Determine the Mass of Solvent

Next, we need to find the mass of the solvent, which is the water. Since the density of the lake water is 1.25 g/L, we can convert this to kilograms:

1 L of water = 1.25 kg (since 1 g = 0.001 kg)

Step 3: Calculate Molality

Now we can calculate the molality using the formula:

Molality (m) = Moles of solute / Mass of solvent in kg

Molality = 4 moles / 1.25 kg = 3.2 m

Final Result

The molality of Na⁺ ions in the lake water is 3.2 m.