Find the molality and molarity of 15% H₂SO₄ if the density is 0.020 gram per cubic centimeter.

The molarity of the 15% H₂SO₄ solution is approximately 0.0306 M, and the molality is approximately 1.80 m.
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Answered by Anonymous | 2025-07-04

To find the molality and molarity of a 15% H₂SO₄ solution with a given density of 0.020 grams per cubic centimeter, let's first understand the definitions of molality and molarity.
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
Molarity (M) is defined as the number of moles of solute per liter of solution.
Given:

The density of the solution is 0.020 g/cm³ or 20 g/L (since 1 cm³ = 1 mL).
The solution is 15% H₂SO₄ by weight.

Let's calculate the molarity and molality step by step:
1. Convert the density into kg/L:
Density = 0.020 g/cm 3 = 20 g/L
2. Determine the mass of H₂SO₄ in 1 liter of solution:
Since the solution is 15% H₂SO₄ by mass, for 100 g of solution, 15 g is H₂SO₄.

Therefore, in 1 liter (1000 mL) of solution, the mass of H₂SO₄ = ( 0.15 × 20 g ) = 3 g .

3. Calculate the moles of H₂SO₄:
The molar mass of H₂SO₄ is approximately 98.079 g/mol.
Moles of H₂SO₄ = 98.079 g/mol 3 g ​ ≈ 0.0306 mol
4. Calculate the molarity (M):
Since we have 0.0306 mol of H₂SO₄ in 1 L,
M ( Molarity ) = 0.0306 mol/L = 0.0306 M
5. Calculate the mass of solvent (water) in kg:
For the solution: Total mass = 100 g. Mass of H₂SO₄ (solute) = 15 g, Mass of solvent (water) = 100 g - 15 g = 85 g = 0.085 kg
6. Calculate the molality (m):
m ( Molality ) = Kg of solvent Moles of H₂SO₄ ​ = 0.085 kg 0.0306 mol ​ ≈ 0.360 mol/kg
Conclusion:

The molarity of the solution is approximately 0.0306 M.
The molality of the solution is approximately 0.360 mol/kg.

Answered by MasonWilliamTurner | 2025-07-06