Final answer:
The calculated molality of the sulfuric acid solution is 40.71 mol/kg. However, this answer does not match any of the given options, suggesting there might be an error in the provided question values or options.
Step-by-step explanation:
To calculate the molality of a 15 M H2SO4 solution with a density of 1.84 g/ml, first we need to find the mass of the solution and the number of moles of the solute (H2SO4).
Assuming 1 L of solution, we have:
- Mass of the solution = density × volume = 1.84 g/ml × 1000 ml = 1840 g
- Moles of H2SO4 = molarity × volume = 15 mol/L × 1 L = 15 moles
The mass of the water (solvent) can be found by subtracting the mass of the solute from the total mass of the solution.
- Mass of H2SO4 = moles × molar mass = 15 moles × 98.1 g/mol = 1471.5 g
- Mass of water = mass of solution - mass of H2SO4 = 1840 g - 1471.5 g = 368.5 g
- Mass of water in kilograms = 368.5 g ÷ 1000 = 0.3685 kg
Now we can calculate the molality:
- Molality = moles of solute / mass of solvent in kilograms = 15 moles / 0.3685 kg = 40.71 mol/kg
However, none of the options given match the calculated molality of 40.71 mol/kg. Please double-check the values provided in the question for accuracy. If you have copied the question correctly, it seems there might be a mistake in the options provided.