Final answer:
The molarity of a 40.0% by mass aqueous solution of sulfuric acid, with a density of 1.3057 g/mL, is found to be 5.326 M, yet the closest provided answer option is a) 6.45 M. Note that an exact match to the calculated result is not among the options listed.
Step-by-step explanation:
To find the molarity of a 40.0% by mass aqueous solution of sulfuric acid, H₂SO₄, with a density of 1.3057 g/mL, you would follow these steps:
- First, calculate the mass of 1 liter (1000 mL) of the solution by multiplying the density by the volume (1.3057 g/mL × 1000 mL = 1305.7 g).
- Next, find the mass of the solute (sulfuric acid) by taking 40.0% of the total mass of the solution (0.40 × 1305.7 g = 522.28 g).
- Calculate the number of moles of H₂SO₄ by dividing the mass of the solute by its molar mass (98.079 g/mol for H₂SO₄).
- Finally, calculate the molarity by taking the number of moles of solute and dividing it by the volume of the solution in liters. The number of moles of H₂SO₄ is 522.28 g ÷ 98.079 g/mol = 5.326 moles. The molarity is then 5.326 moles ÷ 1 L = 5.326 M, which is closest to option a) 6.45 M.
It's important to note that the options provided in the question don't match the calculated result. Since they are predefined, you must select the closest answer, assuming that there is a likelihood of rounding or different significant figures being considered. The closest option provided is 6.45 M, yet it does not match the exact calculation.