Final answer:
To find the volume of a 40% sucrose solution needed for 1.5 mol of carbon atoms, calculate the moles of sucrose needed, convert that to mass, and use the solution's density to find the volume. Due to a mismatch between the calculated answer and the provided options, there seems to be an error in the question or choices.
Step-by-step explanation:
To calculate the volume of a 40% sucrose solution needed to furnish 1.5 mol of carbon atoms, first note that sucrose is C12H22O11 and thus contains 12 mol of carbon atoms per mol of sucrose. Therefore, to get 1.5 mol of carbon atoms, we need 1.5 / 12 = 0.125 mol of sucrose.
Knowing the density of the sucrose solution is 0.911 g/mL, we can calculate the mass of this volume of solution:
Mass = Density × Volume
Mass of sucrose = 0.125 mol × 342.3 g/mol (molar mass of sucrose).
The mass of sucrose required is therefore 0.125 × 342.3 = 42.7875 g. As the solution is 40% sucrose, this mass is 40% of the total mass of solution, which is 42.7875 g / 0.40 = 106.96875 g. Using the density (0.911 g/mL), we find the volume required:
Volume = Mass / Density = 106.96875 g / 0.911 g/mL = 117.41 mL.
However, none of the answer choices match this calculation, which indicates that there may be a mistake in the original question or the answer choices provided.