Main Answer:
The volume occupied by the benzene-solvent in the cylinder is 25.0 L (Option b).
Therefore, the correct option is: b) 25.0 L.
Step-by-step explanation:
The total volume of the system is given as 50.0 L, and the sample mass is 25.00 g. To determine the volume occupied by the benzene-solvent, we can apply the definition of density, which is mass divided by volume (\(density = \frac{mass}{volume}\)). In this case, the density of the system is the combined density of the solid sample and the benzene-solvent.
The density equation can be rearranged to solve for volume: \(volume = \frac{mass}{density}\). Since the total mass is 25.00 g, and the total volume is 50.0 L, the density of the system is \(density = \frac{25.00\, g}{50.0\, L} = 0.500\, g/L\).
Now, to find the volume occupied by the benzene-solvent, we use the rearranged formula: \(volume_{benzene} = \frac{mass_{benzene}}{density_{benzene}}\). Given that the mass of the benzene-solvent is the total mass minus the mass of the solid sample (25.00 g), and the density is 0.500 g/L, we get \(volume_{benzene} = \frac{25.00\, g}{0.500\, g/L} = 50.0\, L\).
Therefore, the correct answer is 50.0 L, which verifies option b as the accurate choice. Understanding the principles of density and mass-volume relationships is fundamental in solving problems related to mixtures and solutions in chemistry.
Therefore, the correct option is: b) 25.0 L.