Final answer:
To calculate the volume of a solvent given the density of a solute, subtract the mass of the solute from the total mass of the solution to find the mass of the solvent. Then, divide the mass of the solvent by its density to find the volume. When mixing liquids, use volume percent to determine the concentration.
Step-by-step explanation:
To calculate the volume of a solvent when you know the density of the solute, you first need to understand the relationship between mass, volume, and density. Density is defined as mass per unit volume (D = m/v). If you're given the density of a solute, you can use this relationship to find the mass of the solute needed for a particular solution concentration.
For example, suppose you want to prepare a solution using 150 g of NaCl (sodium chloride). If you have a target total mass for the solution, say 3000 g, you need to subtract the mass of the NaCl to find the mass of the solvent, which would be 3000 g - 150 g = 2850 g.
Knowing that the solvent is water, with a density of roughly 1 g/mL (1000 kg/m³), you can then calculate the volume of the water that needs to be added. The volume is the mass divided by the density, so in this case, it would be 2850 g ÷ 1 g/mL, which equals 2850 mL or 2.85 L of water.
When dealing with solutions where both solute and solvent are liquids, the volume percent can be quite useful. For example, mixing 40 mL of ethanol with 20 mL of water results in 60 mL of solution. The volume percent of ethanol would be (40 mL ÷ 60 mL) × 100%, yielding a 66.67% by volume concentration.