What is the final volume V2 in milliliters when 0.551 L of a 50.0% (m/v) solution is diluted to 23.5% (m/v)?

To calculate the final volume (V2) when diluting a solution, you can use the concept of the conservation of mass. The mass of the solute before and after dilution remains constant.

Let's calculate the mass of the solute in the initial solution. We are given a 50.0% (m/v) solution, which means there is 50.0 g of solute in every 100 mL of solution.

First, convert the initial volume from liters to milliliters (there are 1000 milliliters in 1 liter): 0.551 L = 0.551 * 1000 mL = 551 mL

Now, calculate the mass of the solute in the initial solution: Mass of solute = Volume of solution * Percentage concentration (in g/mL) Mass of solute = 551 mL * 50.0 g/100 mL = 275.5 g

This mass of solute will remain the same after dilution. To find out the final volume (V2) needed for a 23.5% (m/v) solution, rearrange the concentration formula: Percentage concentration (m/v) = Mass of solute (g) / Volume of solution (mL)

Plug in the known values (mass of solute and final concentration) and solve for V2: 23.5% = 275.5 g / V2

V2 = 275.5 g / 23.5% = 275.5 g / 0.235 g/mL

V2 ≈ 1172.34 mL

So the final volume V2 is approximately 1172.34 milliliters.