75.0 mL of a 1.50 M solution is diluted to a total volume of 278 mL. A 139-mL portion of that solution is diluted by adding 139 mL of water. What is the final concentration? Assume the volumes are additive.
1.50 M x (75.0 mL/278 mL) x [139 mL/(139+139)] = ?
To find the final concentration, we can use the concept of dilution.
Dilution is a process in which the concentration of a solution is reduced by adding additional solvent (in this case, water).
Here's how we can calculate the final concentration:
1. Calculate the amount (moles) of solute before dilution:
moles of solute = initial concentration × initial volume
moles of solute = 1.50 M × 75.0 mL
2. Calculate the final volume after dilution:
final volume = initial volume + volume of water
final volume = 75.0 mL + 139 mL
3. Calculate the final concentration using the moles of solute and final volume:
final concentration = moles of solute / final volume
Let's calculate the values step by step:
1. Calculate the amount (moles) of solute before dilution:
moles of solute = 1.50 M × 75.0 mL
moles of solute = 0.1125 moles
2. Calculate the final volume after dilution:
final volume = 75.0 mL + 139 mL
final volume = 214 mL
3. Calculate the final concentration using the moles of solute and final volume:
final concentration = moles of solute / final volume
final concentration = 0.1125 moles / 214 mL
Now, to simplify the final concentration, we need to convert mL to liters:
final concentration = 0.1125 moles / 0.214 L
final concentration = 0.525 M
Therefore, the final concentration is 0.525 M.