75.0 mL of a 1.80 M solution is diluted to a volume of 258 mL. A 129-mL portion of that solution is diluted using 187 mL of water. What is the final concentration?
To find the final concentration, we need to understand how dilution affects concentration. Dilution is the process of adding a solvent, usually water, to decrease the concentration of a solute.
First, let's calculate the amount of solute present in the 75.0 mL of the 1.80 M solution. The formula for calculating the amount of solute is:
Amount of solute = Concentration × Volume
Amount of solute = 1.80 M × 75.0 mL = 135.0 mmol
Next, let's calculate the total volume of the diluted solution. We start with 75.0 mL and add 258 mL of water:
Total volume = 75.0 mL + 258 mL = 333 mL
Now, let's calculate the final concentration of the solution after dilution. The formula for calculating concentration is:
Concentration = Amount of solute / Total volume
Concentration = 135.0 mmol / 333 mL
To get the concentration in molarity (M), we need to convert milliliters (mL) to liters (L). Since 1 L is equal to 1000 mL, we divide the total volume by 1000:
Concentration = 135.0 mmol / (333 mL ÷ 1000) L
Concentration = 135.0 mmol / 0.333 L
Concentration ≈ 405.41 M
Therefore, the final concentration of the solution after dilution is approximately 405.41 M.