54.0 mL of a 1.50 M solution is diluted to a total volume of 258 mL. A 129-mL portion of that solution is diluted by adding 165 mL of water. What is the final concentration?
1.50M x (54.0/258) x [129/(129+165)] = ?M and this assumes that the 129 + 165 volumes are additive to give a final volume of 294 mL.
0.0944
To find the final concentration, we need to calculate the number of moles of solute in the initial solution and then divide it by the final volume.
Step 1: Calculate the moles of solute in the initial solution.
moles of solute = volume of solution (in liters) × molarity
moles of solute = (54.0 mL ÷ 1000 mL/L) × 1.50 mol/L
moles of solute = 0.081 mol
Step 2: Find the final volume of the solution after dilution.
final volume = initial volume + volume added
final volume = 54.0 mL + 165 mL
final volume = 219 mL
Step 3: Calculate the final concentration.
final concentration = moles of solute ÷ final volume
final concentration = 0.081 mol ÷ (219 mL ÷ 1000 mL/L)
final concentration = 0.370 M
Therefore, the final concentration of the solution is 0.370 M.
To find the final concentration, we need to consider the dilution of the original solution.
The original solution has a volume of 54.0 mL and a concentration of 1.50 M.
First, let's calculate the moles of solute in the original solution:
moles of solute = concentration × volume
moles of solute = 1.50 M × 54.0 mL
Next, let's only consider the diluted volume. The final volume is 258 mL, but we are only interested in a 129 mL portion. Let's calculate the moles of solute in this portion:
moles of solute in 129 mL = (moles of solute in original solution) × (final volume of 129 mL / original volume of 54.0 mL)
moles of solute in 129 mL = (1.50 M × 54.0 mL) × (129 mL / 54.0 mL)
Now, let's calculate the final volume of the diluted solution after adding 165 mL of water to the 129 mL portion:
final volume of diluted solution = 129 mL + 165 mL
Finally, let's calculate the final concentration using the moles of solute calculated earlier and the final volume:
final concentration = (moles of solute in 129 mL) / (final volume of diluted solution)
By plugging in the values, you can find the final concentration.