63.0 mL of a 1.30 M solution is diluted to a total volume of 248 mL. A 124-mL portion of that solution is diluted by adding 173 mL of water. What is the final concentration? Assume the volumes are additive.
1.30 M x (63 mL/248 mL) x [124 mL/(124+173)] = ? M
To find the final concentration, we need to consider the original solution and the dilution that occurred.
First, let's determine the number of moles of solute in the original solution using the formula:
moles of solute = concentration × volume
Given:
concentration of original solution = 1.30 M
volume of original solution = 63.0 mL
moles of solute in original solution = 1.30 M × 63.0 mL
moles of solute in original solution = 81.9 mmol (millimoles)
Now, let's consider the dilution that occurs when the 124 mL portion is diluted by adding 173 mL of water.
The total volume after dilution = 124 mL + 173 mL
The total volume after dilution = 297 mL
Since the volumes are additive, we know that the final volume is 297 mL.
We can now find the final concentration using the formula:
final concentration = moles of solute / final volume
Given:
moles of solute = 81.9 mmol
final volume = 297 mL
final concentration = 81.9 mmol / 297 mL
To express the concentration in Molarity (M), we need to convert mmol to moles and mL to liters:
final concentration = (81.9 mmol / 1000) / (297 mL / 1000)
final concentration = 0.275 M
Therefore, the final concentration of the solution is 0.275 M.