74.0 mL of a 1.80 M solution is diluted to a volume of 248 mL. A 124-mL portion of that solution is diluted using 135 mL of water. What is the final concentration?
1.80M x (74.0/248) x (124.0/259)= ? and that's assuming that the 124 mL + 135 mL are additive (to make a solution of 259 mL). Some solutions are not additive.
To find the final concentration of the solution, we need to calculate the amount of solute present before and after dilution and then divide it by the volume of the final solution.
Step 1: Calculate the amount of solute before dilution.
The amount of solute before dilution can be calculated using the formula:
Amount of solute before dilution = Concentration * Volume
Given:
Concentration before dilution = 1.80 M
Volume before dilution = 74.0 mL
Amount of solute before dilution = 1.80 M * 74.0 mL
Step 2: Calculate the amount of solute after the first dilution.
The amount of solute after dilution can be calculated by subtracting the volume of the solvent (water) from the total volume of the solution after dilution.
Volume of solute after dilution = Volume before dilution - Volume of water added
Given:
Volume before dilution = 248 mL
Volume of water added = 135 mL
Volume of solute after dilution = 248 mL - 135 mL
Step 3: Calculate the final concentration.
The final concentration can be calculated using the formula:
Concentration = Amount of solute after dilution / Volume of the final solution
Given:
Volume of the final solution = 124 mL + 135 mL (volume of solute after dilution + volume of water added)
Concentration = (Amount of solute after dilution) / (Volume of the final solution)
Now, let's substitute the values we calculated:
Concentration = (Volume before dilution * Concentration before dilution) / (Volume before dilution - Volume of water added + Volume of water added)
Concentration = (74.0 mL * 1.80 M) / (248 mL)
Now, we can calculate the final concentration using this formula.