53.0 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 195 mL of water. What is the final concentration? Assume the volumes are additive.
1.50M x (53.0/258) x [129/(129+195)]
0.123
To find the final concentration of the solution, we need to use the concept of molarity (M), which is defined as moles of solute per liter of solution.
First, let's find the number of moles of the solute in the original 1.50 M solution. We can use the following formula:
moles of solute = molarity (M) × volume (L)
moles of solute in original solution = 1.50 M × 0.053 L
moles of solute in original solution = 0.0795 mol
Now, let's consider the dilution process.
The 53.0 mL solution is diluted to a total volume of 258 mL. This means that the total volume of the final solution is 258 mL.
The 129 mL portion of the original solution is diluted by adding 195 mL of water. This means that the final volume of the solution is:
final volume = original volume + volume added
final volume = 129 mL + 195 mL
final volume = 324 mL
Now, we can calculate the final concentration of the solution.
The final concentration (C final) can be calculated using the formula:
C final = moles of solute / final volume (in liters)
C final = 0.0795 mol / (324 mL × 1 L/1000 mL)
C final = 0.0795 mol / 0.324 L
C final ≈ 0.245 M
Therefore, the final concentration of the solution is approximately 0.245 M.