51.0 mL of a 1.20 M solution is diluted to a total volume of 248 mL. A 124-mL portion of that solution is diluted by adding 125 mL of water. What is the final concentration? Assume the volumes are additive.
How many mols did you start with? That's M x L = 1.20 x 0.051 = 0.0612 and that is in 248 so the concn of the first solution is 0.0612/0.248 = about 0.25 but you should redo it for more accuracy.
Then 124 mL of that is diluted.
New concn is about 0.25 x [(124/(124+125)] = ?
To find the final concentration of a solution, we need to use the formula:
C1V1 = C2V2
Where:
C1 is the initial concentration of the solution
V1 is the initial volume of the solution
C2 is the final concentration of the solution
V2 is the final volume of the solution
Let's work through the problem step by step:
Step 1: Calculate the final volume of the initial solution.
The initial volume of the solution is 51.0 mL, and it is diluted to a total volume of 248 mL. To find the final volume of the initial solution, we subtract the volume of water added from the total volume of the solution.
Final volume of the initial solution = Total volume - Volume of water added
Final volume of the initial solution = 248 mL - 125 mL
Final volume of the initial solution = 123 mL
Step 2: Calculate the final concentration of the initial solution.
Using the formula C1V1 = C2V2, we can plug in the values we have:
Initial concentration (C1) = 1.20 M
Initial volume (V1) = 51.0 mL
Final concentration (C2) = ?
Final volume (V2) = 123 mL
1.20 M * 51.0 mL = C2 * 123 mL
C2 = (1.20 M * 51.0 mL) / 123 mL
C2 = 0.498 M
Step 3: Calculate the final concentration of the solution after dilution with water.
We are given that a 124 mL portion of the solution is diluted by adding 125 mL of water. So, the final volume of the solution is the sum of the volume of the portion and the volume of water added.
Final volume of solution = Volume of portion + Volume of water added
Final volume of solution = 124 mL + 125 mL
Final volume of solution = 249 mL
The final concentration of the solution after dilution with water can be calculated using the formula C1V1 = C2V2:
Initial concentration (C1) = 0.498 M (calculated in Step 2)
Initial volume (V1) = 124 mL
Final concentration (C2) = ?
Final volume (V2) = 249 mL
0.498 M * 124 mL = C2 * 249 mL
C2 = (0.498 M * 124 mL) / 249 mL
C2 = 0.248 M
Therefore, the final concentration of the solution after dilution with water is 0.248 M.