71.0 mL of a 1.30 M solution is diluted to a total volume of 238 mL. A 119-mL portion of that solution is diluted by adding 105 mL of water. What is the final concentration? Assume the volumes are additive.
To find the final concentration, we need to consider the dilution of the original solution and the dilution of the portion taken from it.
1. Dilution of the original solution:
Given:
- Initial volume (V1) = 71.0 mL
- Initial concentration (C1) = 1.30 M
- Final volume (V2) = 238 mL
We can use the dilution formula to calculate the final concentration (C2) of the original solution after dilution:
C1V1 = C2V2
Substituting the values:
1.30 M * 71.0 mL = C2 * 238 mL
Solving for C2:
C2 = (1.30 M * 71.0 mL) / 238 mL
C2 = 0.386 M
So, the concentration of the original solution after dilution is 0.386 M.
2. Dilution of the portion taken:
Given:
- Initial volume (V1) = 119 mL
- Amount of water added (V2) = 105 mL
Since the volumes are additive, the final volume (Vf) can be calculated as the sum of the initial volume and the volume of water added:
Vf = V1 + V2
Vf = 119 mL + 105 mL
Vf = 224 mL
The amount of solute remains the same after dilution, so the concentration (Cf) of the portion taken can be calculated using the formula:
Cf = C1V1 / Vf
Substituting the values:
Cf = (0.386 M * 119 mL) / 224 mL
Cf = 0.205 M
Therefore, the final concentration after diluting the portion taken with water is 0.205 M.
To determine the final concentration, we can use the formula:
C1V1 = C2V2
Where:
C1 = initial concentration
V1 = initial volume
C2 = final concentration
V2 = final volume
First, let's calculate the initial volume of the 1.30 M solution:
C1 = 1.30 M
V1 = 71.0 mL
Next, let's calculate the final volume of the solution after dilution:
Initial volume + Volume of water added = Final volume
V1 + Volume of water added = 238 mL
Now, let's calculate the final concentration after dilution:
C2 = (C1 x V1) / V2
Given that a 119 mL portion of the solution is diluted by adding 105 mL of water, we can calculate the final concentration using the formula:
C2 = (1.30 M x 119 mL) / (119 mL + 105 mL + 238 mL)
First, calculate the numerator:
Numerator = (1.30 M) x (119 mL) = 154.7 mol
Next, calculate the denominator:
Denominator = (119 mL) + (105 mL) + (238 mL) = 462 mL
Finally, calculate the final concentration using the values obtained:
C2 = 154.7 mol / 462 mL = 0.3352 M
Therefore, the final concentration after dilution is approximately 0.3352 M.