Final answer:
The concentration of dye in Solution C is 1.945 M after performing the serial dilutions.
Step-by-step explanation:
To find the concentration of dye in Solution C after serial dilutions, we can use the dilution equation which states that the concentration times the volume before dilution (C1V1) is equal to the concentration times the volume after dilution (C2V2), or C1V1 = C2V2.
For Solution B, the initial concentration is 20.422 M (C1) and the initial volume is 2 mL (V1). This solution is diluted with 12 mL water, so the final volume (V2) is 2 mL + 12 mL = 14 mL. Using the dilution equation, we calculate the concentration of Solution B (C2).
(20.422 M)(2 mL) = (C2)(14 mL)
C2 = (20.422 M)(2 mL) / (14 mL) = 2.917 M
Next, we perform a second dilution to create Solution C. We take 2 mL of Solution B and add 1 mL of water, giving a final volume of 3 mL. Again, we use the dilution equation to find the concentration of Solution C.
(2.917 M)(2 mL) = (C3)(3 mL)
C3 = (2.917 M)(2 mL) / (3 mL) = 1.945 M
Therefore, the concentration of dye in Solution C is 1.945 M, rounded to three significant figures.