Questions: A chemist must dilute 14.5 mL of 159 mM aqueous potassium dichromate (K2Cr2O7) solution until the concentration falls to 8.00 mM. She'll do this by adding distilled water to the solution until it reaches a certain final volume. Calculate this final volume, in liters. Be sure your answer has the correct number of significant digits.

Solution Steps

The problem requires us to dilute a solution of potassium dichromate from an initial concentration of 159 mM to a final concentration of 8.00 mM. We need to find the final volume of the solution after dilution.

The dilution formula is given by:

\[ C_1 V_1 = C_2 V_2 \]

where:

• \(C_1\) is the initial concentration (159 mM),
• \(V_1\) is the initial volume (14.5 mL),
• \(C_2\) is the final concentration (8.00 mM),
• \(V_2\) is the final volume in mL.

Rearrange the dilution formula to solve for \(V_2\):

\[ V_2 = \frac{C_1 V_1}{C_2} \]

Substitute the known values:

\[ V_2 = \frac{159 \, \text{mM} \times 14.5 \, \text{mL}}{8.00 \, \text{mM}} \]

Calculate \(V_2\):

\[ V_2 = \frac{2305.5 \, \text{mM} \cdot \text{mL}}{8.00 \, \text{mM}} = 288.1875 \, \text{mL} \]

Convert the final volume from milliliters to liters:

\[ V_2 = 288.1875 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.2882 \, \text{L} \]

Final Answer