A chemist must dilute 97.9 mL of 2.19 M aqueous silver nitrate (AgNO3) solution until the concentration falls to 1.00 M. He'll do this by adding distilled water to the solution until it reaches a certain final volume.

Calculate this final volume, in liters. Round your answer to 3 significant digits.

1 answer

To find the final volume \( V_f \) required to dilute the solution, we can use the dilution equation, which is given by:

\[ C_1 V_1 = C_2 V_2 \]

where:

  • \( C_1 \) = initial concentration (2.19 M)
  • \( V_1 \) = initial volume (97.9 mL)
  • \( C_2 \) = final concentration (1.00 M)
  • \( V_2 \) = final volume (unknown)

First, we need to convert the initial volume from mL to liters:

\[ V_1 = 97.9 , \text{mL} = 0.0979 , \text{L} \]

Now we can use the dilution equation. We have:

\[ C_1 V_1 = C_2 V_2 \]

Substituting in the known values:

\[ (2.19 , \text{M})(0.0979 , \text{L}) = (1.00 , \text{M})(V_2) \]

Calculating the left-hand side:

\[ 2.19 \times 0.0979 = 0.2147 , \text{mol} \]

Then we can set this equal to the expression for \( V_2 \):

\[ 0.2147 = 1.00 \times V_2 \]

This simplifies to:

\[ V_2 = 0.2147 , \text{L} \]

Now, rounding this result to three significant digits gives:

\[ V_2 \approx 0.215 , \text{L} \]

Thus, the final volume required to achieve a concentration of 1.00 M is

\[ \boxed{0.215 , \text{L}} \]