A scientist has 500 mL of a 2.1 M stock solution. She dilutes the solution, and the volume of the solution after the dilution is 3.25 L. What is the molarity (M) of the diluted solution? (2 points) Responses 323.08 M 323.08 M 13.65 M 13.65 M 0.01 M 0.01 M 0.32 M

1 answer

To find the molarity of the diluted solution, we can use the dilution equation:

\[ C_1 V_1 = C_2 V_2 \]

Where:

  • \( C_1 \) is the concentration of the stock solution (2.1 M),
  • \( V_1 \) is the volume of the stock solution (500 mL),
  • \( C_2 \) is the molarity of the diluted solution,
  • \( V_2 \) is the volume of the diluted solution (3.25 L, which is 3250 mL).

First, we need to convert the volumes to the same unit. Since \( V_1 \) is in mL and \( V_2 \) is in L, we'll convert \( V_2 \) to mL:

\[ V_2 = 3.25 \text{ L} \times 1000 \text{ mL/L} = 3250 \text{ mL} \]

Now, we can plug in the values into the dilution equation:

\[ (2.1 \text{ M})(500 \text{ mL}) = C_2 (3250 \text{ mL}) \]

Calculating the left side:

\[ (2.1 \text{ M})(500 \text{ mL}) = 1050 \text{ M mL} \]

Now, we plug in the values to solve for \( C_2 \):

\[ 1050 \text{ M mL} = C_2 (3250 \text{ mL}) \]

Now, divide both sides by 3250 mL:

\[ C_2 = \frac{1050 \text{ M mL}}{3250 \text{ mL}} \]

Calculating \( C_2 \):

\[ C_2 = 0.3231 \text{ M} \]

So the molarity of the diluted solution is approximately 0.32 M.

The correct response is 0.32 M.