Question

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? (1 point) Responses 13.65 M 13.65 M 323.08 M 323.08 M 0.01 M 0.01 M 0.32 M

Answer 1

To find the molarity (M) of the diluted solution, we can use the dilution formula:

\[
C_1V_1 = C_2V_2
\]

where:
- \(C_1\) is the initial concentration (2.1 M),
- \(V_1\) is the initial volume (500 mL),
- \(C_2\) is the final concentration (which we want to find),
- \(V_2\) is the final volume (3.25 L).

First, we need to convert the volume from liters to milliliters for consistency:

\[
V_2 = 3.25 \, \text{L} = 3250 \, \text{mL}
\]

Now we can plug the values into the dilution formula:

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

Calculating the left side:

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

Now we set this equal to the right side:

\[
1050 = C_2(3250)
\]

To find \(C_2\), we rearrange the equation:

\[
C_2 = \frac{1050}{3250}
\]

Calculating this gives:

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

Rounding to two decimal places, we get:

\[
C_2 \approx 0.32 \, \text{M}
\]

Therefore, the molarity of the diluted solution is **0.32 M**.