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

0.01 M
0.01 M

0.32 M
0.32 M

13.65 M
13.65 M

323.08 M

Answer 1

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

\[ C_1V_1 = C_2V_2 \]

where:
- \( C_1 \) is the initial concentration (molarity) of the stock solution,
- \( V_1 \) is the initial volume of the stock solution,
- \( C_2 \) is the concentration (molarity) of the diluted solution,
- \( V_2 \) is the final volume of the diluted solution.

Given:
- \( C_1 = 2.1 \, \text{M} \)
- \( V_1 = 500 \, \text{mL} = 0.500 \, \text{L} \)
- \( V_2 = 3.25 \, \text{L} \)

We can plug these values into the equation to solve for \( C_2 \):

\[
(2.1 \, \text{M})(0.500 \, \text{L}) = C_2(3.25 \, \text{L})
\]

Calculating the left side:

\[
2.1 \times 0.500 = 1.05 \, \text{mol}
\]

Now, we substitute this value into the equation:

\[
1.05 = C_2(3.25)
\]

To solve for \( C_2 \):

\[
C_2 = \frac{1.05}{3.25}
\]

Calculating this:

\[
C_2 \approx 0.323 \, \text{M}
\]

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

Thus, the correct response is **0.32 M**.