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?
A. 13.65 M
B. 323.08 M
C. 0.01 M D
D. 0.32 M

Answer 1

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

\[
M_1V_1 = M_2V_2
\]

where:
- \( M_1 \) is the molarity of the stock solution,
- \( V_1 \) is the volume of the stock solution,
- \( M_2 \) is the molarity of the diluted solution,
- \( V_2 \) is the volume of the diluted solution.

Given:
- \( M_1 = 2.1 \, \text{M} \)
- \( V_1 = 500 \, \text{mL} = 0.5 \, \text{L} \)
- \( V_2 = 3.25 \, \text{L} \)

We want to find \( M_2 \).

Plugging in the values into the formula:

\[
(2.1 \, \text{M})(0.5 \, \text{L}) = M_2(3.25 \, \text{L})
\]

Calculating the left side:

\[
1.05 = M_2(3.25)
\]

Now, solve for \( M_2 \):

\[
M_2 = \frac{1.05}{3.25}
\]

Calculating \( M_2 \):

\[
M_2 \approx 0.32 \, \text{M}
\]

Therefore, the molarity of the diluted solution is **0.32 M** (Option D).