Solutes and Solvents Quick Check

Question

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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 of the diluted solution, we can use the dilution equation:

\[ C_1V_1 = C_2V_2 \]

Where:

• \( C_1 \) = initial concentration (M) of the stock solution
• \( V_1 \) = initial volume (L) of the stock solution
• \( C_2 \) = final concentration (M) of the diluted solution
• \( V_2 \) = final volume (L) of the diluted solution

From the problem, we have:

• \( C_1 = 2.1 , \text{M} \)
• \( V_1 = 500 , \text{mL} = 0.5 , \text{L} \)
• \( V_2 = 3.25 , \text{L} \)

Now we can plug these values into the equation:

\[ 2.1 , \text{M} \times 0.5 , \text{L} = C_2 \times 3.25 , \text{L} \]

Calculating the left side:

\[ 2.1 \times 0.5 = 1.05 , \text{mol} \]

Now, we can solve for \( C_2 \):

\[ 1.05 , \text{mol} = C_2 \times 3.25 , \text{L} \]

\[ C_2 = \frac{1.05 , \text{mol}}{3.25 , \text{L}} \]

Calculating \( C_2 \):

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

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

The correct response is:

0.32 M