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.