Question

what volume of solution (in ml) is needed to dilute a 2.0 m hi solution to make 75.0 ml of a 0.10 m solution?
○ 3.75 ml
○ 4.92×10⁻⁴ ml
○ 10.0 ml
○ 59.0 ml

Explanation:

Step1: Recall Dilution Formula

The dilution formula is \( M_1V_1 = M_2V_2 \), where \( M_1 \) is the initial molarity, \( V_1 \) is the initial volume, \( M_2 \) is the final molarity, and \( V_2 \) is the final volume.

Step2: Identify Known Values

We know \( M_1 = 2.0 \, \text{M} \), \( M_2 = 0.10 \, \text{M} \), and \( V_2 = 75.0 \, \text{mL} \). We need to find \( V_1 \).

Step3: Rearrange Formula for \( V_1 \)

Rearranging the dilution formula gives \( V_1 = \frac{M_2V_2}{M_1} \).

Step4: Substitute Values

Substitute \( M_2 = 0.10 \, \text{M} \), \( V_2 = 75.0 \, \text{mL} \), and \( M_1 = 2.0 \, \text{M} \) into the formula:
\( V_1 = \frac{0.10 \, \text{M} \times 75.0 \, \text{mL}}{2.0 \, \text{M}} \)

Step5: Calculate \( V_1 \)

First, multiply \( 0.10 \) and \( 75.0 \): \( 0.10 \times 75.0 = 7.5 \). Then divide by \( 2.0 \): \( \frac{7.5}{2.0} = 3.75 \, \text{mL} \).

Answer:

3.75 mL