Question

you want to determine the volume of 2.5 m lithium nitrate solution needed to make 150 ml of a 1.0 m solution. what is v₁ (volume of the concentrated solution) for this dilution? the unknown 1.0 m lino₃ 150 ml

Explanation:

Step1: Recall Dilution Formula

The dilution formula is \( M_1V_1 = M_2V_2 \), where \( M_1 \) is the molarity of the concentrated solution, \( V_1 \) is its volume, \( M_2 \) is the molarity of the diluted solution, and \( V_2 \) is its volume.

Step2: Identify Known Values

We know \( M_1 = 2.5 \, M \), \( M_2 = 1.0 \, M \), \( V_2 = 150 \, \text{mL} \), and we need to find \( V_1 \).

Step3: Rearrange Formula for \( V_1 \)

Rearrange \( M_1V_1 = M_2V_2 \) to solve for \( V_1 \): \( V_1 = \frac{M_2V_2}{M_1} \).

Step4: Substitute Values

Substitute \( M_2 = 1.0 \, M \), \( V_2 = 150 \, \text{mL} \), and \( M_1 = 2.5 \, M \) into the formula: \( V_1 = \frac{1.0 \, M \times 150 \, \text{mL}}{2.5 \, M} \).

Step5: Calculate \( V_1 \)

Simplify the expression: \( V_1 = \frac{150}{2.5} = 60 \, \text{mL} \).

Answer:

\( 60 \, \text{mL} \)