Question

what volume of a 2.5 m lithium nitrate solution would be needed to make 150 ml of a 1.0 m solution by dilution?
m₁ = 2.5 m v₁ = ? ml
m₂ = 1.0 m v₂ = 150 ml
m₁v₁ = m₂v₂
? ml lino₃

Explanation:

Step1: Recall Dilution Formula

The formula for dilution 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: Rearrange for \( V_1 \)

We need to solve for \( V_1 \), so rearrange the formula: \( V_1=\frac{M_2V_2}{M_1} \).

Step3: Substitute Values

Substitute \( M_1 = 2.5\ M \), \( M_2 = 1.0\ M \), and \( V_2 = 150\ mL \) into the formula: \( V_1=\frac{1.0\ M\times150\ mL}{2.5\ M} \).

Step4: Calculate

First, multiply \( 1.0\ M \) and \( 150\ mL \) to get \( 150\ M\cdot mL \). Then divide by \( 2.5\ M \): \( \frac{150\ M\cdot mL}{2.5\ M}=60\ mL \).

Answer:

60