Question

you want to determine the volume of \\(2.5\text{ m}\\) lithium nitrate solution needed to make \\(150\text{ ml}\\) of a \\(1.0\text{ m}\\) solution. what is \\(v_1\\) (volume of the concentrated solution) for this dilution?

the unknown \\(1.0\text{ m } \text{lino}_3\\) \\(150\text{ ml}\\)

Explanation:

Identify the given values

We analyze the problem statement to identify the variables for the dilution equation:

• Initial concentration \(M_1 = 2.5\text{ M}\)
• Final concentration \(M_2 = 1.0\text{ M}\)
• Final volume \(V_2 = 150\text{ mL}\)

Identify the target unknown

The question asks to identify \(V_1\), which is the volume of the concentrated solution needed.

• Since we want to determine this volume, it is not yet known.

Match with the options

We compare our target unknown with the provided choices:

• "the unknown"
• "1.0 M \(\text{LiNO}_3\)"
• "150 mL"

Since \(V_1\) is the value we want to find, it represents the unknown.

Answer:

• (A) the unknown (Correct answer)
• (B) 1.0 M \(\text{LiNO}_3\)
• (C) 150 mL