Questions: Linnea diluted 1.50 liters, L , of 0.90 M solution into a final volume of 4.0 L . What is the concentration of the solution Linnea prepared?

Solution Steps

Dilution involves adding solvent to a solution, which decreases the concentration of the solute. The amount of solute remains constant before and after dilution. The relationship between the initial and final concentrations and volumes is given by the dilution equation:

\[ C_1 V_1 = C_2 V_2 \]

where:

• \(C_1\) is the initial concentration,
• \(V_1\) is the initial volume,
• \(C_2\) is the final concentration,
• \(V_2\) is the final volume.

From the problem, we know:

• Initial concentration, \(C_1 = 0.90 \, \text{M}\)
• Initial volume, \(V_1 = 1.50 \, \text{L}\)
• Final volume, \(V_2 = 4.0 \, \text{L}\)

We need to find the final concentration, \(C_2\).

Using the dilution equation:

\[ C_1 V_1 = C_2 V_2 \]

Substitute the known values:

\[ 0.90 \, \text{M} \times 1.50 \, \text{L} = C_2 \times 4.0 \, \text{L} \]

Rearrange the equation to solve for \(C_2\):

\[ C_2 = \frac{0.90 \, \text{M} \times 1.50 \, \text{L}}{4.0 \, \text{L}} \]

Calculate \(C_2\):

\[ C_2 = \frac{1.35 \, \text{mol}}{4.0 \, \text{L}} = 0.3375 \, \text{M} \]

Final Answer