A 0.167 M solution contains 5.0 g of NaOH. What is the volume of the solution in liters?

• A. 0.30 L
• B. 0.75 L
• C. 0.71 L
• D. 0.50 L

Answer: (C)

Verified step by step guidance

1. Identify the known values: the molarity (M) of the solution is 0.167 M, and the mass of NaOH dissolved is 5.0 g.
2. Calculate the number of moles of NaOH using its molar mass. The molar mass of NaOH is approximately 40.0 g/mol, so use the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{5.0\ \text{g}}{40.0\ \text{g/mol}}\).
3. Recall the definition of molarity: \(M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\). Rearrange this formula to solve for volume: \(V = \frac{\text{moles of solute}}{M}\).
4. Substitute the moles of NaOH calculated in step 2 and the given molarity into the rearranged formula to find the volume: \(V = \frac{\text{moles}}{0.167\ \text{M}}\).
5. Perform the division to find the volume in liters. This volume corresponds to the total volume of the solution containing 5.0 g of NaOH at 0.167 M concentration.