Question

The molarity of an aqueous solution containing 0.4g of NaOH (molar mass=40g/mol) in 250mL of a solution is

• A. 0.04M
• B. 0.02M
• C. 0.20M
• D. 0.40M
• E. 0.08M

Hint:

For common volumes like \(250 \text{ mL}\), \(500 \text{ mL}\), or \(100 \text{ mL}\), think of them as fractions of a liter (\(1/4\), \(1/2\), \(1/10\)).
Multiply the moles by the reciprocal of the fraction (e.g., \(\times 4\) for \(250 \text{ mL}\)) to get the molarity quickly.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Molarity (\(M\)) is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per liter of solution.

Step 2: Key Formula or Approach:
The formula for molarity is given by:
\[ M = \frac{\text{Mass of solute (g)}}{\text{Molar mass of solute (g/mol)}} \times \frac{1000}{\text{Volume of solution (mL)}} \]

Step 3: Detailed Explanation:
First, identify the given values from the question:
Mass of NaOH (\(w\)) = \(0.4 \text{ g}\)
Molar mass of NaOH (\(GMM\)) = \(40 \text{ g/mol}\)
Volume of the solution (\(V\)) = \(250 \text{ mL}\)
Now, calculate the number of moles of NaOH:
\[ \text{Moles} = \frac{0.4}{40} = 0.01 \text{ moles} \]
Finally, calculate the molarity:
\[ M = \frac{0.01 \times 1000}{250} \]
\[ M = 0.01 \times 4 = 0.04 \text{ M} \]

Step 4: Final Answer:
The molarity of the NaOH solution is \(0.04 \text{ M}\).