To convert percent w/v to molarity for a substance with molecular weight MW, which formula gives M?

• A. M = (%w/v / MW)
• B. M = (%w/v / MW) x 10
• C. M = MW / (%w/v)
• D. M = (%w/v) x 10

Answer: (B)

Percent w/v means grams of solute per 100 mL of solution, and molarity is moles per liter. To bridge the two, first convert the amount per 100 mL to per liter by multiplying by 10 (that gives grams per liter). Then convert grams to moles by dividing by the molecular weight (g per mol). Put together, the molarity equals (grams per liter) divided by MW, which is the same as (percent w/v × 10) divided by MW. In other words, M = (%w/v / MW) × 10.

For example, a 4% w/v solution with MW 180 g/mol gives M = (4 × 10) / 180 ≈ 0.222 M. This aligns with the idea that 4% w/v is 40 g/L, and 40 g/L ÷ 180 g/mol ≈ 0.222 M.

The other forms miss the necessary conversion step or misplace the order of operations, so they don’t produce the correct molarity.