MCAT® ExamChemical and Physical Foundations of Biological SystemsMedium
A laboratory technician is preparing a solution for an experiment. They need to dilute a 2.0 M stock solution of hydrochloric acid (HCl) to obtain 500 mL of a 0.25 M HCl solution. What volume of the stock solution is required for this dilution?
- A50.0 mL
- B62.5 mL
- C125 mL
- D25.0 mL
Show answer & explanationAnswer & explanation
Correct answer: B. 62.5 mL
This is a dilution problem that can be solved using the formula M₁V₁ = M₂V₂. Given: M₁ = 2.0 M (stock concentration), V₁ = ? (volume of stock), M₂ = 0.25 M (desired concentration), V₂ = 500 mL (desired volume). Rearranging the formula to solve for V₁: V₁ = (M₂V₂) / M₁. V₁ = (0.25 M × 500 mL) / 2.0 M V₁ = 125 M⋅mL / 2.0 M V₁ = 62.5 mL.
Why the other options are wrong
- A. Incorrect calculation: (0.25 * 500) / 2.5
- C. Incorrect calculation: (0.50 * 500) / 2.0
- D. Incorrect calculation: (0.25 * 500) / 5.0
Dilution Equation
The dilution equation, M₁V₁ = M₂V₂, is used to calculate the concentration or volume of a solution before or after dilution, assuming the amount of solute remains constant.
- M₁ = initial molarity (concentration of stock solution).
- V₁ = initial volume (volume of stock solution needed).
- M₂ = final molarity (desired concentration of diluted solution).
- V₂ = final volume (desired total volume of diluted solution).
- Units for volume must be consistent (e.g., both mL or both L).
Memory trick: Mighty Vials Make Very easy dilutions!