ACT (Enhanced)MathematicsMedium
A chemist is preparing a solution. She needs to dilute a 20% acid solution to a 5% acid solution. If she starts with 500 mL of the 20% solution, how much water (in mL) must she add to achieve the 5% solution?
- A1000 mL
- B2000 mL
- C500 mL
- D1500 mL
Show answer & explanationAnswer & explanation
Correct answer: D. 1500 mL
First, calculate the amount of acid in the initial solution: 20% of 500 mL = 0.20 * 500 = 100 mL of acid. For the final solution, this 100 mL of acid must represent 5% of the total volume. Let V be the final total volume. So, 0.05 * V = 100 mL, which means V = 100 / 0.05 = 2000 mL. The amount of water to add is the final volume minus the initial volume: 2000 mL - 500 mL = 1500 mL.
Why the other options are wrong
- A. This would result in a 6.67% solution (100mL acid in 1500mL total).
- B. This is the final total volume, not the amount of water added.
- C. This would result in a 10% solution (100mL acid in 1000mL total).
Dilution Calculation
Dilution calculations involve determining the amount of solvent needed to change the concentration of a solution while keeping the amount of solute constant.
- Amount of solute (e.g., acid) remains constant during dilution.
- Concentration is typically expressed as a percentage or molarity.
- Total volume changes with added solvent.
Memory trick: Solute stays same, Volume changes, Concentration shifts.