Ethanol Dilution with a Stock-Use Limit
A student must prepare 750 mL of a 25% (v/v) ethanol solution for a lab practical. The stock bottle is labeled 70% (v/v) ethanol. The instructor limits use of the 70% stock to no more than 400 mL per student to reduce waste. The student has a 500 mL graduated cylinder and a 1.0 L volumetric flask. The student first measures 400 mL of stock, adds 300 mL of distilled water, and obtains a final volume of 700 mL in the cylinder. A partner says the solution is now 40% ethanol and that adding 50 mL more water will make it 25%. The student is unsure whether to start over or adjust. The instructor asks for the required stock volume, the correct final dilution procedure, and a check of the partner's claim.
1. Calculate the volume of 70% stock needed to make 750 mL of 25% ethanol, and describe the correct dilution procedure.
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The final solution must contain 0.25 × 750 mL = 187.5 mL of pure ethanol. The stock is 70% ethanol, so the stock volume is 187.5 / 0.70 = 267.9 mL. This is below the 400 mL limit, so the preparation is allowed. The correct procedure is to measure 267.9 mL of the 70% stock, transfer it to the 1.0 L volumetric flask, and add distilled water up to the 750 mL mark. The water should be added to volume, not as a separately measured 482.1 mL, because ethanol-water volumes are not strictly additive and the final volume must be 750 mL. Mix thoroughly after filling to the mark. Using the 500 mL graduated cylinder to measure the stock is acceptable for this approximate concentration, but the final dilution should be made in the volumetric flask.
2. Evaluate the partner's claim that 400 mL stock plus 300 mL water gives 40% ethanol and that adding 50 mL more water will make it 25%.
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The partner's first calculation is correct: 400 mL of 70% stock contains 0.70 × 400 = 280 mL ethanol. In a total volume of 700 mL, the concentration is 280/700 = 0.40, or 40% v/v. The second claim is wrong. Adding 50 mL of water makes the total volume 750 mL, but the ethanol amount remains 280 mL. The new concentration is 280/750 = 0.373, or 37.3% v/v, not 25%. Dilution with water cannot remove ethanol. To reach 25% at 750 mL, the solution must contain only 187.5 mL ethanol, so the student cannot salvage the 400 mL stock preparation by adding water. The student should discard it and start over with 267.9 mL of stock, then dilute to 750 mL in the volumetric flask.