Question 1: A science experiment uses a solution where the concentration of a substance is given by the formula: (Amount of substance) / (Total solution volume). If the amount of substance is 3/4 liters and the total volume is 2 liters, what is the concentration? Express your answer as a fraction.

Answer: 3/8

Question 2: Rearrange the formula: Concentration = (Amount of substance) / (Total solution volume) to find Total solution volume in terms of the amount and concentration.

Answer: Total volume = (Amount of substance) / (Concentration)

Question 3: If a scientist has 5/6 liters of a chemical and needs a solution with a concentration of 1/3, how much total solution volume should she prepare?

Answer: 10 liters

Question 4: Calculate the amount of substance needed if the total solution volume is 12 liters and the concentration is 2/3.

Answer: 8 liters

Question 5: A solution contains 3/5 liters of chemical A and 2/5 liters of chemical B. If the total solution is 1 liter, what is the concentration of chemical A as a fraction?

Answer: 3/5

Question 6: Problem Solving: A lab requires mixing solutions with a ratio of chemicals A to B as 4/7 to 3/7. If the total volume of the mixture is 14 liters, how much of chemical A should be used?

Answer: 8 liters

Question 7: In an experiment, the formula relates the mass of a chemical to the volume of solution as: Mass = (Fraction of chemical) * (Total volume). If the total volume is 15 liters and the mass of the chemical is 9 liters, what is the fraction of the chemical?

Answer: 3/5

Question 8: Construct a scenario where the concentration of a solution is doubled by adjusting the amount of chemical used. Describe the initial and new amounts assuming initial total volume remains constant.

Answer: Initial: Chemical amount is (initial concentration) times total volume. Doubling concentration means chemical amount becomes twice as much, so initial amount multiplied by 2.

Question 9: A student makes a mistake by flipping the numerator and denominator when rearranging the formula: Total volume = (Amount of substance) / (Concentration). Identify and correct this mistake.

Answer: Correct formula: Total volume = (Amount of substance) / (Concentration). The mistake is flipping numerator and denominator; it should be as given.

Question 10: Challenge: A scientist wants a solution where the amount of chemical is 2/3 liters and the total volume is 9 liters. If they want to increase the concentration to 1/2, what should the new amount of chemical be?

Answer: 3 liters

Question 11: Evaluate the following: If the initial concentration is 1/4 and the total volume is 16 liters, what is the amount of chemical needed? Then, if the total volume is doubled, what is the new amount of chemical needed to maintain the same concentration?

Answer: Initial: 4 liters; New amount = 8 liters