Question

How much water should be added to 30 mL of 16% alcohol solution to reduce the concentration to 15%?

A. 1 mL
B. 2 mL
C. 3 mL
D. 4 mL

Answer 1

To dilute a 30 mL solution of 16% alcohol to a concentration of 15%, 2 mL of water must be added.

Step-by-step explanation:

To determine how much water should be added to 30 mL of 16% alcohol solution to dilute it to a concentration of 15%, we apply the concept of dilution of solutions. Here's a step-by-step calculation:

• Let x be the volume of water added in milliliters.
• The amount of alcohol in the original solution is 16% of 30 mL, which equals 4.8 mL.
• After adding x mL of water, the total volume becomes 30 mL + x mL.
• To find the new concentration, we set up the equation (4.8 mL) / (30 mL + x mL) = 15%.
• Converting 15% to a decimal gives us 0.15. The equation now is 4.8 / (30 + x) = 0.15.
• Multiplying both sides by (30 + x) gives us 4.8 = 0.15(30 + x).
• Simplifying the equation: 4.8 = 4.5 + 0.15x.
• Subtracting 4.5 from both sides gives us 0.3 = 0.15x.
• Dividing both sides by 0.15 yields x = 2.

Thus, the answer is that 2 mL of water needs to be added to the solution to decrease the alcohol concentration to 15%.