How much pure alcohol must be added to 400 mL of a 15% solution to make its strength 32%?

To determine how much pure alcohol needs to be added to a 400 mL solution that is 15% alcohol to achieve a final concentration of 32%, we can use a straightforward calculation.

Step-by-Step Calculation

First, let's find out how much alcohol is currently in the solution:

• Current volume of solution: 400 mL
• Current concentration: 15%

The amount of pure alcohol in the solution is:

Amount of alcohol = 400 mL × 0.15 = 60 mL

Setting Up the Equation

Let x be the volume of pure alcohol to be added. After adding x mL of pure alcohol, the total volume of the solution will be:

Total volume = 400 mL + x

The new concentration of alcohol will be:

New concentration = (60 mL + x) / (400 mL + x)

Creating the Equation

We want this new concentration to equal 32%, so we set up the equation:

(60 + x) / (400 + x) = 0.32

Solving the Equation

Now, we can solve for x:

• Cross-multiply: 60 + x = 0.32(400 + x)
• Expand: 60 + x = 128 + 0.32x
• Rearrange: x - 0.32x = 128 - 60
• Simplify: 0.68x = 68
• Finally, x = 68 / 0.68 = 100 mL

Final Result

To achieve a 32% alcohol concentration, you need to add 100 mL of pure alcohol to the original 400 mL of 15% solution.