How many mL of 80% v/v ethanol do you need to make 200 mL of a 50% ethanol solution in water?

To determine the volume of 80% v/v ethanol needed to make a 50% ethanol solution, we can use the formula:

%1 * V1 + %2 * V2 = %total * Vtotal

where %1 and %2 are the percentages of the two solutions being mixed, V1 and V2 are the volumes of the two solutions, and %total is the desired final percentage, and Vtotal is the total volume of the final solution.

In this case:
%1 = 80%
%2 = 0% (water)
V2 = 200 mL (water)
%total = 50%
Vtotal = 200 mL

Plugging in these values into the formula, we can calculate V1:

80% * V1 + 0% * 200 mL = 50% * 200 mL

Simplifying the equation, we get:
0.8V1 = 0.5 * 200 mL

Dividing both sides by 0.8, we find:
V1 = (0.5 * 200 mL) / 0.8

Calculating the right side of the equation:
V1 = 100 mL / 0.8
V1 = 125 mL

Therefore, you need 125 mL of 80% v/v ethanol to make 200 mL of a 50% ethanol solution in water.