How many milliliters each of a 2% w/v solution and a 7% w/v solution should be used in preparing 1 gallon of a 3.5% w/v solution?

Answer 1

To find out how many milliliters of each solution should be used, we need to convert the gallon to milliliters.

1 gallon is equal to 3,785.41 milliliters.

Let's assume x milliliters of the 2% solution should be used.
Therefore, (3,785.41 - x) milliliters of the 7% solution should be used.

To calculate the concentration of the final solution, we need to sum up the concentrations of the individual solutions multiplied by their respective volumes.

The equation for this would be:

2% * x + 7% * (3,785.41 - x) = 3.5% * 3,785.41

0.02x + 0.07(3,785.41 - x) = 0.035(3,785.41)

Simplifying the equation, we get:

0.02x + 265.98 - 0.07x = 132.48

Combining like terms:

-0.05x + 265.98 = 132.48

Subtracting 265.98 from both sides:

-0.05x = -133.5

Dividing both sides by -0.05:

x ≈ 2670

Rounding to the nearest whole number, we get x ≈ 2670 milliliters of the 2% solution should be used.

Therefore, (3,785.41 - 2670) ≈ 1,115 milliliters of the 7% solution should be used.