Question

1. chemistry a lab technician has 40 gallons of a 15% iodine solution. how many gallons of a 40% iodine solution must he add to make a 20% iodine solution?

Explanation:

Step1: Let the amount of 40% iodine solution be $x$ gallons.

The amount of iodine in the 15% solution is $0.15\times40$ gallons, and the amount of iodine in the 40% solution is $0.4x$ gallons. The total volume of the final 20% solution is $(40 + x)$ gallons, and the amount of iodine in it is $0.2(40 + x)$ gallons.

Step2: Set up the iodine - conservation equation.

$0.15\times40+0.4x=0.2(40 + x)$
$6 + 0.4x=8+0.2x$

Step3: Solve the equation for $x$.

Subtract $0.2x$ from both sides: $6 + 0.4x-0.2x=8+0.2x-0.2x$, which gives $6 + 0.2x=8$.
Subtract 6 from both sides: $0.2x=8 - 6=2$.
Divide both sides by 0.2: $x=\frac{2}{0.2}=10$.

Answer:

10 gallons