Question

1. you have a solution mixed at a concentration of 5 g/ml and need 100 gal mixed at 4 g/ml. what do you do?

c₁·v₁ = c₂·v₂

Explanation:

Step1: Identify the formula

We use the formula \(C_1\cdot V_1 = C_2\cdot V_2\), where \(C_1 = 5\ g/ml\), \(C_2=4\ g/ml\), and \(V_2 = 100\ gal\)

Step2: Solve for \(V_1\)

Rearrange the formula to \(V_1=\frac{C_2\cdot V_2}{C_1}\)
Substitute the values: \(V_1=\frac{4\ g/ml\times100\ gal}{5\ g/ml}\)
\(V_1 = 80\ gal\)

Step3: Determine the amount of diluent

The total volume \(V_2 = 100\ gal\), and the volume of the concentrated solution \(V_1 = 80\ gal\)
The amount of diluent (water, for example) is \(V_2 - V_1=100 - 80=20\ gal\)

Answer:

Take \(80\) gallons of the \(5\ g/ml\) solution and add \(20\) gallons of diluent (such as water) to make \(100\) gallons of the \(4\ g/ml\) solution.