You need 3.0-L of 0.13 M salt solution. All you can find is 0.40 M salt solution. How much of that solution will you need in order to make your desired solution (in liters)?
You dilute 0.4 M salt to 0.13 M , this is a dilution factor of 3.077. Thus, to make 3 L of final solution, you need 3L/3.077 = 974 ml or 0.974 L
To find out how much of the 0.40 M salt solution you will need to make your desired 3.0-L 0.13 M salt solution, you can use the formula for dilution:
C₁V₁ = C₂V₂
Where:
C₁ = concentration of the starting solution
V₁ = volume of the starting solution
C₂ = concentration of the desired solution
V₂ = volume of the desired solution
Let's assign the variables:
C₁ = 0.40 M
V₁ = unknown (what we're trying to find)
C₂ = 0.13 M
V₂ = 3.0 L
Plugging in the values into the formula:
(0.40 M)(V₁) = (0.13 M)(3.0 L)
Rearranging the formula to find V₁:
V₁ = (0.13 M)(3.0 L) / (0.40 M)
Simplifying the expression:
V₁ = 9.0 L / 0.40
V₁ = 22.5 L
Therefore, you will need to use 22.5 liters of the 0.40 M salt solution to make your desired 3.0-L 0.13 M salt solution.