Chemistry Molarity question (In description due to unable to type in the title)

Question

What volume of 4.2 M Ca(OH)₂ is needed to make 500mL of 1.5M solution

Answer 1

Simply use V1M1 = V2M2

V1 = initial volume; M1 = initial molarity; V2 = final volume: M2 = final molarity

(x ml)(4.2 M) = (500 ml)(1.5 M)

x = 179 mls

Answer 2

A 1.5 M solution means it has 1.5 moles/liter. Since there is 500 mL, or 1/2 liter, then there is 0.75 moles of Ca(OH)₂ in the final solution.

Let "x" represent the volume (in liters) of the initial 4.2 M solution

Since you are starting with a 4.2 M solution, or 4.2 moles/liter, then the number of moles is 4.2x and since you want that number of moles to be 0.75 then:

4.2x = 0.75

x = 0.75/4.2 = 0.179 liters or 179 mL