How much water needs to be added to 55 mL of 3.0 M stock solution to
produce a .75 M solution?

165 ml

Explanation:

We are given;

Initial volume; V_a = 55 ml

Initial molarity; M_a = 3 M

Molarity of desired solution; M_b = 0.75 M

Volume of desired solution; V_b = (55 + x) ml

Where x is the volume of water to be added.

To solve for V_b, we will use the equation ;

M_a•V_a = M_b•V_b

V_b = (M_a•V_a)/M_b

V_b = (3 × 55)/0.75

V_b = 220 mL

Thus;

(55 + x) = 220

x = 220 - 55

x = 165 mL