To solve this problem, we can use the formula:
M1V1 = M2V2
where M1 is the concentration of the stock solution, V1 is the volume of the stock solution, M2 is the concentration of the diluted solution, and V2 is the final volume of the diluted solution.
We are given:
M1 = 3.153 M
V1 = unknown
M2 = 1.300 M
V2 = 500.0 mL = 0.500 L
Substituting these values into the formula, we get:
3.153 M x V1 = 1.300 M x 0.500 L
Solving for V1, we get:
V1 = (1.300 M x 0.500 L) / 3.153 M
V1 = 0.206 L = 206 mL (rounded to 1 decimal point)
Therefore, we need 206 mL of the 3.153 M KOH solution to make a 500.0 mL solution of 1.300 M KOH.