We can use the formula:
M1V1 = M2V2
where M1 is the initial molarity, V1 is the initial volume, M2 is the final molarity, and V2 is the final volume.
In this case, we know:
M1 = 12.0 M
V1 = ?
M2 = 0.100 M
V2 = 500.0 mL = 0.500 L (since 1 mL = 0.001 L)
We can rearrange the formula to solve for V1:
V1 = (M2V2) / M1
Substituting the values we know, we get:
V1 = (0.100 M)(0.500 L) / 12.0 M
V1 = 0.00417 L = 4.17 mL
Therefore, we need to measure 4.17 mL of 12.0 M hydrochloric aqueous solution and add it to 500.0 mL of water to prepare 500.0 mL of a 0.100 M diluted solution.