Which of the following result in buffered solutions when equal volumes of the two solutions are mixed?

a.) .1 M HCl and .1 M NH4Cl
b) .1 M HCl and .1 M NH3
c.) .2 HCl and .1 M NH3
d.) .1 M HCl and .2 M NH3

By def. I know that a buffed solution is made from a weak base and it's conjugate acid/or a weak acid and it's conjugate base. Therefore, I don't really understand how to determine the answer since each option includes a strong acid.

A little confusing, perhaps, but answerable.

Isn't a "REAL" buffered solution present in d? (Just as you described it in your question.)
..........HCl + NH3 ==> NH4Cl
I.........0.1M..0.2M......0
C........-0.1..-0.1......+0.1
E..........0.....0.1.......0.1

So you end up with NH3, a weak base, with it's conjugate acid, NH4^+. Voila.

To determine whether a solution is buffered when two solutions are mixed, we need to consider the presence of a weak acid and its conjugate base, or a weak base and its conjugate acid. In buffered solutions, these components act as a reservoir of protons (H+) or hydroxide ions (OH-) that help maintain the pH within a certain range.

Let's analyze each option to identify the weak acid / conjugate base or weak base / conjugate acid pairs:

a.) 0.1 M HCl and 0.1 M NH4Cl:
In this case, HCl is a strong acid, not a weak acid. Therefore, this combination does not form a buffered solution.

b.) 0.1 M HCl and 0.1 M NH3:
Similar to the previous option, HCl is a strong acid. Although NH3 is a weak base, without a weak acid to form a conjugate base, this combination also does not produce a buffered solution.

c.) 0.2 M HCl and 0.1 M NH3:
Once again, HCl is a strong acid. Despite NH3 being a weak base, this combination does not have a weak acid to form a buffered solution.

d.) 0.1 M HCl and 0.2 M NH3:
Again, HCl is a strong acid, not a weak acid. Even though NH3 is a weak base, the absence of a weak acid means this combination does not create a buffered solution.

Unfortunately, none of the options presented results in a buffered solution as they all involve a strong acid without a corresponding weak acid.