How do the following solutions show the properties of a buffer?

1) 50 ml 0.10 M NH3 + 50 ml 0.10 M NH4NO3

2) 10 ml solution #1 + 5 ml H2O + 1 ml 0.10 M HCl

3) 10 ml solution #1 + 6 ml 0.10 M HCl

4) 10 ml solution #1 + 5 ml H2O + 1 ml 0.10 M NaOH

I don't know what kind of an answer you want here. You might try re-phrasing the question.

To understand how the given solutions show the properties of a buffer, let's first discuss what a buffer is.

A buffer is a solution that resists changes in pH when small amounts of acid or base are added to it. It is composed of a weak acid (or base) and its conjugate base (or acid), which are present in roughly equal concentrations.

Now, let's analyze each solution and see how they demonstrate the properties of a buffer:

1) 50 ml 0.10 M NH3 + 50 ml 0.10 M NH4NO3:
This solution contains ammonia (NH3), which acts as a weak base, and ammonium nitrate (NH4NO3), which is its conjugate acid. When a small amount of acid is added to this buffer, such as HCl, the NH4NO3 provides additional NH4+ ions, which can react with the added HCl to form more NH3, effectively neutralizing the added acid and maintaining the pH of the solution.

2) 10 ml solution #1 + 5 ml H2O + 1 ml 0.10 M HCl:
In this case, a small amount of HCl (a strong acid) is added to the buffer solution from earlier. The presence of excess water doesn't affect the buffer properties. The NH4+ ions from the original buffer solution can now react with the added HCl to form NH3 and maintain the pH of the solution.

3) 10 ml solution #1 + 6 ml 0.10 M HCl:
Similar to the previous scenario, a small amount of HCl is added to the buffer. The increased volume of HCl doesn't change the buffer nature but provides more H+ ions for the NH4+ ions to react with, thus maintaining the pH.

4) 10 ml solution #1 + 5 ml H2O + 1 ml 0.10 M NaOH:
In this case, a small amount of NaOH (a strong base) is added to the buffer solution. The NH3 from the buffer can react with the added OH- ions from NaOH, thus neutralizing them and maintaining the pH of the solution.

In all these scenarios, the buffer solutions show their properties by resisting changes in pH when small amounts of acid or base (HCl, NaOH) are added. The buffer components (NH3 and NH4+) or (NH3 and NH4NO3) react with the added acid or base to minimize any shift in pH.