Which of the following solutions has the greatest buffer capacity?500 mL of 0.1M HC2H3O2 mixed with 500 mL of 0.1M NaC2H3O2400 mL of 0.5M HC2H3O2 mixed with 400 mL of 0.5M NaC2H3O2200 mL of 0.2M HC2H3O2 mixed with 200 mL of 0.2M NaC2H3O2400 mL of 0.2M HC2H3O2 mixed with 200 mL of 0.4M NaC2H3O2

Buffer capacity refers to the ability of a buffer solution to resist changes in pH when an acid or base is added. It is greatest when the concentrations of the weak acid (HC2H3O2) and its conjugate base (NaC2H3O2) are high and approximately equal.

Let's calculate the total moles of HC2H3O2 and NaC2H3O2 in each solution:

1. 500 mL of 0.1M HC2H3O2 mixed with 500 mL of 0.1M NaC2H3O2 Moles of HC2H3O2 = 0.1 mol/L * 0.5 L = 0.05 mol Moles of NaC2H3O2 = 0.1 mol/L * 0.5 L = 0.05 mol

2. 400 mL of 0.5M HC2H3O2 mixed with 400 mL of 0.5M NaC2H3O2 Moles of HC2H3O2 = 0.5 mol/L * 0.4 L = 0.2 mol Moles of NaC2H3O2 = 0.5 mol/L * 0.4 L = 0.2 mol

3. 200 mL of 0.2M HC2H3O2 mixed with 200 mL of 0.2M NaC2H3O2 Moles of HC2H3O2 = 0.2 mol/L * 0.2 L = 0.04 mol Moles of NaC2H3O2 = 0.2 mol/L * 0.2 L = 0.04 mol

4. 400 mL of 0.2M HC2H3O2 mixed with 200 mL of 0.4M NaC2H3O2 Moles of HC2H3O2 = 0.2 mol/L * 0.4 L = 0.08 mol Moles of NaC2H3O2 = 0.4 mol/L * 0.2 L = 0.08 mol

From the calculations, the solution with the greatest buffer capacity is the second one (400 mL of 0.5M HC2H3O2 mixed with 400 mL of 0.5M NaC2H3O2) because it has the highest and equal concentrations of the weak acid and its conjugate base.