Range of suitable indicator for titration of X-Na

Introduction
In a titration, an indicator is used to determine the endpoint of the reaction between the analyte and the titrant. The choice of indicator depends on the nature of the reaction and the pH range over which the analyte changes color. In the case of titrating X-Na with 0.1M HCl, the appropriate indicator should have a pH range that overlaps with the pH range of the equivalence point of the reaction.

Explanation
When X-Na reacts with HCl, X-Na will be neutralized by the acid, resulting in the formation of X-H and NaCl. The reaction can be represented by the following equation:

X-Na + HCl -> X-H + NaCl

The acid dissociation constant (Ka) for X-H is related to the base dissociation constant (Kb) for X-Na through the equation:

Ka x Kb = Kw

where Kw is the ion product of water.

In this case, Kb for X-Na is given as 10^-6. Since Kb is small, X-Na is a weak base and X-H is a weak acid. The pH at the equivalence point of the titration will be slightly acidic because X-H is a weak acid.

To choose a suitable indicator for this titration, we need to consider the pH range over which X-H changes color. Since X-H is a weak acid with a small Ka, its pH range of color change will be relatively narrow.

Range of suitable indicator
To determine the range of suitable indicators, we need to consider the pH range at the equivalence point. This can be calculated using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.

At the equivalence point, [A-] = [HA], so the equation becomes:

pH = pKa + log(1) = pKa

Since Kb = Kw/Ka, we can calculate pKa using the following equation:

pKa = -log(Ka) = -log(Kw/Kb) = -log(Kw) + log(Kb)

Taking the negative logarithm of Kw gives us pKw:

pKw = -log(Kw) = -log(10^-14) = 14

Substituting the given value of Kb into the equation, we can calculate pKa:

pKa = 14 + log(10^-6) = 14 + (-6) = 8

Therefore, the pH at the equivalence point is 8.

Conclusion
Based on the pH at the equivalence point of the titration of X-Na with 0.1M HCl, the indicator chosen should have a pH range that includes 8. The suitable indicators for this titration would be those that change color around pH 8, such as methyl orange or bromothymol blue. These indicators have a pH range that overlaps with the pH at the equivalence point, allowing for accurate determination of the endpoint of the titration.