Dichromate Primary Standards and Phenolphthalein Dissociation Statements

To determine the correct option, let us analyze each statement individually:

1. Analysis of Statement I:

   • A primary standard in volumetric titrations must be extremely pure, stable, non-hygroscopic, and have a well-defined chemical composition.
   • Potassium dichromate ($\text{K}_2\text{Cr}_2\text{O}_7$) is non-hygroscopic, stable, and available in high purity, making it a well-known primary standard.
   • Sodium dichromate ($\text{Na}_2\text{Cr}_2\text{O}_7$), on the other hand, is highly hygroscopic and deliquescent (it readily absorbs moisture from the atmosphere). Consequently, an exact weight of sodium dichromate cannot be accurately measured to prepare a standard solution. Thus, sodium dichromate cannot be used as a primary standard.
   • Since Statement I claims that both sodium dichromate and potassium dichromate are classified as primary standards, Statement I is false.

2. Analysis of Statement II:

   • Phenolphthalein is a weak organic acid (commonly represented as $\text{HIn}$), not a weak base.
   • Its dissociation equilibrium in aqueous solution is represented as: $\text{HIn (colourless)} \rightleftharpoons \text{H}^+ + \text{In}^- \text{ (pink)}$
   • In an acidic medium, due to the high concentration of $\text{H}^+$ ions, the equilibrium is shifted far to the left in accordance with Le Chatelier's principle (common ion effect). As a result, phenolphthalein remains almost completely undissociated (unionized) in acidic solution. It dissociates significantly only in a basic medium where $\text{OH}^-$ ions consume $\text{H}^+$ ions.
   • Therefore, Statement II is false.

Since both Statement I and Statement II are false, the correct option is B.