Which of the following statements is/are false?

First we analyse statement A, namely $$Na_2Cr_2O_7$$ is more soluble than $$K_2Cr_2O_7$$. In general, for salts having the same anion, the sodium salt is more soluble in water than the corresponding potassium salt because the lattice enthalpy decreases more rapidly than the hydration enthalpy when the larger potassium ion replaces the smaller sodium ion. Thus the dissolution process for $$Na_2Cr_2O_7$$ is more exothermic than for $$K_2Cr_2O_7$$, giving the sodium salt the larger solubility. Hence statement A is true.

Now we look at statement B, that the chromate ion $$CrO_4^{2-}$$ is tetrahedral. The chromium atom is in the $$+6$$ oxidation state with the electronic configuration $$[Ar]3d^{0}$$. Four oxide ions, each carrying a double negative charge, coordinate around the metal. According to the Valence Shell Electron Pair Repulsion (VSEPR) model, four electron pairs around a central atom arrange themselves at the corners of a regular tetrahedron to minimise repulsion. Therefore the geometry of $$CrO_4^{2-}$$ is indeed tetrahedral. So statement B is also true.

We next consider statement C, which claims that $$Na_2Cr_2O_7$$ is the primary standard in volumetry. A primary standard must satisfy two main conditions: it should be (i) available in high purity and (ii) non-hygroscopic so that its mass remains constant during weighing. However, $$Na_2Cr_2O_7$$ is markedly hygroscopic; it absorbs moisture from the air, so its mass cannot be measured accurately without special precautions. On the other hand, $$K_2Cr_2O_7$$ is non-hygroscopic and hence is the salt actually employed as a primary standard for redox titrations. Consequently statement C is false.

Finally we examine statement D, the assertion that the dichromate ion $$Cr_2O_7^{2-}$$ possesses a $$Cr-O-Cr$$ bridge. The structure of dichromate consists of two $$CrO_4$$ tetrahedra sharing one common oxygen atom. Writing the ion explicitly, we have

$$O_3Cr-O-CrO_3^{2-}$$

where the central oxygen atom is bonded to each chromium, forming a $$Cr-O-Cr$$ linkage. Hence statement D is true.

Summarising the individual results:

A: true,   B: true,   C: false,   D: true

Only statement C is false. Hence, the correct answer is Option C.