The compound \(\mathrm{VCl}_{4}\) undergoes dimerization in solution:

\[2 \mathrm{VCl}_{4} ightleftharpoons \mathrm{V}_{2} \mathrm{Cl}_{8}\]

When \(6.6834 \mathrm{~g}\) of \(\mathrm{VCl}_{4}\) is dissolved in \(100.0 \mathrm{~g}\) of carbon tetrachloride, the freezing point is lowered by \(5.97^{\circ} \mathrm{C}\). Calculate the value of the equilibrium constant for the dimerization of \(\mathrm{VCl}_{4}\) at this temperature. (The density of the equilibrium mixture is \(1.696 \mathrm{~g} / \mathrm{cm}^{3}\), and \(K_{\mathrm{f}}=29.8^{\circ} \mathrm{C} \mathrm{kg} / \mathrm{mol}\) for \(\mathrm{CCl}_{4}\).)