Question: 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 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 $\mathrm{CCl}_{4}$.)

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