 Solution

With the stipulated $-5.0\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ value and ideal-solution approximations, $\boxed{[\mathrm{HF}]\approx 1.94\mathrm{M}}$ and the initial oxygen-difluoride pressure is $\boxed{p_0\approx 9.01\mathrm{bar}}$. These are estimates for the hypothetical reaction energetics specified in this part.

Take liquid-water activity as one, ideal gases, and aqueous HF activity as $[\mathrm{HF}]/c^{\circ }$, with $c^{\circ }=1\mathrm{M}$. The equilibrium constant isThus $[\mathrm{HF}]=c^{\circ }\sqrt{K/2}=1.9395\mathrm{M}$.

Let the fixed liquid volume be $V_l$ and headspace volume $V_g=4V_l$. If $\xi$ moles react, then $n_{{\mathrm{O}}_2}=\xi$, $n_{\mathrm{O}{\mathrm{F}}_2}=n_0-\xi$, and the pressure ratio gives $\xi /(n_0-\xi )=2$, so $n_0=3\xi /2$. The HF amount is $2\xi =[\mathrm{HF}]V_l$. Thereforeusing $R=0.083145\mathrm{L}\mathrm{bar}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$ with molarity in $\mathrm{mol}{\mathrm{L}}^{-1}$. The equilibrium gas pressures are approximately $6.01$ bar oxygen and $3.00$ bar oxygen difluoride; gas stoichiometry is one molecule to one, so their sum equals the initial gas pressure under these approximations.

Assume negligible gas dissolution, HF vapour, HF dissociation and nonideality, and negligible change of liquid/headspace volumes on reaction. Water consumption is about $0.97$ mol per litre of original liquid, small compared with its roughly $55.5$ mol of water. At nearly $2\mathrm{M}$ HF, the ideal-solution approximation is nevertheless a substantive limitation: without activity coefficients and an acid-speciation model, a precise real-solution pressure cannot be deduced from the supplied data.