An unknown compound has the following chemical formula: $$ \mathrm{P}_{\mathrm{x}} \mathrm{Cl}_{5} $$ where $$ x $$ stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 4.7 mol of phosphorus and 23.59 mol of chlorine. Write the complete chemical formula for the unknown compound.

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The chemical formula for the unknown compound is PCl5. To determine the complete chemical formula for the unknown compound $$\mathrm{P}_{\mathrm{x}} \mathrm{Cl}_{5}$$, we need to find the value of $$x$$. We know from the problem that the sample contains: - 4.7 mol of phosphorus (P) - 23.59 mol of chlorine (Cl) The formula $$\mathrm{P}_{\mathrm{x}} \mathrm{Cl}_{5}$$ indicates that for every $$x$$ moles of phosphorus, there are 5 moles of chlorine. To find the ratio of phosphorus to chlorine, we can set up the following relationship based on the moles present: $$ \frac{\text{moles of P}}{\text{moles of Cl}} = \frac{4.7}{23.59} $$ Now, we can express the ratio of phosphorus to chlorine in terms of $$x$$: $$ \frac{x}{5} = \frac{4.7}{23.59} $$ To find $$x$$, we can cross-multiply: $$ x \cdot 23.59 = 4.7 \cdot 5 $$ Calculating the right side: $$ 4.7 \cdot 5 = 23.5 $$ Now we have: $$ x \cdot 23.59 = 23.5 $$ To solve for $$x$$, we divide both sides by 23.59: $$ x = \frac{23.5}{23.59} \approx 0.995 $$ Since $$x$$ must be a whole number, we round $$0.995$$ to the nearest whole number, which is $$1$$. Thus, the complete chemical formula for the unknown compound is: $$ \mathrm{P}_{1} \mathrm{Cl}_{5} \quad \text{or simply} \quad \mathrm{PCl}_{5} $$

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