An unknown compound has the following chemical formula: \[ \mathrm{C}_{2} \mathrm{~F}_{\mathrm{x}} \] where \( x \) stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 8.7 mol of fluorine and 2.89 mol of carbon. Write the complete chemical formula for the unknown compound.

To determine the complete chemical formula for the unknown compound, we need to find the value of \( x \) in the formula \(\mathrm{C}_{2} \mathrm{~F}_{\mathrm{x}}\). Given: - The compound contains 8.7 mol of fluorine. - The compound contains 2.89 mol of carbon. We can use the molar ratio of fluorine to carbon to find the value of \( x \). The molar ratio of fluorine to carbon is given by: \[ \frac{\text{Moles of fluorine}}{\text{Moles of carbon}} = \frac{8.7}{2.89} \] Now, we can calculate the value of \( x \) by dividing the moles of fluorine by the moles of carbon. \[ x = \frac{8.7}{2.89} \] Let's calculate the value of \( x \) and then write the complete chemical formula for the unknown compound. Calculate the value by following steps: - step0: Calculate: \(\frac{8.7}{2.89}\) - step1: Convert the expressions: \(\frac{\frac{87}{10}}{\frac{289}{100}}\) - step2: Multiply by the reciprocal: \(\frac{87}{10}\times \frac{100}{289}\) - step3: Reduce the numbers: \(87\times \frac{10}{289}\) - step4: Multiply: \(\frac{87\times 10}{289}\) - step5: Multiply: \(\frac{870}{289}\) The value of \( x \) is approximately 3.010381. Since \( x \) represents a whole number, we can round it to the nearest whole number. Therefore, the complete chemical formula for the unknown compound is \(\mathrm{C}_{2} \mathrm{~F}_{3}\).