To determine the empirical formula of the compound, we need to find the simplest whole number ratio of moles of carbon and hydrogen.$\\$Given:$\\$• The compound contains 78% carbon by weight.$\\$• The remaining percentage is hydrogen, which is $100\% - 78\% = 22\%$ hydrogen.$\\$Let's calculate the moles of each element in a 100 g sample of the compound:$\\$• Moles of carbon:$\\ \frac{78 g}{12 g/mol} = 6.5$ moles of carbon$\\$• Moles of hydrogen:$\\ \frac{22 g}{1 g/mol} = 22$ moles of hydrogen$\\$Now, we find the simplest whole number ratio of moles of carbon to hydrogen:$\\$• Divide each by the smallest number of moles:$\\ \frac{6.5}{6.5} = 1$ (for carbon)$\\ \frac{22}{6.5} \approx 3.38$ (for hydrogen)$\\$Since we need whole numbers, we round 3.38 to the nearest whole number, which is 3.$\\$Thus, the empirical formula is $CH_3. \\$Therefore, the correct option is Option 3: $CH_3.$