Based on the reduced numbers for carbon and hydrogen, what would the empirical formula be? \[ \mathrm{CH}_{2} \] \( \mathrm{C}_{2} \mathrm{H}^{2} \) \( \mathrm{CH}_{4} \)

To determine the empirical formula based on the reduced numbers for carbon and hydrogen, we need to simplify the ratio of the elements in the compound. In the case of \(\mathrm{CH}_4\), the ratio of carbon to hydrogen is 1:4. This cannot be reduced further, so the empirical formula remains \(\mathrm{CH}_4\). If you had a compound like \(\mathrm{C}_4\mathrm{H}_8\), then both would simplify to \(\mathrm{CH}_2\), hence demonstrating the reduction process. When figuring out empirical formulas, a common mistake is to assume the molecular formula is the same as the empirical formula. For instance, while \(\mathrm{C}_6\mathrm{H}_{12}\) can reduce down to \(\mathrm{CH}_2\), the molecular formula reflects the actual number of atoms in the molecule and cannot be disregarded. Always double-check whether you've simplified correctly!