The relative atomic mass (Ar) and relative formula mass (Mr) are dimensionless quantities and hence don't have units. They are based on a scale where the carbon-12 isotope has an Ar of exactly 12. This means that Ar and Mr are relative to the mass of the carbon-12 isotope. Since they represent ratios of average atomic or formula masses to one-twelfth the mass of a carbon-12 atom, the units effectively cancel out, leaving these quantities unitless.

Approximation plays a crucial role in empirical formula determination because in practical scenarios, absolute precision is often unattainable. Laboratory measurements have inherent uncertainties, and samples might not be perfectly pure. By using approximations, chemists acknowledge these imperfections and recognise that small deviations won't dramatically alter the derived empirical formula. Moreover, when converting masses to moles, one often encounters decimal values. Rounding these values to the nearest whole number (when appropriate) simplifies the ratio while still providing a representative empirical formula. It's a balance between representing real-world data and maintaining simplicity for conceptual understanding.

Experimental errors can significantly impact the determination of empirical formulas. For instance, if a sample isn't completely dried before weighing, the additional mass from moisture could skew the calculation. Similarly, incomplete combustion during a combustion analysis can lead to inaccurate measurements of carbon and hydrogen content. Moreover, contamination of samples, inaccuracies in measurements, or equipment calibration issues can result in errors. Such errors may produce an incorrect ratio of elements, leading to a faulty empirical formula. Therefore, it's essential to ensure accurate experimental procedures and measurements to derive precise empirical formulas.

The empirical formula represents the simplest whole-number ratio of the elements in a compound. In contrast, the molecular formula indicates the actual number of atoms of each element present in one molecule of the substance. It is possible for two compounds to have the same empirical formula but different molecular formulas. The reason is that the molecular formula can be a multiple of the empirical formula. For instance, ethene (C₂H₄) and butene (C₄H₈) both have the empirical formula CH₂. The molecular formula reflects the actual number of atoms, while the empirical formula simplifies the ratio, which may not always show the full picture.

Yes, two different compounds can indeed share the same empirical formula. Such compounds are known as isomers. For example, ethyne (C₂H₂) and ethene (C₂H₄) both have the empirical formula CH₂. However, their molecular structures and properties differ significantly. Ethyne is an alkyne with a triple bond between the carbon atoms, while ethene is an alkene with a double bond. This showcases that while the empirical formula provides information on the elemental ratio, it doesn't give details about the structural arrangement or actual number of atoms in the molecule.