A gaseous compound containing hydrogen and carbon is decomposed and found to contain \(85.63 \% \mathrm{C}\) and \(14.37 \%\) \(\mathrm{H}\) by mass. The mass of \(258 \mathrm{~mL}\) of the gas, measured at STP, is \(0.646 \mathrm{~g}\). What is the molecular formula of the compound?

The empirical formula of a compound represents the simplest whole-number ratio of elements in the compound. To calculate this, one must first determine the mass of each element present, which is derived from the compound's composition by mass. Once the masses are known, the next step involves converting these masses to moles by dividing them by their respective atomic masses. After obtaining the mole quantities, these are compared to find the smallest number of moles present. All of the mole amounts can then be divided by this smallest value, yielding a ratio for the number of atoms of each element.

For those ratios that aren't whole numbers, they should be multiplied by a common factor to convert them into whole numbers. These converted ratios correspond to the subscripts in the empirical formula. It's crucial to remember that subscripts in a formula must always be whole numbers, and it may sometimes be necessary to round to the closest whole number to achieve this.

Molar mass determination is a fundamental aspect of stoichiometry and plays a key role in converting between mass and moles. To determine the molar mass of a compound, one must sum up the atomic masses of all the atoms represented in the compound's molecular formula.

When it comes to gases, molar mass can also be determined through experimental measures of mass and volume at Standard Temperature and Pressure (STP). At STP, a mole of any gas occupies approximately 22.4 liters. By measuring the mass of a known volume of gas at STP, the molar mass can be calculated using the formula: Molar Mass = (Mass of the gas / Volume of the gas) * Molar Volume at STP. This calculated molar mass is central to identifying the molecular formula from the empirical formula.

Composition by mass, often referred to as percent composition, conveys the relative mass contribution of each element in a compound. It is expressed as a percentage of the total mass of the compound. This information can be determined through laboratory analysis or provided in a problem scenario.

Using these percentages, one can calculate the actual masses of the individual components by applying them to the mass of a sample of the compound. For instance, if a compound is known to be 85.63% carbon, then 85.63% of the mass of any sample of the compound will be carbon. This calculation is the first step in finding the empirical formula of the compound. It is also essential in assessing the purity and formulation of the compound in industrial and research settings.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves calculations that use the coefficients in a balanced chemical equation to relate the amount of one substance to the amount of another. Stoichiometry is based on the law of conservation of mass and the concept that mass is neither created nor destroyed in chemical reactions.

In the context of determining molecular formulas, stoichiometry aids in interpreting the results from empirical formula calculations. Once the empirical formula is known, stoichiometric techniques are applied to compare it with the experimentally determined molar mass to find the molecular formula. Steps in a stoichiometric analysis may include converting grams to moles, using mole ratios, and finding the limiting reactant in chemical reactions.

Standard Temperature and Pressure (STP) is a set of conditions defined by 0 degrees Celsius (273.15 Kelvin) and 1 atmosphere of pressure. These standardized conditions are used for the comparison and documentation of chemical and physical processes, making it possible to compare different experiments and data sets.

For gasses, STP provides the advantage of having a known volume per mole, which is approximately 22.4 liters. This information is essential for the molar mass determination of gases, as evidenced in our example problem. Knowing the volume of gas at STP and its mass allows for the calculation of its molar mass, which is a stepping-stone to discovering the molecular formula of an unknown gaseous compound.