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

Verified step by step guidance

1. Calculate the molar mass of the compound using the ideal gas law at STP. Use the formula: \( \text{Molar mass} = \frac{\text{mass}}{\text{moles}} \). At STP, 1 mole of gas occupies 22.4 L, so convert 258 mL to liters and find the moles of gas.
2. Determine the empirical formula. Assume 100 g of the compound, which gives 85.63 g of C and 14.37 g of H. Convert these masses to moles using the atomic masses of C (12.01 g/mol) and H (1.008 g/mol).
3. Find the simplest whole number ratio of moles of C to H to determine the empirical formula. Divide the moles of each element by the smallest number of moles calculated.
4. Calculate the empirical formula mass by adding the atomic masses of the elements in the empirical formula.
5. Determine the molecular formula by dividing the molar mass (from step 1) by the empirical formula mass. Multiply the subscripts in the empirical formula by this ratio to get the molecular formula.

Key Concepts

Empirical Formula Calculation

The empirical formula represents the simplest whole-number ratio of elements in a compound. To determine it, the mass percentages of each element are converted to moles by dividing by their atomic masses. The resulting mole ratios are then simplified to the smallest whole numbers, providing the empirical formula, which is essential for identifying the compound's composition.

Molar Volume at STP

At standard temperature and pressure (STP), one mole of any ideal gas occupies 22.4 liters. This concept is crucial for converting the volume of a gas to moles, which allows for the determination of the number of moles present in the given mass of the gas. In this problem, the volume of 258 mL can be converted to moles to help find the molecular formula.

Molecular Formula Determination

The molecular formula of a compound indicates the actual number of atoms of each element in a molecule. It can be derived from the empirical formula by comparing the molar mass of the compound to the molar mass of the empirical formula. If the molar mass is known, the ratio of the two can be used to find the molecular formula, which is essential for fully characterizing the compound.