A compound is known to contain carbon and hydrogen. It might also contain oxygen. A sample of the compound is burned. The results of the combustion analysis are \(74.9 \% \mathrm{C}\) and \(25.1 \% \mathrm{H}\). (a) What is the chemical formula for this compound? (b) Write the balanced combustion reaction (reaction with \(\mathrm{O}_{2}\) ) for this compound. Answer (not worked out on purpose-you do it): (a) \(\mathrm{CH}_{4}\) (b) \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\)

Understanding how to determine the chemical formula of a compound is a fundamental aspect of chemistry. In combustion analysis, it is often used to identify the elemental composition of organic molecules, such as those containing carbon and hydrogen.

The process involves analyzing the percentage composition of each element and then converting these percentages into moles using atomic weights. The mole is a unit that measures the quantity of a substance, based on the number of atoms or molecules it contains.

Once the moles are calculated, the next step is to find the simplest whole number ratio among the moles of the different elements. This ratio reflects the relative number of atoms of each element in the compound and thus helps in determining the empirical formula. For instance, in our exercise, using the percentage of carbon and hydrogen, we found a mole ratio that simplifies to CH₄, methane.

Methane's chemical formula reflects that for every one carbon atom, there are four hydrogen atoms, perfectly mirroring the simplest whole number ratio obtained from our calculations.

Balancing a combustion reaction is crucial for understanding the chemical changes occurring during the process. Combustion is a chemical reaction that typically involves a substance (often a hydrocarbon) reacting with oxygen to produce carbon dioxide, water, and energy.

The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction. This principle guides us to balance the equation, ensuring that the number of atoms for each element is the same on both sides of the reaction.

For the equation of methane's combustion, we needed two molecules of oxygen, O₂, to react with one molecule of methane, CH₄, resulting in two molecules of water, H₂O, and one molecule of carbon dioxide, CO₂. This balanced equation allows one to understand the exact stoichiometry and the proportions of reactants and products involved in the reaction.

The calculation of mole ratios is a method used to quantify the relationships between the elements in a chemical reaction or compound. The mole ratio is found by dividing the number of moles of one substance by the number of moles of another.

This concept becomes particularly important when working with chemical equations, as it enables the balancing of these equations accurately and helps predict the amounts of reactants needed or products formed. In our example, calculating the mole ratio was essential for deriving the simplified empirical formula of the compound and for balancing the combustion reaction.

When the mole ratios are not in simple whole numbers, they are adjusted to the closest whole number ratio, which represents the actual number of atoms of each element in the compound. These ratios are also critical when performing stoichiometric calculations, which are predictive in nature and widely used in various branches of chemistry.

Atomic weight, also known as atomic mass, is the weight of a single atom of an element, measured in atomic mass units (amu). It plays a central role in chemistry since it serves as the basis for calculating the moles of an element in a substance.

Knowing the atomic weight of elements allows us to convert the mass of an element into the number of moles, which is necessary when dealing with chemical reactions and stoichiometry. This is evidenced in the example problem where we used the atomic weights of carbon and hydrogen to ascertain their respective mole ratios in the compound.

In educational contexts, atomic weight aids students in visualizing the relative weights of different atoms, making it easier to grasp more complex chemical concepts. By understanding the significance of atomic weight, students are better equipped to perform a broad range of calculations in chemistry that are essential for both theoretical understanding and practical applications.