Question

Determine the number of moles of hydrogen atoms in each sample. a. \(0.0885 \mathrm{~mol} \mathrm{C}_{4} \mathrm{H}_{10}\) b. \(1.3 \mathrm{~mol} \mathrm{CH}_{4}\) c. \(2.4 \mathrm{~mol} \mathrm{C}_{6} \mathrm{H}_{12}\) d. \(1.87 \mathrm{~mol} \mathrm{C}_{8} \mathrm{H}_{18}\)

Short answer

a. 0.885 mol H, b. 5.2 mol H, c. 28.8 mol H, d. 33.66 mol H

Step-by-step solution

- Determine the ratio of hydrogen to the compound

Identify the ratio of hydrogen atoms to the given chemical compound. In each of these compounds, there is a fixed ratio of carbon to hydrogen atoms. For instance, in C4H10, for every mole of compound, there are 4 carbon atoms and 10 hydrogen atoms.

- Calculate moles of hydrogen for each sample

Using the mole ratio of hydrogen to the compound, multiply the given moles of the compound by the number of hydrogen atoms in the formula unit of the compound to find the moles of hydrogen atoms.

- Perform the calculations for each sample

a. For 0.0885 mol of C4H10, multiply by 10 (the number of H atoms): 0.0885 mol x 10 = 0.885 mol H.b. For 1.3 mol of CH4, multiply by 4 (the number of H atoms): 1.3 mol x 4 = 5.2 mol H.c. For 2.4 mol of C6H12, multiply by 12 (the number of H atoms): 2.4 mol x 12 = 28.8 mol H.d. For 1.87 mol of C8H18, multiply by 18 (the number of H atoms): 1.87 mol x 18 = 33.66 mol H.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of the quantities in chemical reactions. It is the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically a ratio of whole integers. For students dealing with stoichiometry, it is crucial to understand the concept of the mole and how it connects to chemical formulas.

Using stoichiometry in our context, to determine the number of moles of hydrogen atoms, we follow a systematic approach that involves understanding the chemical formula and its implications on the number of atoms within a molecule. This means quantifying the individual elements involved in a compound, like carbon and hydrogen in hydrocarbons, and determining how much of one substance reacts with or is produced from another substance.

Mole Concept

The mole concept is a fundamental aspect of chemical science and stoichiometry. It defines a mole as a unit representing 6.022 x 10²³ entities (Avogadro's number) of a substance. This could include atoms, ions, or molecules, depending on the substance's composition.

The mole allows chemists to convert between mass and number of particles, facilitating calculations involving chemical reactions. When applying the mole concept to solve problems such as calculating the number of moles of hydrogen atoms in hydrocarbons, we take the given moles of the compound and apply the ratio from the chemical formula, converting that value into the number of moles of a specific element within the compound.

Chemical Composition

Understanding chemical composition is fundamental to determine the makeup of a substance in terms of its constituent elements. Each substance has a unique chemical formula, which acts like a recipe telling us the ratio in which different atoms are combined. For hydrocarbons, the formula indicates the number of carbon (C) and hydrogen (H) atoms present.

Knowing a substance's chemical composition allows us to explore its properties and behaviors. For instance, being able to calculate moles of hydrogen in a given sample requires awareness of the molecular formula of the hydrocarbon in question. Essence of chemical composition involves acknowledging that the molecular ratios dictate how we convert moles of the molecule into moles of a component element.

Molecular Formula

The molecular formula is a representation of the actual number of each type of atom in a molecule. Unlike empirical formulas, which provide the simplest integer ratio of the constituent atoms, molecular formulas offer specific details about the molecular structure. For hydrocarbons, the molecular formula tells us the exact number of carbon and hydrogen atoms that form a single molecule of that compound.

When performing calculations for the moles of hydrogen in a sample of a hydrocarbon, the molecular formula becomes an indispensable tool, as it directs us to the precise stoichiometric relationship between the constituent elements. It serves as a critical link in the application of stoichiometric principles, effectively bridging the gap between the conceptual understanding of mole ratios and the actual execution of quantitative calculations.