Question

Determine the number of moles of hydrogen atoms in each sample. $$ \begin{array}{l}{\text { a. } 0.0885 \text { mol } \mathrm{C}_{4} \mathrm{H}_{10}} \\ {\text { b. } 1.3 \mathrm{mol} \mathrm{CH}_{4}} \\\ {\text { c. } 2.4 \mathrm{mol} \mathrm{C}_{6} \mathrm{H}_{12}} \\ {\text { d. } 1.87 \mathrm{mol} \mathrm{C}_{8} \mathrm{H}_{18}}\end{array} $$

Short answer

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

Step-by-step solution

Determine the number of hydrogen atoms per molecule

Identify the number of hydrogen atoms in one molecule of the compound. For instance, C4H10 has 10 hydrogen atoms per molecule, CH4 has 4, C6H12 has 12, and C8H18 has 18.

Calculate moles of hydrogen atoms

Multiply the number of moles of the compound by the number of hydrogen atoms per molecule to find the number of moles of hydrogen atoms. For example, 0.0885 moles of C4H10 contains 0.0885 mol * 10 H atoms/mol = 0.885 moles H atoms.

Repeat calculation for each compound

Perform the same calculation for each of the other compounds: (b) 1.3 moles of CH4 corresponds to 1.3 mol * 4 H atoms/mol = 5.2 moles H atoms, (c) 2.4 moles of C6H12 corresponds to 2.4 mol * 12 H atoms/mol = 28.8 moles H atoms, and (d) 1.87 moles of C8H18 corresponds to 1.87 mol * 18 H atoms/mol = 33.66 moles H atoms.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It's a bit like a recipe, but instead of cups and teaspoons, chemists use moles to measure the ingredients. In solving a problem like the one in our exercise, stoichiometry allows us to figure out the exact amount of hydrogen atoms in a sample, based on the proportion of elements in the molecular formula.

Think of it like this: in a cake, the recipe might call for 2 eggs per cake. If you want to make 5 cakes, you'd need 10 eggs. Similarly, if a molecule has 4 hydrogen atoms, and you have 1.3 moles of that molecule, you would have a total of \(1.3 \times 4\) moles of hydrogen atoms. This is the heart of stoichiometry—using mole ratios to calculate the amount of substance involved in a reaction.

Chemical Composition

Chemical composition refers to the identity and quantity of the elements that make up a substance. Every compound has a unique composition that can be described by its chemical formula, like \(C_4H_{10}\) or \(CH_4\). Knowing the chemical composition is crucial because it tells us the ratio of different atoms within a molecule, which we use in stoichiometric calculations.

When we say that \(C_4H_{10}\) has a chemical composition that includes 4 carbon atoms and 10 hydrogen atoms, we can use this information to understand the properties of butane and predict how it will react in various chemical reactions. By understanding the chemical composition, we can accurately perform calculations on samples like in the textbook exercise, and predict how much of a certain element is present.

Molecular Formula

The molecular formula provides the exact number of each type of atom in a molecule. For example, in the molecular formula \(CH_4\), the letter 'C' stands for carbon and 'H' for hydrogen, with the subscript '4' indicating there are four hydrogen atoms for each carbon atom. This formula is a direct reflection of the chemical's composition.

Using the molecular formula is like having the blueprint for a building. It tells you how much of each material you have and how they fit together. So, in a problem like ours, if you know you have 1.3 moles of \(CH_4\), the molecular formula makes it clear that you're dealing with 1.3 moles of carbon atoms and \(1.3 \times 4\) moles of hydrogen atoms, because there are 4 hydrogens for every carbon in methane.

Avogadro's Number

Avogadro's number, \(6.022 \times 10^{23}\), is a constant that represents the number of particles (usually atoms or molecules) in one mole of a substance. It's named after the Italian scientist Amedeo Avogadro. This number is incredibly large because atoms and molecules are incredibly small.

Why is this number so important? Well, it allows chemists to count atoms by weighing. Since we can't count a mole of atoms individually—they are just too small and too numerous—Avogadro's number provides a bridge between the microscopic world of atoms and the macroscopic world that we can measure. In the context of our exercise, Avogadro's number isn't directly used, but it underpins the concept of moles that we use for measuring amounts of substances like hydrogen atoms.