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

Step-by-step solution

Analyze the Structure of Butane

For compound (a), butane \(C_4H_{10}\), we know there are 4 carbon atoms and 10 hydrogen atoms in each molecule.

Calculate Moles of Hydrogen in Butane

To find the total moles of hydrogen atoms in the butane sample, multiply the number of moles of butane by the number of hydrogen atoms per molecule: \(0.0885 \text{ mol} \times 10 = 0.885 \text{ mol}\) of hydrogen atoms.

Analyze the Structure of Methane

For compound (b), methane \(CH_4\), there is 1 carbon atom and 4 hydrogen atoms in each molecule.

Calculate Moles of Hydrogen in Methane

To calculate the moles of hydrogen in methane, multiply the moles of methane by 4: \(1.3 \text{ mol} \times 4 = 5.2 \text{ mol}\) of hydrogen atoms.

Analyze the Structure of Hexane

For compound (c), hexane \(C_6H_{12}\), there are 6 carbon atoms and 12 hydrogen atoms in each molecule.

Calculate Moles of Hydrogen in Hexane

To find the total moles of hydrogen atoms in hexane, multiply the moles of hexane by the number of hydrogen atoms per molecule: \(2.4 \text{ mol} \times 12 = 28.8 \text{ mol}\) of hydrogen atoms.

Analyze the Structure of Octane

For compound (d), octane \(C_8H_{18}\), there are 8 carbon atoms and 18 hydrogen atoms in each molecule.

Calculate Moles of Hydrogen in Octane

Finally, calculate the moles of hydrogen in octane by multiplying the moles of octane by 18: \(1.87 \text{ mol} \times 18 = 33.66 \text{ mol}\) of hydrogen atoms.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships that govern the combination of elements in chemical reactions. It allows scientists and students alike to make predictions about the outcomes of chemical reactions, providing a way to calculate the amounts of reactants needed or products formed.

For instance, in the given exercise, stoichiometry is applied to determine the number of moles of hydrogen atoms present in several hydrocarbon compounds. This involves using the known stoichiometric ratios derived from the molecular formulas (e.g., in butane, \(C_4H_{10}\), the ratio of carbon to hydrogen atoms is 4:10). By understanding these ratios and applying the principles of stoichiometry, the quantity of hydrogen atoms can be calculated by simple multiplication.

Improving grasp of stoichiometry:

• Recognize that stoichiometric coefficients in balanced equations serve as the conversion factor between moles of reactants and products.
• Practice with various problems to become familiar with converting among grams, moles, and molecules.
• Always check for dimensional consistency in your calculations to ensure no mistakes were made.

Molecular Composition

Molecular composition refers to the types of atoms and the number of each type of atom that compose a molecule. In the context of the given exercise, understanding the molecular composition of hydrocarbons is crucial to solving the problem.

Each hydrocarbon molecule is composed of carbon (C) and hydrogen (H) atoms. The subscripts in the molecular formulas, for example, 10 in butane (\(C_4H_{10}\)), indicate the number of hydrogen atoms associated with a fixed number of carbon atoms. Knowing the molecular composition, we can easily determine the ratio of hydrogen to carbon and thus calculate the number of hydrogen atoms in a given mole of the hydrocarbon compound.

To enhance molecular composition comprehension:

• Study the chemical formula and visualize the structure—knowing that four hydrogen atoms bond to each carbon atom in a typical alkane can inform your calculations.
• Memorize common molecular compositions for basic molecules like water (H2O) and methane (CH4) as a starting point.
• Use molecular models to visualize 3D structures and reinforce the 2D representations found on paper.

Chemical Calculations

Chemical calculations provide the quantitative basis for predicting the results of chemical reactions, analyzing substance composition, and obtaining insights into the kinetic and thermodynamic aspects of chemical processes.

In the context of the homework exercise, chemical calculations involve determining the number of moles of hydrogen atoms present in different moles of hydrocarbon molecules. This is achieved by applying the concepts of stoichiometry, using molar masses, atomic ratios, and Avogadro's number to translate between moles, grams, and the number of atoms.

Key points to excel in chemical calculations include:

• Being adept at converting units, noting that Avogadro's number (\(6.022 \times 10^{23}\) atoms/molecules per mole) is critical in conversions.
• Mastering the application of the mole concept as the bridge between the mass of substances and the number of particles.
• Understanding that these calculations require precision and attention to detail, such as keeping track of significant figures and consistently using the correct units.

A Practical Example

In compound (c), hexane (\(C_6H_{12}\)), the calculation goes as follows: \(2.4 \text{ mol} \times 12 = 28.8 \text{ mol}\) of hydrogen atoms. This demonstrates how molecular composition directly influences the chemical calculations performed in stoichiometric analysis.