Problem 21 - General Chemistry: Principles and Modern Applications

Question

Determine the mass percent \(H\) in the hydrocarbon isooctane, \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right)_{2}\)

Step-by-Step Solution

Answer

The mass percent of Hydrogen (H) in the hydrocarbon isooctane is approximately 15.88%.

Step 1: Determine the composition of isooctane

First, dissect the given compound formula \(C(CH_{3})_{3}CH_{2}CH(CH_{3})_{2}\). Isooctane contains 8 Carbon (C) atoms, 18 Hydrogen (H) atoms.

Step 2: Calculate the molar mass of Hydrogen and Carbon

Use the atomic masses from the periodic table to find the molar masses. For Carbon (C), it is 12.01 g/mol and for Hydrogen (H), it is 1.008 g/mol.

Step 3: Calculate the total molar mass of isooctane

We must calculate the total molar mass of the compound. Multiply the molar mass of Carbon by 8 and add the product of the molar mass of Hydrogen and 18. The result is 114.22 g/mol.

Step 4: Calculate the total molar mass of Hydrogen in isooctane

Multiply the molar mass of Hydrogen by 18 to find the total molar mass contributed by Hydrogen. The result is 18.144 g/mol.

Step 5: Calculate the mass percent of Hydrogen

To calculate the mass percent of Hydrogen, divide the total molar mass of Hydrogen by the total molar mass of isooctane and multiply by 100. The result is approximately 15.88%.

Key Concepts

Molar Mass

To calculate the molar mass of a compound, you need the sum of the masses of all the atoms in a molecule. Molar mass helps in finding out the mass of a mole of substance and is expressed in grams per mole (g/mol). You can find the molar mass by:

• Identifying each element in the molecule and its atomic mass from the periodic table.
• Multiplying the atomic mass by the number of atoms of that element in the compound.
• Adding up these values for all the elements.

For example, in isooctane, which has 8 Carbon and 18 Hydrogen atoms, the molar mass is calculated as:\[ (8 \times 12.01) + (18 \times 1.008) = 114.22 \, \text{g/mol} \]

Isooctane

Isooctane, known chemically as C\((CH_3)_3CH_2CH(CH_3)_2\), is a hydrocarbon frequently used as a reference standard in the octane rating of fuels. Its molecular structure comprises several carbon branches, making it an isomer of octane with specific characteristics:

• It is highly branched, which contributes to its high octane rating.
• Typically represented by its systematic name 2,2,4-Trimethylpentane.

Understanding isooctane's chemical formula is important for calculations, like determining its molar mass, as it helps in knowing the number and type of atoms in the compound.

Atomic Mass

Atomic mass is the mass of a single atom of a chemical element and is primarily determined by the number of protons and neutrons in the atom's nucleus.
It is measured in atomic mass units (amu). Key points about atomic mass:

• It reflects the average mass of the atoms of an element, accounting for the occurrence of isotopes.
• Used to calculate the molar mass of a compound by adding together the atomic masses of its constituent elements.

For the calculation involving isooctane, the atomic mass of Carbon (12.01 amu) and Hydrogen (1.008 amu) were used to determine the molar mass of the compound.

Chemical Composition

Chemical composition describes the types and quantities of atoms in a molecule. For any given substance, knowing its chemical composition allows us to understand properties like molar mass and to calculate concentrations or percentages, such as mass percent.
In isooctane, the chemical composition involves:

• 8 Carbon atoms and 18 Hydrogen atoms.
• This composition is crucial for finding how much Hydrogen is present relative to the entire compound.

The mass percent of an element in a compound is calculated by dividing the total mass of the element by the total molar mass of the compound, then multiplying by 100. For Hydrogen in isooctane, this results in a mass percent of approximately 15.88%.