Find the molar mass of isopropyl alcohol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH},\) used as rubbing alcohol.

Short Answer

Expert verified
The molar mass of isopropyl alcohol, \(C_{3}H_{7}OH\), is 60.096 g/mol.

Step by step solution

01

Identify the atomic masses

First, identify the atomic masses of each atom in the isopropyl alcohol molecule. For Carbon (\(C\)), Hydrogen (\(H\)), and Oxygen (\(O\)), the atomic masses are approximately 12.01g/mol, 1.008g/mol, and 16.00g/mol respectively.
02

Count the number of atoms

Next, count the number of each atom in the isopropyl alcohol molecule. There are 3 Carbon atoms, 8 Hydrogen atoms, and 1 Oxygen atom.
03

Multiply atomic mass by the number of atoms

Multiply atomic mass for each element by the number of atoms of that element in the molecule. For Carbon, it would be \(3 \times 12.01\ g/mol\). For Hydrogen, it would be \(8 \times 1.008\ g/mol\). And for Oxygen, it would be \(1 \times 16.00\ g/mol\).
04

Sum up all the masses

Add together the masses calculated in the previous step to determine the molar mass of isopropyl alcohol. \(3 \times 12.01\ g/mol + 8 \times 1.008\ g/mol + 1 \times 16.0\ g/mol\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isopropyl Alcohol
Isopropyl alcohol, known more commonly as rubbing alcohol, is a compound that finds extensive use in household antiseptics and disinfectants. The formula for isopropyl alcohol is \(C_3H_7OH\), indicating the molecule consists of carbon, hydrogen, and oxygen atoms. With three carbon atoms (\(C\)), seven hydrogen atoms (\(H\)), and one oxygen atom (\(O\)), understanding its structure can play a significant role in the study of organic chemistry. When considering the molar mass calculation, we must account for each atom's contribution to the compound's overall mass.

To interpret the structure and to perform calculations such as the molar mass, a foundational knowledge of organic chemistry, namely the various functional groups it may contain, is beneficial. In this case, the hydroxyl group (\(-OH\)) attached to a carbon chain is what characterizes isopropyl alcohol as a member of the alcohol family.
Atomic Mass
The atomic mass is essentially the weight of a single atom of an element. It is expressed in atomic mass units (u), with one unit roughly equivalent to one-twelfth of the mass of a carbon-12 atom. However, for practical chemistry purposes, we often use the unified atomic mass unit 'gram per mole' (g/mol) that connects atomic scale masses to macroscopic quantities.

In the context of calculating the molar mass of compounds such as isopropyl alcohol, each element's atomic mass acts as a fundamental constant, essential for our computations. Consider the atomic masses of carbon (\(12.01\text{g/mol}\)), hydrogen (\(1.008\text{g/mol}\)), and oxygen (\(16.00\text{g/mol}\)). These constants are derived from the average masses of the element's isotopes and their abundance.
Stoichiometry
Stoichiometry is a branch of chemistry that involves the calculation of the quantities of reactants and products in chemical reactions. When it comes to understanding compounds, stoichiometry allows us to calculate molar masses, determine percent composition, and predict product amounts in reactions, among others.

Using stoichiometry to calculate molar mass follows a simple but crucial procedure. First, the number of atoms of each element in a molecule needs to be counted. Then, each of these counts is multiplied by the atomic mass of the respective element. Finally, the sum total of these products gives us the molar mass of the molecule. This process not only helps in comprehending the molecular composition, but also lays the groundwork for more advanced chemical equations and reactions.

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