Question

How many atoms of hydrogen are found in \(2.31 \mathrm{~mol}\) of propane, \(\mathrm{C}_{3} \mathrm{H}_{8} ?\)

Short answer

There are \(\left(2.31 \times 6.022 \times 10^{23}\right) \times 8\) atoms of hydrogen in 2.31 mol of propane.

Step-by-step solution

Understanding the Composition of Propane

Propane, with a chemical formula of \(\mathrm{C}_3\mathrm{H}_8\), consists of 3 carbon atoms and 8 hydrogen atoms per molecule.

Calculating the Total Number of Propane Molecules

Use Avogadro's number to calculate the total number of propane molecules in 2.31 mol of propane. Avogadro's number is \(6.022 \times 10^{23}\) entities per mole. Thus, the total number of propane molecules is \(2.31 \mathrm{~mol} \times 6.022 \times 10^{23} \mathrm{molecules/mol}\).

Calculating the Total Number of Hydrogen Atoms

Since each propane molecule has 8 hydrogen atoms, the total number of hydrogen atoms in 2.31 mol of propane is the total number of propane molecules multiplied by 8. This is calculated as \(\left(2.31 \times 6.022 \times 10^{23}\right) \times 8\).

Key concepts

Mole Concept

The mole concept is a fundamental aspect of chemistry that allows for the counting of particles, such as atoms, molecules, and ions, by relating them to a specific quantity. Essentially, a mole is like a chemist's dozen, except instead of 12, it represents approximately \(6.022 \times 10^{23}\) particles. This number is known as Avogadro's number.

When dealing with substances, it is often impractical to count each particle due to their minuscule size and large numbers. The mole concept mitigates this by providing a bridge between the microscopic world of atoms and the macroscopic world we interact with. For instance, when we say we have 1 mole of propane, we are referring to \(6.022 \times 10^{23}\) molecules of propane.

To calculate the number of atoms in a given number of moles, you multiply the number of moles by Avogadro's number and then by the number of atoms of that element in the molecule. If we follow this for hydrogen in propane, we first understand that 1 mole of propane contains 8 moles of hydrogen atoms since there are 8 hydrogen atoms in each molecule.

Avogadro's Number

Avogadro's number, \(6.022 \times 10^{23}\), is a constant that represents the quantity of particles found in one mole of any substance. It is named after the Italian scientist Amedeo Avogadro who first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules, regardless of the type of gas.

This number is incredibly important as it allows chemists to work with the submicroscopic world in a convenient, manageable way. It forms the foundation of stoichiometry, which is the calculation of reactants and products in chemical reactions. To put it into perspective, every mole of any substance contains exactly the same number of particles as there are in 12 grams of carbon-12, which is Avogadro's number.

Knowing this, we can link moles of substances to their mass, and measure out exact amounts needed for reactions, which is exactly what was done in step 2 of the solution where the number of propane molecules was determined by multiplying the moles given by Avogadro's number.

Chemical Composition

Chemical composition refers to the identity and ratio of the elements that make up any particular compound. Every chemical substance has a unique composition represented by a chemical formula, like \(\mathrm{C}_3\mathrm{H}_8\) for propane. This formula tells us that a single molecule of propane consists of three carbon atoms \(\mathrm{(C)}\) and eight hydrogen atoms \(\mathrm{(H)}\).

Understanding the chemical composition is crucial for determining the amount of each element in a substance. This knowledge is applied in stoichiometry for predicting the outcomes of chemical reactions and ensuring that reactants are mixed in the correct proportions. In the exercise, knowing the chemical composition of propane allows us to figure out that 1 mole of propane will have 8 moles of hydrogen atoms due to the 8 hydrogen atoms present in each molecule.

Subsequently, if we need to find the total number of hydrogen atoms in 2.31 moles of propane, we consider the chemical composition of propane to determine the number of hydrogen atoms present and use it in calculations as shown in step 3 of the solution.