Problem 137 - Chemistry An Atoms First Approach

Question

The empirical formula of styrene is \(\mathrm{CH}\); the molar mass of styrene is \(104.14 \mathrm{g} / \mathrm{mol} .\) What number of \(\mathrm{H}\) atoms are present in a 2.00-g sample of styrene?

Step-by-Step Solution

Answer

In a 2.00-g sample of styrene, there are approximately \(1.15 * 10^{22}\) hydrogen atoms present.

Step 1: Calculate moles of styrene in the sample

First, we need to find out how many moles of styrene are present in the 2.00-g sample. To do this, we'll use the molar mass of styrene, which is 104.14 g/mol. The formula to calculate moles is: Moles = mass / molar mass In this case: Moles of styrene = \( \frac{2.00\ \mathrm{g}}{104.14\ \mathrm{g/mol}} \)

Step 2: Calculate the number of styrene molecules in the sample

Next, we need to determine the number of styrene molecules in the 2.00-g sample. To do this, we will use Avogadro's number, which is \(6.022*10^{23}\) particles/mol. The formula to calculate the number of molecules is: Number of molecules = moles * Avogadro's number So: Number of styrene molecules = Moles of styrene * Avogadro's number

Step 3: Calculate the number of hydrogen atoms in the sample

Finally, we can calculate the number of hydrogen atoms in the sample. Since the empirical formula of styrene is CH (meaning there is one hydrogen atom for every styrene molecule), we can multiply the number of styrene molecules by the number of hydrogen atoms per molecule to find the total number of hydrogen atoms in the sample. Number of hydrogen atoms = Number of styrene molecules * hydrogen atoms per styrene molecule Calculating the above equations for the given problem, we get: Moles of styrene = \( \frac{2.00\ \mathrm{g}}{104.14\ \mathrm{g/mol}} = 0.0192\ \mathrm{mol} \) Number of styrene molecules = 0.0192 mol * (6.022*10^{23} molecules/mol) ≈ 1.15 * 10^{22} molecules Number of hydrogen atoms = 1.15 * 10^{22} molecules * 1 H atoms/molecule = 1.15 * 10^{22} H atoms So, there are approximately \(1.15 * 10^{22}\) hydrogen atoms present in a 2.00-g sample of styrene.

Key Concepts

Moles to Grams Conversion

Understanding how to convert between moles and grams is an essential skill in chemistry. A mole is a unit that represents a very large quantity of particles, be it atoms, molecules, ions, or others. The molar mass of a substance tells us how much one mole of this substance weighs in grams. To convert from grams to moles, you need to divide the mass of your sample by its molar mass, following the formula:
\( \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \).

For the given problem with styrene, its molar mass is \(104.14 \text{g/mol}\). So, for a 2.00-gram sample of styrene, the calculation is \(\frac{2.00\text{g}}{104.14\text{g/mol}}\). This conversion is the first step to further calculations such as determining the number of particles in a sample.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry representing the number of particles in a mole. This value is approximately \(6.022 \times 10^{23}\) and applies universally to atoms, ions, molecules, or other entities.

When you determine the number of moles of a substance, you can find out how many actual particles you have by multiplying the moles by Avogadro's number:
\( \text{Number of particles} = \text{moles} \times \text{Avogadro's number} \).

In the exercise example, once you’ve found the number of moles of styrene, you multiply by Avogadro's number to find the total number of styrene molecules in the sample.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It includes calculating reactant and product quantities during chemical processes.

In the context of the given problem, stoichiometry is applied by using the empirical formula of styrene, which indicates a 1:1 ratio of carbon to hydrogen atoms. Knowing the number of styrene molecules allows for the direct calculation of hydrogen atoms since there is one hydrogen atom per molecule of styrene. The stoichiometric ratio from the empirical formula establishes this one-to-one relationship and facilitates the final calculation of hydrogen atoms present in the sample.
Understanding stoichiometry is crucial for chemists in predicting the outcomes of reactions and determining the required amounts of materials.