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The molar mass is a fundamental concept in chemistry that helps to determine the mass of one mole of a chemical substance. It is measured in grams per mole (\(\text{g/mol}\)). To compute the molar mass, simply sum up the atomic masses of all atoms present in the molecule.
For instance, in the case of styrene, we first need the empirical formula, which is \(\text{CH}\), to calculate its molar mass. This entails adding the molar masses of carbon and hydrogen:

• Carbon (C) has a molar mass of 12.01 \(\text{g/mol}\).
• Hydrogen (H) has a molar mass of 1.01 \(\text{g/mol}\).

So, the molar mass of \(\text{CH}\) is 13.02 \(\text{g/mol}\).
Understanding the molar mass is crucial as it serves as the bridge between the mass of a substance and the number of particles contained in that mass.

Calculating moles is a central task when dealing with chemical substances. The formula used is: \[\text{Number of moles} = \frac{\text{mass of the sample}}{\text{molar mass}}\]This calculation translates the macroscopic mass of a sample into a number that reflects how many microscopic particles, or moles, it contains.
Using styrene as an example, with a given molar mass of 104.14 \(\text{g/mol}\), if we have a 2.00 g sample, the number of moles is:

• \(\frac{2.00 \text{ g}}{104.14 \text{ g/mol}} \approx 0.0192 \text{ moles}\)

This calculation, \(0.0192\) moles, indicates the amount of substance present in the sample, making it easier to determine further properties like the number of atoms.

Avogadro's number is a large constant used in chemistry to relate moles to individual entities like atoms or molecules. It is given as: \(6.022 \times 10^{23}\) atoms/mol or molecules/mol.
This constant allows for the conversion from the macroscopic mole concept to a microscopic count of atoms. In our styrene sample, having determined the moles, we convert this to the actual number of hydrogen atoms:

• First, find the moles of hydrogen in styrene by multiplying the moles of styrene by the number of hydrogen atoms per molecule.
• Next, convert these moles to atoms using Avogadro's number.
• In the example, \((0.1536 \text{ moles})\times(6.022 \times 10^{23} \text{ atoms/mol}) \approx 9.23 \times 10^{22} \text{ atoms}\)

This vast number gives a feel for the multitude of atoms present even in small chemical amounts.

Chemical formulas are the written symbol representation of the elements present in a compound, showcasing the proportions in which they combine. They can be empirical, molecular, or structural.
The chemical formula not only identifies the elements but also indicates the proportions. For styrene, the empirical formula is \(\text{CH}\), which represents the simplest whole-number ratio of carbon to hydrogen atoms in the compound.
This simplifies to signify that the compound contains eight times this ratio in a full molecular depiction, as seen in step 2 of our solution.
Understanding the chemical formula provides insights into chemical reactions and properties, serving as the fundamental language of chemistry. It allows chemists to convey a vast amount of information about the nature and composition of chemical substances efficiently.