Calculate the molar mass of a particular polyethylene sample, \(\mathrm{fCH}_{2}-\mathrm{CH}_{2}-\mathrm{r}_{n},\) where \(n=4600\)

Polyethylene is a common plastic composed of a long chain of ethylene units. Its properties, like strength and melting point, depend on the length of the chain, which is signified by the number of ethylene units, 'n.' To understand the molar mass of polyethylene, it's important to know that it's the total mass of one mole of the polymer. The molar mass is calculated by multiplying the molar mass of a single ethylene unit by the number of units in the chain ().

For example, with ) being 4600, as in the exercise presented, the molar mass of one ethylene unit is found to be 28.06 g/mol. Therefore, the molar mass of the polyethylene is 4600 * 28.06 g/mol = 129076 g/mol), which gives us an understanding of the size and molecular weight of this particular polyethylene sample.

The ethylene unit, a fundamental building block of polyethylene, is a small molecule consisting of two carbon atoms double-bonded together, each with two hydrogen atoms attached ((CH2=CH2))). The molar mass of this unit is critical for calculating the mass of larger polymer chains such as polyethylene.

Each atom contributes to the overall molar mass based on its atomic weight: one mole of carbon atoms weighs 12.01 grams, and one mole of hydrogen atoms weighs approximately 1.01 grams. By adding together the atomic masses of the atoms in the ethylene unit, chemists can determine its molar mass.

Understanding the periodic table is crucial for chemistry calculations. Each element's atomic weight is listed, typically in atomic mass units (amu) or grams per mole (g/mol). These values are used to calculate the molar mass of compounds, based on the number and type of atoms present.

When calculating the molar mass of an ethylene unit, we use the atomic weights of carbon (2 atoms, each at 12.01 g/mol) and hydrogen (4 atoms, each at 1.01 g/mol) from the periodic table. Combining these values gives us the molar mass of the ethylene unit and enables further calculations for polymers like polyethylene.

Performing chemistry calculations often requires a systematic approach, especially when determining molar masses. The step-by-step method ensures accuracy and helps students grasp the conceptual reasoning behind the calculations.

Starting with the basic building blocks (like the ethylene unit), we sum the atomic weights to find the molar mass of the compound. This approach is not only used for single molecules but also for calculating the masses of larger and more complex structures, such as polymers, by scaling up these base values. It is the fundamental technique that allows chemists and students alike to understand and predict the behaviour of substances in various conditions.