Question

Which among the following is the heaviest? (a) One mole of oxygen (b) One molecule of sulphur trioxide (c) 100 amu of uranium (d) \(44 \mathrm{~g}\) of carbon dioxide

Short answer

44 grams of carbon dioxide is the heaviest.

Step-by-step solution

Determine the mass of one mole of oxygen

Molecular oxygen ( ext{O}_2) has a molar mass of 32 g/mol. Therefore, one mole of oxygen weighs 32 grams.

Determine the mass of one molecule of sulfur trioxide

The molar mass of sulfur trioxide (SO_3) is calculated by adding the atomic masses of sulfur (32.07 amu) and three oxygen atoms (16 amu each): \( ext{Molar mass of SO}_3 = 32.07 + 3 imes 16 = 80.07 ext{ amu} \)One molecule of SO_3 weighs 80.07 amu.

Assess the mass of 100 amu of uranium

Given is 100 amu of uranium. This is just a straight value of 100 amu since we do not need to calculate further.

Determine the mass of 44 grams of carbon dioxide

Given directly is the 44 grams of CO_2. No calculation is needed since the mass is already given.

Compare the masses

Convert any non-gram masses to grams if necessary for easy comparison. - 32 grams for one mole of O_2 - 80.07 amu of SO_3 (convert via 1 amu = 1.66 imes 10^{-24} g, but not necessary since it is low anyway relative to grams) - 100 amu of uranium (convert: 100 imes 1.66 imes 10^{-24} g, but it is still very small relative to grams) - Directly 44 grams for CO_2 Upon comparison, 44 grams of CO_2 is greater than 32 grams of O_2.

Key concepts

Mole Concept

The mole concept is a fundamental aspect of chemistry that helps us quantify the amount of substance in terms that are manageable and relate directly to the atoms and molecules involved. A mole is defined as the quantity containing exactly 6.022 x 10^{23} elementary entities, be they atoms, molecules, ions, or other particles. This value is known as Avogadro's number.
For example, when we talk about one mole of oxygen, we are referring to 6.022 x 10^{23} molecules of ext{O}_2. Each molecule of oxygen has a molar mass of 32 grams per mole, which means one mole of oxygen weighs 32 grams. The beauty of the mole concept is its ability to bridge the macroscopic scale, which we can measure directly, with the atomic scale, which we calculate based on the number of entities involved.
In practice, the mole allows chemists to convert between atoms or molecules and grams, making it easier to carry out reactions and calculate yields. The use of moles helps in understanding stoichiometry – the calculation of reactants and products in chemical reactions.

Atomic Mass Unit (amu)

The atomic mass unit, often abbreviated as 'amu', is a standard unit of mass that quantifies mass at the atomic or molecular scale. One amu is defined as one twelfth of the mass of a carbon-12 atom, which is approximately 1.66 x 10^{-24} grams.
To understand better, consider the atomic mass of sulfur or oxygen: sulfur has an atomic mass of approximately 32.07 amu, while an oxygen atom is about 16 amu. When these elements form compounds like sulfur trioxide (SO_3), the sum of the individual atomic masses of its constituent atoms gives the molecular mass of the compound. For sulfur trioxide, this would be 32.07 amu for sulfur and 3 x 16 amu for the three oxygen atoms, totaling to an approximate molecular mass of 80.07 amu.
The use of amu allows for easy comparison and calculation of the molecular masses of different compounds, providing a basis for converting these tiny masses into something measurable, such as grams.

Molecular Mass Calculation

Calculating molecular mass is crucial for understanding the properties of substances and predicting the outcomes of chemical reactions. The molecular mass is the total mass of a molecule, which is obtained by summing up the atomic masses of all the atoms present in the molecule.
The process involves simply adding the atomic masses of each atom. For example, in a molecule of sulfur trioxide (SO_3), you assemble the masses as follows: one sulfur atom with an atomic mass of 32.07 amu plus three oxygen atoms each with an atomic mass of 16 amu, resulting in a total molecular mass of 80.07 amu.
Molecular mass calculations help in determining how much of a substance is required to achieve a certain amount of product in a reaction. It also assists in converting moles to grams and vice versa, aiding in practical laboratory measurements. This calculation becomes even more powerful when applied in stoichiometry, giving clear insights into how different molecules interact in chemical processes.