Problem 20 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

One mole of oxygen (32 g) is the heaviest option available.

Step 1: Determine Molar Mass of Oxygen

The atomic mass of oxygen is approximately \(16 \text{ u}\). Since one mole of oxygen consists of \(O_2\), its molar mass is \(2 \times 16 = 32 \text{ u/mol}\). Therefore, one mole of oxygen weighs \(32 \text{ grams}\).

Step 2: Determine Mass of One Molecule of Sulphur Trioxide

The atomic masses are approximately \(S = 32 \text{ u}\) and \(O = 16 \text{ u}\). Therefore, the mass of one molecule of \(SO_3\) is \(32 + 3 \times 16 = 80 \text{ u}\). Since an amu conversion to grams is very negligible, the mass in comparison to others would be inconsequential.

Step 3: Determine Mass of 100 amu of Uranium

Uranium's atomic mass is \(238 \text{ u}\), so 100 amu of uranium is much lighter than its atomic mass. Therefore, it weighs much less than 1 gram and is negligible in comparison to the others.

Step 4: Determine Mass Comparison with Carbon Dioxide

The atomic masses for carbon and oxygen are \(C = 12 \text{ u}\) and \(O = 16 \text{ u}\), so \(CO_2\) is \(12 + 2 \times 16 = 44 \text{ u/mol}\). Given \(44 \text{ grams}\) of \(CO_2\), it exactly equals 1 mole of \(CO_2\).

Key Concepts

Mole Concept

The mole concept is a fundamental idea in chemistry for quantifying the amount of a substance. A "mole" indicates an amount so large that it is used to count extremely tiny particles like atoms and molecules. One mole is equivalent to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles.

In practice, the mole helps bridge the gap between the atomic scale and the macroscopic world. When you know the number of moles of a substance, you can determine its mass, volume, or the number of particles it contains. In the aforementioned exercise, one mole of oxygen refers to a quantity containing \(6.022 \times 10^{23}\) molecules of \(O_2\). This concept enables us to calculate the molar mass and directly relate it to a measurable quantity in grams.

Atomic Mass

Atomic mass, often referred to as atomic weight, represents the mass of an individual atom compared to a twelfth of the mass of a carbon-12 atom. This is expressed in atomic mass units (amu), where 1 amu is defined as one twelfth of the mass of a carbon-12 atom.

For example, the atomic mass of oxygen is approximately \(16 ext{ u}\). The atomic masses of elements are crucial for making stoichiometric calculations. In practice, these weights enable chemists to convert between grams and moles, achieving a more practical way to measure the substances involved in chemical reactions. In the exercise above, atomic masses are used to determine the mass of full molecules like \(SO_3\) and \(CO_2\).

Molecule Weight

Molecular weight is essentially the sum of the atomic weights of all atoms in a molecule. It is a specific type of "formula weight" and is helpful in determining how heavy a molecule is compared to a single atom. Just like the mole concept, molecular weight allows a bridge between microscopic molecules and macroscopic mass.

To calculate the molecule weight of \(SO_3\), for example, you add up the atomic weights of sulphur (\(32 ext{ u}\)) and oxygen (three times \(16 ext{ u}\)), resulting in \(80 ext{ u}\). Using the molecular weight, we can calculate the mass of even a single molecule. Despite this process, in large quantity measurements (like amu conversion), these values can be negligible compared to grams.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves the use of conversion factors derived from balanced chemical equations and is vital for predicting mass, volume, and the number of moles of substances.

In the problem you provided, stoichiometry isn't directly applied as in chemical reactions but understanding stoichiometric concepts can help compare different quantities. With stoichiometry knowledge, we can assess how much of a substance is required or produced in a reaction and compare masses, like in this exercise, where different substances are quantified and compared based on their mass rather than their chemical reactivity. This involves understanding how many grams correspond to a given number of moles or atomic mass units, ensuring correct conversions and comparisons.