Problem 106

Question

Rearrange the following (I to IV) in the order of in creasing masses and choose the correct answer from (a), (b), (c), (d). (atomic masses: \(\mathrm{N}=14, \mathrm{O}=\) \(16, \mathrm{Cu}=63)\) I. 1 molecule of oxygen II. 1 atom of nitrogen III. \(1 \times 10^{10} \mathrm{~g}\) molecular weight of oxygen IV. \(1 \times 10^{-18} \mathrm{~g}\) atomic weight of copper (a) II \(<\mathrm{I}<\mathrm{IV}<\mathrm{III}\) (b) IV < III < II

Step-by-Step Solution
Verified

Answer

(a) II < I < IV < III.

1Step 1: Determine the Mass of Each Entity

1. **Oxygen Molecule (I)**: An oxygen molecule consists of two oxygen atoms. The atomic mass of oxygen is 16, so the molecular mass is \(2 \times 16 = 32 \text{ u}\). 2. **Nitrogen Atom (II)**: The atomic mass of nitrogen is given as 14 u. 3. **Molecular Weight of Oxygen (III)**: \(1 \times 10^{10} \text{ g}\) is the given mass, without needing further calculation as it is a large number. 4. **Atomic Weight of Copper (IV)**: \(1 \times 10^{-18} \text{ g}\) is the given mass, very small. This is for one atom of copper.

2Step 2: Compare and Order the Masses

We'll arrange the values from the smallest to largest. 1 atom of nitrogen (14u) < 1 molecule of oxygen (32u) since 14 < 32, then move next to the given weights. Since \(1 \times 10^{-18} \text{ g}\) is much smaller than \(1 \times 10^{10} \text{ g}\), we know it will come after atomic nitrogen and oxygen on mass scale, but before the large molecular weight of oxygen. Thus the full order becomes: 1 atom nitrogen < 1 molecule oxygen < \(1 \times 10^{-18} \text{ g}\) copper < \(1 \times 10^{10} \text{ g}\) oxygen.

3Step 3: Select the Correct Order from Options

Based on our ordering from smallest to largest (II < I < IV < III), we compare with the given options. - (a) does correctly match \(\text{II} < \text{I} < \text{IV} < \text{III}\). Thus, the correct option is **(a).**

Key Concepts

Atomic StructureMolecular WeightChemistry Problem Solving

Atomic Structure

Atomic structure is the foundation of understanding how atoms combine to form molecules. Atoms are the smallest units of elements that retain the properties of that element. They are composed of three primary subatomic particles: protons, neutrons, and electrons.

Protons have a positive charge and reside in the nucleus.

Neutrons are neutral and, along with protons, make up the nucleus, contributing to most of the atom's mass.

Electrons are negatively charged and orbit the nucleus in electron clouds or shells.

The atomic mass is mostly contained in the nucleus due to the protons and neutrons. This mass is crucial in comparing the weights of different atoms or molecules, as seen in the exercise where the atomic masses of nitrogen, oxygen, and copper dictate the order of their increasing masses. Understanding atomic mass helps in determining how atoms will interact with each other chemically.

Molecular Weight

Molecular weight or molecular mass is the sum of the atomic masses of all atoms in a molecule. It is measured in atomic mass units (u). To find a molecule's weight, we add up the weights of its constituent atoms. For example, an oxygen molecule consists of two oxygen atoms. With each oxygen atom having a mass of 16 u, the molecular weight of an oxygen molecule is \[ 2 \times 16 = 32 ext{ u} \].
Molecular weight is used in calculating the proportions in which different chemicals react, ensuring that reactions are based on equal and correct amounts of substances. This concept is vital for solving problems in chemistry where you may need to calculate the mass of a reactant or product in a chemical reaction. Understanding molecular weight is key in evaluating chemical formulas and solving quantitative chemistry problems effectively.

Chemistry Problem Solving

Solving chemistry problems often requires clear understanding and application of basic chemical principles and concepts. It involves:

Identifying relevant data and information, such as atomic and molecular weights.

Understanding the relationships between different substances, including how to order them by weight or reactivity.

Applying mathematical skills to manipulate units and perform calculations.

In the exercise given, the aim is to order different atoms and molecules by their weight. This requires calculating and comparing the atomic and molecular weights of the entities. Using systematic steps: - Start by calculating individual masses based on known atomic weights. - Arrange these calculated values in order from smallest to largest. - Finally, match your result with the given options to determine the correct solution. Developing these problem-solving skills in chemistry not only aids in exercises but also prepares students for more complex concepts in real-world chemical processes.

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