Problem 18 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which has maximum number of atoms? (a) \(24 g\) of \(C(12)\) (b) \(56 \mathrm{~g}\) of \(\mathrm{Fe}(56)\) (c) \(27 \mathrm{~g}\) of \(\mathrm{Al}(27)\) (d) \(108 \mathrm{~g}\) of \(\operatorname{Ag}(108)\)

Step-by-Step Solution

Answer

24 g of carbon has the maximum number of atoms.

Step 1: Calculate moles for each element

To determine the number of atoms in each sample, first calculate the moles of each element using the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \] For (a) Carbon: \( \text{moles of } C = \frac{24}{12} = 2 \). For (b) Iron: \( \text{moles of } Fe = \frac{56}{56} = 1 \). For (c) Aluminium: \( \text{moles of } Al = \frac{27}{27} = 1 \). For (d) Silver: \( \text{moles of } Ag = \frac{108}{108} = 1 \).

Step 2: Determine number of atoms for each element

Use Avogadro's number to find the number of atoms for each sample. Avogadro's number is \(6.022 \times 10^{23}\) atoms per mole. Calculate the atoms: (a) Carbon: \(2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{24}\) atoms. (b) Iron: \(1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23}\) atoms. (c) Aluminium: \(1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23}\) atoms. (d) Silver: \(1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23}\) atoms.

Step 3: Compare number of atoms

Compare the number of atoms calculated for each element. Carbon, with \(1.2044 \times 10^{24}\) atoms, has more atoms than Iron, Aluminium, and Silver, which each have \(6.022 \times 10^{23}\) atoms.

Key Concepts

Number of Atoms

When we talk about the number of atoms in a given sample, we're essentially counting the tiny particles that make up a chemical element. Every substance is made of atoms, and knowing how many are in a sample requires a clever method due to their minuscule size.
To find the number of atoms in a sample, we multiply the number of moles by Avogadro's Number. Avogadro's Number is a constant represented by \(6.022 \times 10^{23}\), which tells us how many atoms or molecules are in one mole of any substance.
Let's break it down into steps for clarity:

• Calculate the moles of the substance using its mass and molar mass.
• Use Avogadro's Number to convert moles to number of atoms: \[ \text{Number of atoms} = \text{moles} \times 6.022 \times 10^{23} \]

This two-step process allows us to make sense of the massive number of atoms in even the smallest sample.

Moles Calculation

The concept of moles is central to understanding chemistry because it offers a way to convert between the mass of a substance and the number of its constituent particles. A "mole" is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles. One mole equals exactly \(6.022 \times 10^{23}\) particles, thanks to Avogadro's Number.
To calculate moles, we use the formula: \[ \text{moles} = \frac{\text{mass of the substance}}{\text{molar mass of the substance}} \]
Here's how the process works:

• Identify the given mass of the substance in grams.
• Find out the molar mass of the substance in grams per mole, usually from the periodic table.
• Divide the mass by the molar mass, which gives you the number of moles.

This approach is useful in allowing scientists and students to relate a substance's weight to its particle count, thus translating visible quantities to atomic scale interpretations.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). It is a key piece in many calculations in chemistry as it links the mass of a substance to its moles. Understanding molar mass lets you navigate between the scale of grams and the world of the molecule.
Molar mass is determined from the atomic masses of the element(s) in the substance, as reported on the periodic table. The atomic mass of an element provides the average weight of its atoms.

To calculate molar mass:

• Refer to the periodic table to find the atomic mass of each element in the compound.
• Sum these atomic masses according to the number of each type of atom in the compound's formula.

For instance, in a single element sample, like Carbon \(C\), the molar mass is the atomic mass (12.01 g/mol). Accurately calculating molar mass is crucial for converting measurements in chemistry and understanding the properties of substances.