Problem 66 - A Complete Resource Book in Chemistry for JEE Main

Question

Number of atoms in \(4.25 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) is approximately (a) \(6 \times 10^{23}\) (b) \(15 \times 10^{23}\) (c) \(1.5 \times 10^{23}\) (d) \(2.5 \times 10^{23}\)

Step-by-Step Solution

Answer

(a) Approximately, it is \(6 \times 10^{23}\) atoms.

Step 1: Calculate the Molar Mass of NH3

First, determine the molar mass of ammonia, \(\text{NH}_3\). The atomic mass of nitrogen (N) is approximately 14 g/mol, and the atomic mass of hydrogen (H) is about 1 g/mol. Therefore, the molar mass of \(\text{NH}_3\) is calculated as: \(\text{Molar mass of } NH_3 = 14 + 3 \times 1 = 17\, \text{g/mol}.\)

Step 2: Determine the Number of Moles in 4.25 g of NH3

Use the molar mass to convert grams of \(\text{NH}_3\) to moles. This is done by dividing the mass of the sample by the molar mass: \[\text{Number of moles} = \frac{4.25\, \text{g}}{17\, \text{g/mol}} = 0.25\, \text{mol}.\]

Step 3: Calculate Number of Molecules in the Moles of NH3

To find the number of molecules, multiply the number of moles by Avogadro's number, \(6.022 \times 10^{23}\): \[\text{Number of molecules} = 0.25\, \text{mol} \times 6.022 \times 10^{23}\, \text{molecules/mol} = 1.5055 \times 10^{23}\, \text{molecules}.\]

Step 4: Determine Total Number of Atoms

Each molecule of \(\text{NH}_3\) contains 4 atoms (1 N and 3 H). Multiply the number of molecules by 4 to find the total number of atoms: \[\text{Total Number of Atoms} = 1.5055 \times 10^{23} \times 4 = 6.022 \times 10^{23}\, \text{atoms}.\]

Step 5: Select the Closest Answer

The calculated number of atoms is \(6.022 \times 10^{23}\). Comparing this with the given options, the closest option is \(6 \times 10^{23}\), which corresponds to option (a).

Key Concepts

Avogadro's Number

Avogadro's Number is a fundamental constant of chemistry that provides a link between the macroscopic and molecular world. Named after the scientist Amedeo Avogadro, it defines the number of representative particles, usually atoms or molecules, contained in one mole of a substance. Avogadro's Number is approximately equal to \(6.022 \times 10^{23}\). This means that one mole of any substance contains \(6.022 \times 10^{23}\) elementary entities, whether they are atoms, molecules, or ions.
For instance, using Avogadro's Number, we can determine how many molecules are present in a set amount of a compound, as shown in the original exercise where it was used to calculate the number of molecules in 0.25 moles of \(\text{NH}_3\).
Understanding Avogadro's Number is crucial in calculating the total number of atoms when looking at chemical reactions or compound compositions, translating minute molecular amounts into bulk quantities used in laboratory or industrial settings.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the quantities of substances involved. In essence, stoichiometry allows us to predict how much of a substance is needed or produced in a given reaction, ensuring that reactions occur with the correct proportions.
In the context of the given exercise,

• It was used to convert grams to moles of \(\text{NH}_3\).
• This required understanding the stoichiometric relationships established by the molar mass of the compounds and Avogadro's Number.

Using stoichiometry, the mass of any reactant or product can be converted into moles, which can further be used to calculate the number of molecules involved in a reaction. This is a vital concept in chemistry, helping chemists to accurately measure quantities for reactions.

Atomic Mass

Atomic Mass is a fundamental concept referring to the mass of an atom, typically expressed in atomic mass units (amu). The atomic mass of an element is approximately equivalent to the total number of protons and neutrons in its nucleus. This makes it a useful number when calculating the mass of a moles of elements and compounds.
For example, in the exercise, the atomic masses of nitrogen and hydrogen were used to find the molar mass of \(\text{NH}_3\):

• Nitrogen has an approximate atomic mass of 14 g/mol.
• Hydrogen has an approximate atomic mass of 1 g/mol.

With these values, the molar mass of ammonia was computed as \(17\, \text{g/mol}\). Having the atomic and molar mass information is essential for converting masses into moles, a key step in the calculation of quantities in chemical reactions and crucial for understanding how much of a substance one is dealing with at the molecular level.