Problem 88 - A Complete Resource Book in Chemistry for JEE Main

Question

88\. Maximum number of molecules will be in (a) \(1 \mathrm{~g}\) of \(\mathrm{H}_{2}\) (b) \(10 \mathrm{~g}\) of \(\mathrm{H}_{2}\) (c) \(22 \mathrm{~g}\) of \(\mathrm{O}_{2}\) (d) \(44 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) 89\. Haemoglobin contains \(0.33 \%\) of iron by weight. The molecular weight of haemoglobin is approximately 67200 . The number of iron atom (at. wt of \(\mathrm{Fe}\) is 56 ) present in one molecule of haemoglobin are (a) 1 (b) 6 (c) 4 (d) 2 90\. The equivalent weight of phosphoric acid \(\left(\mathrm{H}_{3} \mathrm{PO}_{4}\right)\) in the reaction: \(\mathrm{NaOH}+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow \mathrm{NaH}_{2} \mathrm{PO}_{4}+\mathrm{H}_{2} \mathrm{O}\) is (a) 89 (b) 98 (c) 59 (d) 29

Step-by-Step Solution

Answer

1. (b) 10 g of H₂ 2. (c) 4 3. (b) 98

Step 1: Identify Number of Moles of Each Substance

The number of molecules in a substance is proportional to the number of moles. Calculate the moles for each option: For H₂, the molar mass is 2 g/mol. - In 1 g of H₂, moles = \( \frac{1}{2} = 0.5 \) moles- In 10 g of H₂, moles = \( \frac{10}{2} = 5 \) molesFor O₂, the molar mass is 32 g/mol. - In 22 g of O₂, moles = \( \frac{22}{32} \approx 0.6875 \) molesFor CO₂, the molar mass is 44 g/mol.- In 44 g of CO₂, moles = \( \frac{44}{44} = 1 \) mole

Step 2: Determine Maximum Number of Molecules

The number of molecules is directly related to the number of moles (using Avogadro’s number, \(6.022 \times 10^{23}\) molecules/mol). - H₂ in 10 g has 5 moles, which is the highest among given options. Thus, (b) 10 g of H₂ contains the maximum number of molecules.

Step 1: Determine Iron's Mass and Moles in Haemoglobin

Given haemoglobin contains 0.33% iron.- Iron mass in 1 mole of haemoglobin = (0.0033 \times 67200) g = 221.76 g- Moles of iron = \( \frac{221.76}{56} \approx 3.96 \) molesRounding 3.96 gives us approximately 4 atoms of iron per haemoglobin molecule.

Step 2: Find Number of Iron Atoms

Calculate the number of iron atoms per haemoglobin molecule: The 3.96 moles suggests that each haemoglobin molecule contains 4 iron atoms. Thus, the answer is (c) 4.

Step 1: Calculate the Equivalent Weight of H₃PO₄

In the given reaction, only one H⁺ ion from H₃PO₄ reacts with NaOH to form NaH₂PO₄. Equivalent weight = Molar mass / n-factor.For H₃PO₄, n-factor = 1, as only one hydrogen ion is replaced.Equivalent weight = \( \frac{98}{1} = 98 \), confirming option (b).

Key Concepts

Moles and Molecules

Understanding the concept of moles is crucial in chemistry, as it serves as a bridge between the atomic and macroscopic worlds. A mole is a unit that defines a specific number of atoms, molecules, or ions in a given substance. The number, known as Avogadro's number, is approximately \(6.022 \times 10^{23}\) particles per mole.
To find the number of molecules, we first determine how many moles of a substance we have. This is calculated by dividing the mass of the substance by its molar mass (the mass of one mole of that substance).
In the exercise given, we calculated the moles for different substances like \(\mathrm{H}_2\), \(\mathrm{O}_2\), and \(\mathrm{CO}_2\). For instance, in \(10 \mathrm{~g}\) of \(\mathrm{H}_2\) molecules, we calculated \(5\) moles, which equates to \(5 \times 6.022 \times 10^{23}\) molecules, demonstrating that it's the most on the list. This highlights how moles facilitate comparisons based on mass.

Chemical Reactions

Chemical reactions involve transformations where substances, called reactants, undergo changes to become new substances known as products. In the example provided, we observe a reaction between \(\mathrm{NaOH}\) and \(\mathrm{H}_3\mathrm{PO}_4\).
Each reaction can be represented by a balanced chemical equation that reflects the conservation of mass and atoms. Here, \(\mathrm{NaOH}\) reacts with \(\mathrm{H}_3\mathrm{PO}_4\) to form \(\mathrm{NaH}_2\mathrm{PO}_4\) and \(\mathrm{H}_2\mathrm{O}\).
A vital concept in such reactions is the "n-factor," or the number of electrons exchanged or atoms replaced in the reaction. For phosphoric acid, the reaction demonstrates that only one hydrogen ion is replaced, affecting its equivalent weight.

Equivalent Weight

Equivalent weight is a critical concept for understanding stoichiometry in chemical reactions. It refers to the mass of a substance that will react with or displace one mole of hydrogen atoms, electrons, or ions.
To find the equivalent weight, you divide the molar mass of a compound by its n-factor, which indicates the number of electrons transferred or hydrogen ions replaced in the reaction.
In the exercise, the equivalent weight of \(\mathrm{H}_3\mathrm{PO}_4\) was calculated by dividing its molar mass \(98\, \mathrm{g/mol}\) by its n-factor, which in this case was one. Thus, the equivalent weight remained \(98\), corresponding to option (b) in the question. This calculation exemplifies how understanding equivalent weight aids in determining how substances interact in reactions.

Haemoglobin and Iron Content

Haemoglobin is a vital protein in red blood cells responsible for oxygen transport throughout the human body. Its molecular structure includes iron atoms, essential for binding oxygen.
In the given problem, haemoglobin's iron content was specified as \(0.33\%\) by weight. To determine how many iron atoms are present per molecule of haemoglobin, first calculate the total iron mass in one mole of haemoglobin, which has a molecular weight of approximately 67200 g/mol.
Moles of iron in haemoglobin can be found by dividing the iron weight \(221.76\, \mathrm{g}\) by its atomic weight \(56\). This calculation results in approximately \(3.96\) moles, rounded to \(4\) iron atoms per molecule of haemoglobin, confirming that it allows effective oxygen transport capacity for each molecule. Understanding the content and role of iron in haemoglobin is crucial for grasping how our body sustains vital biological processes.