Problem 132 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of oxalic acid molecules in \(100 \mathrm{ml}\) of \(0.02\) N oxalic acid solution is (a) \(6.023 \times 10^{22}\) (b) \(10^{-3}\) (c) \(6.022 \times 10^{20}\) (d) none of these

Step-by-Step Solution

Answer

The number of oxalic acid molecules is \(6.022 \times 10^{20}\); hence, the answer is (c).

Step 1: Determine Normality into Molarity

Given that the oxalic acid solution is 0.02 N. Since oxalic acid is a diprotic acid, each molecule gives 2 hydrogen ions. Therefore, normality equals 2 times the molarity. So, the molarity \(M\) of the solution can be found by dividing the normality by 2.\[ M = \frac{0.02}{2} = 0.01 \text{ M} \]

Step 2: Calculate Number of Moles

Using the formula for moles \( n = MV \), where \(M\) is the molarity and \(V\) is the volume in liters, we find the number of moles of oxalic acid in the solution. Convert 100 mL to liters: \( V = 0.100 \text{ L} \).\[ n = 0.01 \times 0.100 = 0.001 \text{ mol} \]

Step 3: Find Number of Molecules

The number of molecules is calculated by multiplying the number of moles by Avogadro's number \( N_A = 6.022 \times 10^{23} \).\[ \text{Number of molecules} = 0.001 \times 6.022 \times 10^{23} = 6.022 \times 10^{20} \]

Step 4: Select the Correct Answer

Comparing the calculated number of molecules \(6.022 \times 10^{20}\) with the provided options, option (c) \(6.022 \times 10^{20}\) is correct.

Key Concepts

Normality and Molarity

Normality and molarity are two important concepts in chemistry used to express concentration. Although they seem similar, they serve different purposes.
Normality refers to the equivalents per liter. An equivalent depends on the type of reaction being considered. For acid-base reactions, it often involves the number of protons the compound can donate or accept. In the case of oxalic acid, it can donate two protons, making it a diprotic acid. Therefore, normality takes this into account.
Molarity, on the other hand, refers to the moles of solute per liter of solution. Molarity does not consider the ionic interchange and only counts the total number of moles of the solute.

• For diprotic acids like oxalic acid, normality is twice the molarity because it can offer two hydrogen ions per molecule.
• To convert normality to molarity, you simply divide the normality by the number of ions the acid donates.
• For example, if you have a 0.02 N solution of oxalic acid, its molarity is 0.01 M because you divide by 2.

This relationship is crucial when you need to perform calculations for reactions, as it ensures the stoichiometric ratios are correctly utilized.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, which is the starting point for determining the number of elementary entities in a mole of substance. It is defined as the number of atoms, molecules, or particles contained in one mole and is approximately equal to: \[ N_A = 6.022 imes 10^{23} \]
This means that one mole of any substance contains about 6.022 x 10^23 entities of that substance, be it atoms, molecules, ions, or even electrons.
Why is Avogadro's number so crucial? It helps bridge the gap between the macroscopic and microscopic worlds by allowing chemists to calculate the amount of substance involved in chemical reactions.

• In our exercise, once the number of moles of oxalic acid is known, Avogadro's number helps to convert that into the number of molecules.
• The number of molecules can be determined by multiplying the moles by Avogadro's number, giving us a tangible quantity in terms of particles.

For instance, if the number of moles is 0.001, multiplying it by Avogadro's number gives you the total number of molecules involved in the solution, which in this case is \( 6.022 \times 10^{20} \).

Stoichiometry in Chemistry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is a method that uses the quantitative relationship between substances as they participate in chemical reactions.
This concept allows chemists to predict the amounts of substances consumed and produced in a given reaction based on the balanced chemical equation. It involves mole-mole conversions, mass-mass conversions, and even volume-volume conversions when dealing with gases.
Breaking down its importance:

• In reactions and chemical equations, stoichiometry ensures that the law of conservation of mass is obeyed.
• Stoichiometry makes use of molar ratios derived from the balanced equation to calculate usable quantities for reactions.
• In the context of solutions, molarity plays a crucial role in stoichiometric calculations as it allows converting volume to moles and vice-versa.

In the exercise, stoichiometry is applied when moving from the measured normality of the oxalic acid to the number of molecules using the constants and relationships between molarity, normality, Avogadro's number, and volume. Each step integrates stoichiometry to ensure reliable and accurate results for understanding the chemical composition of the solution.