Problem 5 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

1 gram of a carbonate \(\left(\mathrm{M}_{2} \mathrm{CO}_{3}\right)\) on treatment with excess \(\mathrm{HCl}\) produces \(0.01186\) mole of \(\mathrm{CO}_{2}\). The molar mass of \(\mathrm{M}_{2} \mathrm{CO}_{3}\) in \(\mathrm{g} \mathrm{mol}^{-1}\) is : [Main 2017] (a) 1186 (b) \(84.3\) (c) \(118.6\) (d) \(11.86\)

Step-by-Step Solution

Answer

The molar mass of \( \text{M}_2\text{CO}_3 \) is \( 84.3 \text{ g/mol} \).

Step 1: Balanced Chemical Equation

First, we need to write the balanced chemical equation for the reaction of the carbonate compound with hydrochloric acid. The equation is: \[ \text{M}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{MCl} + \text{CO}_2 + \text{H}_2\text{O} \] This tells us that 1 mole of \( \text{M}_2\text{CO}_3 \) produces 1 mole of \( \text{CO}_2 \).

Step 2: Identify Moles of Carbonate

We know that the reaction produced \( 0.01186 \) moles of \( \text{CO}_2 \). According to the stoichiometry of the reaction, \( 0.01186 \) moles of \( \text{CO}_2 \) corresponds to \( 0.01186 \) moles of \( \text{M}_2\text{CO}_3 \).

Step 3: Molar Mass Calculation

The mass of \( \text{M}_2\text{CO}_3 \) used is 1 gram and this quantity corresponds to \( 0.01186 \) moles. To find the molar mass, we use the formula: \[ \text{Molar Mass of } \text{M}_2\text{CO}_3 = \frac{\text{Mass}}{\text{Moles}} = \frac{1 \text{ gram}}{0.01186 \text{ moles}} \] Calculating gives the molar mass as \( 84.3 \text{ g/mol} \).

Step 4: Compare with Given Options

Upon examination of the calculated molar mass, \( 84.3 \text{ g/mol} \), we find that it matches option (b).

Key Concepts

Stoichiometry

Stoichiometry is like the recipe of chemistry. It helps chemists to know exactly how much of a reactant they need to produce a desired quantity of product. It's all about the relationships between the amounts of reactants and products in a chemical reaction.

Using stoichiometry, you can calculate how much of each reactant is needed, or how much of each product you can get. This involves using a balanced chemical equation, which tells you the exact ratio of molecules or moles of each substance involved in the reaction. For example, a balanced equation might tell you that 1 mole of a reactant will produce 1 mole of a product, as was the case in our exercise with the reaction of carbonate and hydrochloric acid.

Some key points:

• Stoichiometry measures the quantitative aspects of chemical reactions.
• Think of it as a bridge between the macroscopic measurements you can observe and the molecular-scale reactions happening in the background.
• Conversions using stoichiometry are based on the balanced equation of the reaction.

This is why stoichiometry is crucial for chemists when they want to understand how much of a substance is produced, given the quantity of another substance consumed in the reaction.

Balanced Chemical Equation

A balanced chemical equation is essential for understanding chemical reactions. It ensures that the number of atoms for each element is the same on both the reactant and product sides of the equation.

When a chemical equation is balanced, it follows the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Simply put, what you start with is what you end up with, just in different forms.

In our example with carbonate and hydrochloric acid, the equation is:
\[ \text{M}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{MCl} + \text{CO}_2 + \text{H}_2\text{O} \]
This tells us that 1 mole of \( \text{M}_2\text{CO}_3 \) reacts with 2 moles of \( \text{HCl} \). As a result, products formed include 2 moles of \( \text{MCl} \), 1 mole of carbon dioxide (\( \text{CO}_2 \)), and water (\( \text{H}_2\text{O} \)). Knowing this ratio allows us to relate the quantities of reactants and products.

• Balancing equations is the first and necessary step in stoichiometry.
• It ensures that calculations based on the equation are accurate.
• Each substance's coefficient in the balanced equation gives the ratio in which substances react and are produced.

Thus, mastering balanced equations is crucial for understanding any chemical reaction's quantitative details.

Chemical Reactions

Chemical reactions are the processes where reactants transform into products. These reactions might involve the forming or breaking of bonds, leading to the creation of new substances.

A chemical reaction will often involve reactants combining to form new products in a series of transformations. During these reactions, there's often a visible sign like color change, temperature change, formation of a precipitate, or gas evolution, which indicates a reaction has taken place.

In our exercise concerning the carbonate reaction with HCl, the reaction's outcome was the production of carbon dioxide gas. This transformation is an example of a gas-evolving reaction, often noticed by bubbling or fizzing.

The crucial steps in analyzing chemical reactions include:

• Identifying reactants and products.
• Understanding the type of reaction (e.g., synthesis, decomposition, single displacement, double displacement).
• Carefully observing changes to confirm a reaction.

Chemical reactions are more than just changes in substances; they are fundamental processes that result in the transformation of matter, powering various phenomena from simple biological actions to complex industrial operations. Understanding them helps in predicting and manipulating outcomes in practical scenarios.