Problem 107 - A Complete Resource Book in Chemistry for JEE Main

Question

\(10 \mathrm{~g}\) of \(\mathrm{CaCO}_{3}\) is completely decomposed to \(\mathrm{X}\) and \(\mathrm{CaO} . \mathrm{X}\) is passed into an aqueous solution containing one mole of sodium carbonate. What is the number of moles of sodium bicarbonate formed? (Mol. wt of \(\mathrm{CaCO}_{3}=100, \mathrm{Na}_{2} \mathrm{CO}_{3}=106\) \(\mathrm{NaHCO}_{3}=84\) ) (a) \(0.010\) (b) \(0.2\) (c) \(0.4\) (d) 10

Step-by-Step Solution

Answer

0.2 moles of sodium bicarbonate (\( \text{NaHCO}_3 \)) are formed.

Step 1: Determine Moles of CaCO3

First, we need to find the number of moles of \( \text{CaCO}_3 \). Given its mass is 10 g and the molar mass is 100 g/mol, we can calculate it using the formula:\[ \text{moles of CaCO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{10 \, \text{g}}{100 \, \text{g/mol}} = 0.1 \, \text{moles} \]

Step 2: Write Decomposition Reaction

Calcium carbonate \( \text{CaCO}_3 \) decomposes according to the following reaction:\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]This means 1 mole of \( \text{CaCO}_3 \) produces 1 mole of \( \text{CO}_2 \). Thus, 0.1 moles of \( \text{CaCO}_3 \) will produce 0.1 moles of \( \text{CO}_2 \) (denoted as \( \text{X} \)).

Step 3: Reaction with Sodium Carbonate

The \( \text{CO}_2 \) reacts with \( \text{Na}_2\text{CO}_3 \) to form sodium bicarbonate \( \text{NaHCO}_3 \). The balanced chemical reaction is:\[ \text{CO}_2 + \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} \rightarrow 2\text{NaHCO}_3 \]0.1 moles of \( \text{CO}_2 \) react with 1 mole of \( \text{Na}_2\text{CO}_3 \), forming 0.2 moles of \( \text{NaHCO}_3 \). This is because each mole of \( \text{CO}_2 \) generates 2 moles of \( \text{NaHCO}_3 \).

Step 4: Conclusion

Calculate the number of moles of sodium bicarbonate formed. Since every 0.1 moles of \( \text{CO}_2 \) produce 0.2 moles of \( \text{NaHCO}_3 \), the answer is that 0.2 moles of \( \text{NaHCO}_3 \) are formed.

Key Concepts

Chemical Reactions

Chemical reactions are the processes where substances, called reactants, are transformed into different substances, known as products.
During a chemical reaction, chemical bonds are rearranged, leading to changes in the composition and properties of the substances involved.
In a reaction, we often use chemical equations to describe the transformation, stating what reactants are consumed and what products are produced.

• A balanced chemical equation accurately represents the conservation of mass, where the number of atoms for each element is the same on both sides of the equation.
• Chemical reactions can vary widely, including synthesis, decomposition, single replacement, and double replacement reactions.

Understanding chemical reactions allows us to predict how substances will behave and what substances will form when they interact. These predictions are essential in fields ranging from industrial applications to biological processes.

Decomposition Reaction

A decomposition reaction involves breaking down a single compound into two or more simpler substances.
This type of reaction is characterized by a single reactant and multiple products, often requiring energy input, such as heat or electricity, to occur.

• An example of a decomposition reaction is the breakdown of calcium carbonate (\( \text{CaCO}_3 \)), which decomposes into calcium oxide (\( \text{CaO} \)) and carbon dioxide (\( \text{CO}_2 \)).
• Such reactions are crucial in industries, for instance, in the manufacturing of lime (\( \text{CaO} \)) from limestone (\( \text{CaCO}_3 \)).

This fundamental reaction not only forms an important part of geological processes but also serves practical applications in materials production and waste breakdown.

Mole Concept

The mole concept is pivotal in chemistry, allowing chemists to count particles such as atoms, ions, or molecules by weighing them.
A mole is defined as Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) entities. This makes it possible to discuss amounts of substances on a manageable scale.
For instance, knowing the number of moles of a substance from its mass helps in predicting how it will react with other substances.

• The number of moles can be calculated using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
• This conversion is crucial in balancing chemical reactions and in calculating the proportions of reactants and products.

Mastering the mole concept gives a robust foundation for understanding chemical processes and solving stoichiometry problems.

Reaction Stoichiometry

Reaction stoichiometry involves the calculation of reactants and products in chemical reactions. It is based on the balanced chemical equation of the reaction.
By using stoichiometric coefficients, which are the numbers in front of molecules in a balanced equation, we can determine the amount of any substance involved in the reaction.

• In the example of \( \text{CaCO}_3\) decomposition, if 0.1 moles of \( \text{CaCO}_3 \) decompose, stoichiometry indicates 0.1 moles of \( \text{CO}_2 \) are formed, because the coefficients of \( \text{CaCO}_3 \) and \( \text{CO}_2 \) in the equation are both one.
• Stoichiometry is also used to find limiting reactants, excess reactants, and the yield of products.

This branch of chemistry enables accurate predictions of quantities in chemical reactions, vital for laboratory research and industrial processes.