Problem 156 - A Complete Resource Book in Chemistry for JEE Main

Question

When \(16.8 \mathrm{~g}\) of white solid \(\mathrm{X}\) were heated, \(4.4 \mathrm{~g}\) of acid gas A that turned lime water milky was driven off together with \(1.8 \mathrm{~g}\) of a gas \(\mathrm{B}\) which condensed to a colourless liquid. The solid that remained, \(Y\), dissolved in water to give an alkaline solution, which with excess barium chloride solution gave a white precipitate \(Z\). The precipitate effervesced with acid giving off carbon dioxide. Identify A, B and Y and write down the equation for the thermal decomposition of \(\mathrm{X}\). Here (A) and (B) are respectively: (a) \(\mathrm{CO}_{2}\) and \(\mathrm{N}_{2}\) (b) \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\) (c) \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{CO}_{2}\) and \(\mathrm{NH}_{3}\)

Step-by-Step Solution

Answer

A is \(\text{CO}_2\), B is \(\text{H}_2\text{O}\), and Y is likely \(\text{Na}_2\text{CO}_3\). The decomposition is \(\text{Na}_2\text{CO}_3\cdot 10\text{H}_2\text{O} \rightarrow \text{Na}_2\text{CO}_3 + \text{CO}_2 + 10\text{H}_2\text{O}.\)

Step 1: Analyze gas A

The gas A is described as an acid gas that turns lime water milky. This is a characteristic reaction of carbon dioxide \(\text{CO}_2\), which reacts with lime water (calcium hydroxide, \(\text{Ca(OH)}_2\)) to form calcium carbonate \((\text{CaCO}_3)\), causing the solution to turn milky.

Step 2: Analyze gas B

The gas B condensed to a colorless liquid. This suggests it could be water vapor \(\text{H}_2\text{O}\), which is a colorless liquid at room temperature.

Step 3: Analyze the remaining solid Y

The solid Y dissolved in water to give an alkaline solution, indicating it likely contains a base. When Y reacts with excess barium chloride, a white precipitate Z that effervesces with acid is formed. Such behavior is typical of barium carbonate \(\text{BaCO}_3\), which reacts with acid to release carbon dioxide, consistent with the presence of a carbonate in Y, such as a metal carbonate like \(\text{Na}_2\text{CO}_3\) or \(\text{K}_2\text{CO}_3\).

Step 4: Identify the reaction and expressions

From the mass data, we assume \(\text{X}\) decomposes into \(\text{CO}_2\), \(\text{H}_2\text{O}\), and a carbonate \(\text{Y}\). Suppose \(\text{X}\) originally contains a hydrated metal carbonate, such as \(\text{Na}_2\text{CO}_3\cdot 10 \text{H}_2\text{O}\). The decomposition equation is: \[ \text{Na}_2\text{CO}_3\cdot 10\text{H}_2\text{O} \rightarrow \text{Na}_2\text{CO}_3 + 10\text{H}_2\text{O}. \] Confirming back the masses, \(4.4 \text{ g} + 1.8 \text{ g} + m_Y = 16.8 \text{ g}\) lets you finalize \(\text{Y}\) as sodium carbonate when considering stoichiometry and common substances.

Step 5: Conclusion

From the analysis, A is \(\text{CO}_2\), B is \(\text{H}_2\text{O}\), and Y involves a carbonated compound like \(\text{Na}_2\text{CO}_3\).The balanced chemical equation for the thermal decomposition of \(\text{X}\) involves hydrated sodium carbonate: \[ \text{Na}_2\text{CO}_3\cdot 10\text{H}_2\text{O} \rightarrow \text{Na}_2\text{CO}_3 + \text{CO}_2 + 10\text{H}_2\text{O}. \]

Key Concepts

Understanding Hydrated Metal Carbonate

Hydrated metal carbonates are compounds that contain a metal carbonate and water molecules integrated into their structure. A common example of this is sodium carbonate decahydrate, or \( \text{Na}_2\text{CO}_3 \cdot 10 \text{H}_2\text{O} \). This means the compound consists of sodium carbonate combined with ten molecules of water.

In chemistry, the water associated with these compounds is often referred to as "water of crystallization." It is trapped within the crystal lattice of the compound. This water can be released upon heating, which is an essential step in the decomposition of the compound.

When applying heat, these hydrated metal carbonates lose their water content, transforming into anhydrous compounds. This process demonstrates how heat energy affects chemical bonds and is a classic example of thermal decomposition.

The Role of Sodium Carbonate

Sodium carbonate, often known as washing soda, is a strong alkali commonly used in many cleaning products. It can also be found as a by-product of the thermal decomposition of hydrated metal carbonates.

In our reaction, the thermal decomposition of sodium carbonate decahydrate results in the formation of sodium carbonate (\( \text{Na}_2\text{CO}_3 \). This substance is known for its ability to dissolve in water, producing an alkaline solution, which confirms the presence of a strong base.

When sodium carbonate encounters barium chloride in excess, it reacts to form barium carbonate, a white precipitate. This reaction is an important characteristic enabling us to identify sodium carbonate through precipitation tests in various chemical analyses.

The Significance of Carbon Dioxide

Carbon dioxide \( (\text{CO}_2) \) is a significant by-product of the decomposition of hydrated metal carbonates. It is known for its ability to turn lime water milky due to the formation of calcium carbonate when it reacts with calcium hydroxide.

This gas is an acid gas, but its appearance in such reactions doesn't just stop at this visual transformation. It's also a key reaction product, demonstrating that a metal carbonate was involved.

In many laboratory settings, the ability to identify carbon dioxide through its reaction with lime water is a critical skill. It helps indicate the presence of carbonate compounds and confirms their thermal decomposition.

The Thermal Decomposition Equation

Thermal decomposition involves breaking down a compound using heat. In the case of a hydrated metal carbonate, the compound decomposes into its anhydrous form along with water and carbon dioxide. The equation depicting this process is helpful to understand the chemical changes occurring.

For sodium carbonate decahydrate, the thermal decomposition equation is: \[\text{Na}_2\text{CO}_3\cdot 10\text{H}_2\text{O} \rightarrow \text{Na}_2\text{CO}_3 + 10\text{H}_2\text{O} + \text{CO}_2.\] This balanced equation shows the breakdown of the compound into sodium carbonate, releasing water vapor and carbon dioxide upon heating.

Understanding and writing down these equations is crucial for predicting and explaining the outcomes of chemical reactions, which is a valuable skill in both academic and practical chemistry applications.