When \(\mathrm{NaNO}_{3}\) is heated with \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) a colourless gas \& a residue is obtained. The colour of residue is (a) Red (b) Brown (c) White (d) Black

Chemical decomposition, also known as chemical breakdown, is a fundamental concept in chemistry that involves the breaking down of a compound into smaller chemical species, typically through the application of energy, such as heat. In the case of the exercise involving sodium nitrate (\text{NaNO}_3) and ammonium sulfate (\text{(NH\text{\(_4\)})\text{\(_2\)}SO\text{\(_4\)}}), when heated, they undergo a decomposition reaction. This type of reaction is endothermic, meaning it absorbs heat from the surroundings.

During the decomposition process, the ammonium nitrate that forms first decomposes further, releasing a colorless gas, dinitrogen oxide (\text{N\text{\(_2\)}O}), commonly known as laughing gas, due to its euphoriant effects. The remainder of the reactants forms the solid residue, sodium sulfate (\text{Na\text{\(_2\)}SO\text{\(_4\)}}). It's important to recognize that other side reactions may occur under certain conditions, potentially forming different products or gases.

Ammonium nitrate (\text{NH\text{\(_4\)}NO}_3) formation is observed as an intermediate step in the chemical reaction between sodium nitrate and ammonium sulfate. Although it isn't the final product of the reaction, its creation is a critical stage in the process. Ammonium nitrate forms via a double displacement reaction, where the \text{Na}^+ ions from sodium nitrate switch places with the \text{NH\text{\(_4\)}}^+ ions from ammonium sulfate.

However, ammonium nitrate is unstable at high temperatures and rapidly decomposes to produce the colorless gas, \text{N\text{\(_2\)}O}, upon continued heating. This instability and the subsequent release of gas are key phenomena that significantly contribute to understanding how various reactants behave under heat and the types of reactions that can follow initial compound formation.

Sodium sulfate (\text{Na\text{\(_2\)}SO\text{\(_4\)}}) is an important chemical compound with characteristic properties that are relevant to our exercise. One of its defining features, which is essential for correctly answering the textbook question, is that it is a white crystalline solid. When \text{NaNO}_3 is heated with \text{(NH\text{\(_4\)})\text{\(_2\)}SO\text{\(_4\)}}, sodium sulfate is formed as the residue.

Sodium sulfate is known for its high solubility in water, inertness, and non-toxic nature. It's used in a variety of applications, from detergents to papermaking. In the context of the exercise, the white color of sodium sulfate is a visual cue to conclude that the correct answer to the color of the residue is indeed white (option c). Knowing the physical properties of compounds can greatly aid in the prediction and analysis of chemical reactions.