Question

'X' gram of calcium carbonate was completely burnt in air. The weight of solid residue formed is \(28 \mathrm{~g}\). What is the value of ' \(\mathrm{X}\) ' (in grams)? (a) 50 (b) 100 (c) 150 (d) 200

Short answer

The value of X is 50 grams.

Step-by-step solution

Understand the Reaction Equation

Calcium carbonate (   ) decomposes upon heating to form calcium oxide (  ) and carbon dioxide ( ).The decomposition reaction is as follows:\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

Calculate Molar Masses

Calculate the molar masses of calcium carbonate (CaCO3) and the residue, calcium oxide (CaO). The molar mass of CaCO3 = 40 (Ca) + 12 (C) + 3*16 (O) = 100 g/mol. The molar mass of CaO = 40 (Ca) + 16 (O) = 56 g/mol.

Set Up a Mass Ratio

From the reaction equation, 100 grams of CaCO3 gives 56 grams of CaO.

Calculate the Mass of CaCO3 Required

We are given that the mass of CaO (the residue) is 28 grams.Since 56 grams of CaO arises from 100 grams of CaCO3, we set up the proportionality: \[ \frac{100}{56} = \frac{X}{28} \]Solve this equation to find X:\[ X = \frac{100 \times 28}{56} \]

Solve for X

Calculate the value of X from the proportional equation:\[ X = \frac{100 \times 28}{56} = 50 \]

Key concepts

Understanding Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into new substances, called products. They can be identified by a change in energy, color, or gas production. These reactions are depicted using chemical equations that detail the reactants and products involved. For instance, the decomposition of calcium carbonate, a common laboratory demonstration, involves the breakdown of a single reactant into multiple products.
In chemical equations, reactants appear on the left, products on the right, separated by an arrow indicating the direction of the reaction. This equation must always observe the law of conservation of mass, meaning the mass of the reactants should equal the mass of the products. Chemical reactions are not limited to decomposition but can also include synthesis, single replacement, double replacement, and combustion reactions. Each type represents a unique way atoms reconfigure to form products.

The Importance of Molar Mass

Molar mass is a key concept in stoichiometry, acting as a bridge between atomic-level analysis and practical, weights-and-measures chemistry. It allows chemists to convert between grams and moles, the latter being a unit that helps in counting atoms and molecules. Molar mass is calculated by summing the standard atomic weights of all atoms in a molecule's formula.
For example, the molar mass of calcium carbonate (CaCO3) is calculated as follows: adding the atomic mass of calcium (40 g/mol), carbon (12 g/mol), and three oxygens (3 * 16 g/mol), resulting in 100 g/mol. Understanding this allows us to quantify the amount of substance involved in a chemical reaction. Thus, molar mass is fundamental in connecting the balanced equation to the real-world amounts of reactants and products.

Significance of Mass Ratio

A mass ratio in chemistry refers to the proportional relationship of reactants and products based on their molar masses within a balanced chemical equation. This ratio is critical because it enables chemists to predict the quantities of products yielded and reactants required, using the known masses of other substances in the reaction.
In the case of calcium carbonate's decomposition, the stoichiometric equation indicates that 100 grams of CaCO3 yield 56 grams of calcium oxide (CaO). With this mass ratio, one can calculate that if 56 grams of CaO are produced from 100 grams of CaCO3, then only 28 grams of CaO would be derived from a proportional amount of CaCO3, leading us to apply this ratio to solve the problem.

Understanding Decomposition Reaction

A decomposition reaction is a type of chemical reaction where one compound breaks down into two or more simpler substances. This reaction is a fundamental part of chemistry, showing how complex molecules can simplify under certain conditions, like heating. In our exercise, calcium carbonate ( CaCO_3 ) decomposes into calcium oxide ( CaO ) and carbon dioxide ( CO_2 ) when heated.
Decomposition reactions are generally endothermic, meaning they require the absorption of heat to proceed. These reactions are not only significant in academic settings but also have practical implications, such as processes in industries that break down raw materials. Understanding decomposition provides insights into chemical stability and reactivity, which are crucial for predicting how substances behave under different conditions.