A gaseous alkane on complete combustion gives \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). If the ratio of moles of \(\mathrm{O}_{2}\) needed for combustion and moles of \(\mathrm{CO}_{2}\) formed is \(5: 3\) find out the formula of alkane.

When it comes to understanding chemical reactions, stoichiometry is the section of chemistry that deals with the calculation of the quantities of reactants and products. It can be a challenging topic, but it's essential for solving problems like the combustion of alkanes. Stoichiometry is founded on the laws of conservation of mass and fixed proportions, which states that in a chemical reaction, matter is neither created nor destroyed and that elements combine in fixed ratios.

Applying these principles, we can figure out the balanced equation for an alkane's combustion. The key is to ensure that the number of atoms for each element is the same on both sides of the equation. This gives us a proportional relationship between the reactants and products, which is crucial when we look into the moles of oxygen used and carbon dioxide produced in the given exercise. By setting up the correct molar ratios, we ensure the reaction adheres to stoichiometry, allowing us to solve for the alkane formula step by step.

Balancing chemical reactions is like solving a puzzle where each piece must fit perfectly, aligning with the law of conservation of mass. When presented with the raw equation for the combustion of an alkane, the initial task is to determine the correct coefficients - these are the numbers placed before compounds that indicate the number of moles involved in the reaction.

Without balancing, the equation would suggest that matter might be lost or gained, which contradicts scientific laws. By assigning a variable 'x' to represent the unknown amount of oxygen and 'n' to represent the moles of carbon, we're laying the groundwork to find a solution. Through a series of mathematical steps, we apply the given mole ratio, alignment of oxygen atoms, and solve for 'n' to arrive at the balanced equation. The process of balancing ensures stoichiometry is respected and that the equation reflects the true nature of the chemical reaction.

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. A mole, in chemistry, represents a sheer quantity (Avogadro's number: 6.022×10^23) of particles, whether they're atoms, ions, or molecules. In the burning of alkanes, we use the mole concept to express quantities of gaseous reactants and products.

The idea of moles helps us transform a measured mass into an amount that we can work with in equations. For the problem at hand, the mole concept allows us to take the abstract ratio of 5 moles of oxygen to 3 moles of carbon dioxide and turn it into a solvable mathematical equation. This is pivotal because it is this mole ratio that ultimately leads us to the stoichiometric relationship required to identify the correct alkane formula, exemplified by n in our exercise. Understanding the mole concept is crucial for students, bridges the gap between theoretical chemistry and practical exercises, and stands at the core of solving quantitative chemistry problems.