What mass of oxygen is required to burn 688 g of octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) completely?

Understanding chemical reaction calculations is essential for figuring out how much of each substance is involved in a reaction. In our original example, we're looking to determine the mass of oxygen needed to completely burn a given amount of octane. To perform this calculation, one must understand the concept of a chemical reaction itself, which is a process where reactants are transformed into products.

Initially, the process involves two key steps: calculating the number of moles of the reactant (octane in this case) and then using the balanced chemical equation to determine how much of another reactant (oxygen) is required to react with octane. This approach applies universally, whether you are burning fuel, cooking with a recipe, or conducting a complex multi-step synthesis in a laboratory.

Molar mass is a fundamental concept in stoichiometry; it's the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For any chemical calculation, knowing the molar mass allows you to convert between mass and moles, bridging the gap between the physical world and the molecular world. In our example exercise, the molar mass of octane, which is a sum of the masses of all the carbon and hydrogen atoms in one molecule, is crucial to find the starting amount of substance we have.

How to Calculate Molar Mass

To calculate the molar mass of a compound, sum up the atomic masses of all the atoms present in a single molecule. This can typically be found on the periodic table and will be the basis for further stoichiometric calculations.

Balancing chemical equations is like solving a puzzle where each side of the equation must have the same number of atoms for each element. It ensures the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. In balanced equations, the stoichiometric coefficients (the numbers in front of the chemical formulas) tell us the ratio in which substances react and are produced.

For instance, in our octane burning scenario, the chemical equation must be balanced to understand the ratio of octane to oxygen. This helps determine the precise amount of oxygen needed to react with a known mass of octane.

The stoichiometric ratio is the heart of stoichiometry, as it gives the proportional relationship between reactants and products in a chemical reaction, based on the balanced equation. It is used to calculate the quantities of reactant and products involved in the reaction. In the example given, for every 2 moles of octane, 25 moles of oxygen are required, which simplifies to a 1:12.5 ratio for octane to oxygen.

Using Stoichiometric Ratios

Once the stoichiometric ratio is known, it can then be applied to find out how many moles of one reactant are required for a certain number of moles of another. By multiplying the moles of octane by the stoichiometric ratio, we find the moles of oxygen needed. Subsequently, through this calculated amount of moles, and knowing the molar mass of oxygen, the mass of oxygen required for the reaction can be computed.