Natural gas is burned in homes for heat according to the following reaction: $$ \mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} $$ Determine how many grams of \(\mathrm{CO}_{2}\) would be formed for each of the following amounts of methane (assume unlimited amounts of oxygen): a. \(2.3 \mathrm{~mol} \mathrm{CH}_{4}\) b. \(0.52 \mathrm{~mol} \mathrm{CH}_{4}\) c. \(11 \mathrm{~g} \mathrm{CH}_{4}\) d. \(1.3 \mathrm{~kg} \mathrm{CH}_{4}\)

Understanding how substances change and create new products is key in the world of chemistry. Chemical reactions are the processes where reactants transform into products through breaking and forming of chemical bonds. In our exercise, we observe a combustion reaction, a specific type of chemical reaction where a substance, usually a hydrocarbon like methane (CH₄), reacts with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O). This reaction is important for many applications, including heating our homes.

It's essential to have a balanced chemical equation to understand fully the stoichiometry of the reaction. Balancing the equation ensures that the number of atoms for each element is the same on both the reactant and product sides, complying with the conservation of mass. In the given problem, we have a balanced equation, which is the foundation for correctly performing mole calculations and predicting the amounts of products formed.

The concept of the mole is fundamental in stoichiometry, allowing chemists to measure substances in the laboratory. A mole is a unit that represents 6.022 x 10²³ particles (Avogadro's number). Whether we're discussing atoms, molecules, or ions, one mole of these particles has the same number, enabling us to connect the microscopic world of atoms to the macroscopic world we can measure.

Applying Mole Calculations

In the context of our exercise, mole calculations enable us to determine the amount of carbon dioxide produced when a known quantity of methane reacts. By knowing that one mole of methane produces one mole of carbon dioxide, we can calculate the mass of CO₂ generated from the given moles of methane, taking into consideration the one-to-one ratio derived from the balanced equation.

The molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It is a bridge between the atomic scale and the real-world scale. The molar mass of a molecule is found by adding up the atomic masses of all the atoms within the molecule.

Finding the Molar Mass

For methane (CH₄), the molar mass is calculated by adding the atomic mass of carbon (C) with four times the atomic mass of hydrogen (H). In our exercise, we used the molar mass of methane (16.042 g/mol) and carbon dioxide (44.01 g/mol) in the calculations to convert between moles and grams. This step is crucial as it allows converting given masses of methane to moles and finding the corresponding mass of CO₂ produced.

Balancing chemical equations is the process of ensuring that the number of atoms of each element is the same on both sides of the equation, abiding by the Law of Conservation of Mass. A balanced equation is foundational for stoichiometric calculations as it provides the ratio of moles of reactants to moles of products.

Importance in Calculations

In our scenario, we see that one molecule of methane reacts with two molecules of oxygen to produce two molecules of water and one molecule of carbon dioxide. This ratio is vital as it guides the stoichiometric calculations. When balancing equations, it is important not to change the chemical formulas of the reactants or products; instead, only the coefficients should be adjusted to achieve balance.