In a combustion reaction, \(46.0 \mathrm{g}\) of ethanol reacts with \(96.0 \mathrm{g}\) of oxygen to produce water and carbon dioxide. If \(54.0 \mathrm{g}\) of water is produced, what mass of carbon dioxide is produced?

Understanding chemical reactions begins with chemical equations, which are written representations of the changes that occur during a chemical reaction. In its simplest form, a chemical equation shows the reactants transforming into products, and it must be balanced to obey the Law of Conservation of Mass. For instance, the combustion of ethanol can be represented by the balanced equation:
\[C_2H_5OH + 3O_2 \rightarrow 2CO_2 + 3H_2O\]
This equation tells us that one molecule of ethanol reacts with three molecules of oxygen to produce two molecules of carbon dioxide and three molecules of water. The coefficients before each chemical formula indicate the relative amounts of each substance involved in the reaction and are essential for stoichiometry calculations.

In chemical reactions, the limiting reactant is the substance that is completely consumed first and therefore limits the amount of product that can be formed. To identify the limiting reactant, we compare the mole ratio of the reactants used to the ratio given by the balanced equation.

Identifying the Limiting Reactant

Using the balanced equation from our ethanol combustion reaction: 1 mole of ethanol reacts with 3 moles of oxygen, yet our starting materials are 1 mole of ethanol and 3 moles of oxygen. Since the mole ratio of the reactants matches the balanced equation, ethanol is our limiting reactant, suggesting it will determine the extent of the reaction and the amount of products formed.

Molar mass is defined as the mass in grams of one mole of a substance. It is a critical concept for converting between the mass of a substance and the number of moles. The molar mass of a compound is calculated by summing the molar masses of its constituent elements, multiplied by the number of atoms of each element in one molecule of the compound.

Calculation Example

For ethanol (\(C_2H_5OH\)), the calculation would be: \[2 \times 12.01 + 6 \times 1.01 + 16.00 = 46.07\,g/mol\] Understanding molar mass allows us to translate the mass of reactants or products into moles, a step essential in stoichiometry.

Converting moles to grams is a fundamental skill in chemistry that involves the use of a substance's molar mass as a conversion factor. The process is straightforward: the number of moles is multiplied by the molar mass of the substance.

How to Convert

The mass of carbon dioxide produced in our previous example was determined by converting the calculated moles of CO2 to grams:
\[2.00\,moles \times 44.01\,g/mol = 88.0\,g\]
This conversion is essential in predicting the mass of products formed from a given amount of reactants, and it demonstrates the direct link between the theoretical stoichiometry in balanced equations and practical, measurable quantities in the laboratory.