Question

Write a balanced chemical equation for the fermentation of sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) by yeasts in which the aqueous sugar reacts with water to form aqueous ethyl alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and carbon dioxide gas.

Short answer

The balanced chemical equation for the fermentation of sugar is \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} \rightarrow 4\mathrm{C}_2\mathrm{H}_5\mathrm{OH} + 4\mathrm{CO}_2\).

Step-by-step solution

Identify reactants and products

The reactants for the fermentation of sugar are sugar \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}\) and water (\(\mathrm{H}_2\mathrm{O}\)). The products are ethyl alcohol (\(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\)) and carbon dioxide (\(\mathrm{CO}_2\)).

Write the unbalanced chemical equation

Put the reactants on the left side of the equation and the products on the right side, with an arrow pointing from left to right, indicating the direction of the reaction: \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{C}_2\mathrm{H}_5\mathrm{OH} + \mathrm{CO}_2\).

Balance the chemical equation

Balance the elements in the equation one by one, adjusting coefficients as necessary to ensure the same number of each type of atom on both sides of the equation. For fermentation, the balanced equation becomes: \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow 4\mathrm{C}_2\mathrm{H}_5\mathrm{OH} + 4\mathrm{CO}_2\). It's important to note that the water molecule is often omitted in this fermentation reaction because the sugar already contains the required hydrogen and oxygen to form the products. The more commonly used balanced equation is \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} \rightarrow 4\mathrm{C}_2\mathrm{H}_5\mathrm{OH} + 4\mathrm{CO}_2\).

Key concepts

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, transform into new substances, called products. In our everyday life, we observe chemical reactions all the time, such as when baking bread, which involves the fermentation of yeast, much like our example. In the case of fermentation, the reactants include sugar (sucrose) and water, while the products are ethyl alcohol and carbon dioxide. One of the primary goals of understanding chemical reactions is to be able to write a balanced chemical equation that accurately represents the transformation from reactants to products, respecting the law of conservation of mass. This means that atoms are neither created nor destroyed in a chemical reaction, so the number of atoms for each element must be the same on both sides of the equation.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of the quantities of reactants and products in a chemical reaction. It's like a recipe that tells you exactly how much of each ingredient you need to make a dish. Understanding stoichiometry is crucial when you're working to balance a chemical equation, as it determines the ratios in which reactants combine to form products. When we balance the equation for the fermentation of sugar, we make sure that the amount of carbon, hydrogen, and oxygen atoms are the same on both sides. Stoichiometry also helps in predicting the amount of product that can be formed from a given amount of reactants, which is pivotal in industrial applications where maximizing efficiency is key.

Molecular Formula

The molecular formula of a substance provides the exact number of each type of atom in a molecule of that substance. For example, the molecular formula for sugar (sucrose) is \(C_{12}H_{22}O_{11}\), which means a single molecule of sugar contains 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. Understanding the molecular formula is essential when balancing chemical equations because it gives us the necessary information to ensure that the number of atoms on each side of the equation is consistent. When students approach a problem like fermentation, they should be comfortable working with these formulas to successfully balance the equation and understand the mole-to-mole relationships between reactants and products.

Fermentation Process

The fermentation process is a biochemical reaction where yeast converts sugars into alcohol and carbon dioxide in the absence of oxygen. It is utilized in making a variety of products such as bread, beer, and wine. During fermentation, enzymes in yeast break down the sugar molecules to produce ethyl alcohol and CO2 as byproducts. The balanced chemical equation we have derived is a simplified representation of this complex biological process. Fermentation is an important concept not only in chemistry but also in biology and is widely applied in the food and beverages industry as well as in biofuels production. Recognizing the specifics of this process helps students appreciate the practical applications of the reactions they learn in their textbooks.