Question

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

Short answer

\(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow 4\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + 4\mathrm{CO}_2\)

Step-by-step solution

Identify Reactants and Products

Determine the given reactants and products for the fermentation process. The reactants are sucrose \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}\) and water \(\mathrm{H}_2\mathrm{O}\), and the products are ethanol \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\) and carbon dioxide \(\mathrm{CO}_2\) gas.

Write Unbalanced Equation

Write the unbalanced chemical equation by placing the reactants on the left side and the products on the right side of the arrow.\[\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + \mathrm{CO}_2\]

Balance Carbon Atoms

Balance the carbon atoms first. Since there are 12 carbon atoms in sucrose, you need 2 moles of ethanol for every mole of sucrose to balance the carbon atoms. \[\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow 2\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + \mathrm{CO}_2\]

Balance Hydrogen Atoms

Next, balance the hydrogen atoms. Sucrose and water together have 24 hydrogen atoms, and each molecule of ethanol has 6 hydrogen atoms. Therefore, you need 4 moles of ethanol to balance the hydrogen atoms. \[\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow 4\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + \mathrm{CO}_2\]

Balance Oxygen Atoms

Finally, balance the oxygen atoms. There are 12 from sucrose and 1 from water, making 13 oxygen atoms on the reactant side. Each ethanol molecule contains one oxygen, accounting for 4 oxygens, hence you need 9 moles of \(\mathrm{CO}_2\) to balance the rest. \[\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow 4\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + 4\mathrm{CO}_2\]

Combine Steps and Simplify

Combine all the balancing steps and write down the complete balanced chemical equation for the fermentation of sucrose. \[\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} + \mathrm{H}_2\mathrm{O} \rightarrow 4\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + 4\mathrm{CO}_2\]

Key concepts

Balanced Chemical Equation

Understanding a balanced chemical equation is essential in the study of chemistry. It represents a chemical reaction where the number of atoms for each element are the same on both the reactant and product sides, adhering to the Law of Conservation of Mass. For the fermentation of sucrose, it's important to balance the equation to ensure that the atoms of each element are equal on both sides. In the provided solution steps, the balancing process is broken down systematically: starting with carbon atoms, then hydrogen, and finally oxygen atoms. This meticulous approach ensures that we adhere to the fundamental principle of stoichiometry that matter is neither created nor destroyed in a chemical reaction.

In this particular case, we can see the chemical equation evolve from an unbalanced state to a balanced one through careful adjustment of the coefficients, which are the numbers in front of the chemical formulas indicating the relative amounts of reactants and products. The equation culminates in a stoichiometrically balanced form, symbolizing the complete chemical change the reactants undergo during the fermentation process.

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the quantitative relationships of the reactants and products in a chemical reaction. When presented with a task like balancing the fermentation of sucrose, stoichiometry guides us through the precise ratios and proportions of all involved compounds. To visualize this, consider a simple baking recipe: to achieve the perfect cake, it's not enough to know the ingredients; one must measure them in exact quantities. Similarly, stoichiometry involves calculations that determine the amounts of reactants needed to produce a certain amount of product.

In the provided solution, stoichiometry is clearly at play when adjusting the coefficients to balance the equation. It ensures that the quantities on both sides of the equation are based on the same molar relationship, closely linked to Avogadro's number and the concept of moles, effectively turning qualitative data into quantitative insights. This forms the groundwork for predicting the outcome of the fermentation process and is indispensable for applications in fields like biochemistry, environmental science, and industrial chemistry.

Chemical Reaction

A chemical reaction involves the transformation of substances into new materials with distinct properties through the breaking and forming of chemical bonds. The reaction between sucrose and water, catalyzed by yeast, is a testament to the dynamic nature of chemical processes. From a macroscopic perspective, we observe that a sweet-tasting, water-soluble compound, sucrose, along with water, is converted into ethanol, an intoxicating liquid, and carbon dioxide, a gaseous by-product.

Moreover, the steps to balance the chemical equation reflect the intricacies of this reaction at a microscopic level. The process of determining the correct stoichiometric coefficients can be likened to a puzzle, where atoms are rearranged, yet their total number remains constant. The reactants undergo a transformation regulated by factors such as temperature, pressure, and enzyme activity, leading to the observed phenomena during fermentation. Understanding the underlying principles of a chemical reaction not only involves balancing equations but also deciphering the reactivity, energy changes, and the kinetic journey from reactants to products.

Yeast Fermentation Process

The yeast fermentation process is a remarkable biological phenomenon where yeast cells convert sugars into alcohol and carbon dioxide in the absence of oxygen, known as anaerobic respiration. This biochemical process is leveraged in baking, brewing, and winemaking industries due to the desirable products it yields. In our exercise, yeast cells act as the biological catalysts for the fermentation of sucrose. When yeast encounters sucrose, it produces enzymes that first break down the disaccharide into glucose and fructose, which are then metabolized to ethanol and carbon dioxide through a series of enzymatic reactions called glycolysis and fermentation.

The balanced chemical equation provided in the exercise is a simplified representation of this complex biochemistry, capturing the essence of the transformation without delving into the intermediate steps. Nonetheless, it offers essential information on the stoichiometry of the fermentation process, making it possible to calculate the expected yields of ethanol and predict the release of carbon dioxide, both of which have significant practical applications. For instance, in brewing, the amount of carbon dioxide produced can affect the carbonation level of the beverage.