Question

Write a 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 liquid 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 sucrose is \[ \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(aq) + \mathrm{H}_2\mathrm{O}(l) \rightarrow 2\mathrm{C}_2\mathrm{H}_5\mathrm{OH}(aq) + 4\mathrm{CO}_2(g) \].

Step-by-step solution

Write the Unbalanced Equation

Begin by writing down the chemical formulas of the reactants and products. Sucrose reacts with water to form ethyl alcohol and carbon dioxide, so the unbalanced equation is: ewline \[ \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(aq) + \mathrm{H}_2\mathrm{O}(l) \rightarrow \mathrm{C}_2\mathrm{H}_5\mathrm{OH}(aq) + \mathrm{CO}_2(g) \]

Balance the Carbon Atoms

First balance the carbon atoms. There are 12 carbon atoms in sucrose, therefore you need 12 carbon atoms in the products. To achieve this, put a coefficient of 2 in front of \(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\) and 4 in front of \(\mathrm{CO}_2\): ewline \[ \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(aq) + \mathrm{H}_2\mathrm{O}(l) \rightarrow 2\mathrm{C}_2\mathrm{H}_5\mathrm{OH}(aq) + 4\mathrm{CO}_2(g) \]

Balance the Hydrogen Atoms

Sucrose has 22 hydrogen atoms; ethyl alcohol has 6. Balancing those on both sides gives: ewline \[ \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(aq) + \mathrm{H}_2\mathrm{O}(l) \rightarrow 2\mathrm{C}_2\mathrm{H}_5\mathrm{OH}(aq) + 4\mathrm{CO}_2(g) \] ewline This step does not require changes to the coefficients because the hydrogen atoms are already balanced (the sucrose molecule and two ethyl alcohol molecules have a total of 22 hydrogens).

Balance the Oxygen Atoms

Finally, balance the oxygen atoms. There are 11 from sucrose and 1 from water, totaling 12 on the reactant side. On the product side, each ethyl alcohol has 1 oxygen atom and each carbon dioxide has 2, giving a total of 10 (2 from ethyl alcohol and 8 from carbon dioxide). To complete the balancing, add an extra water molecule on the reactant side: ewline \[ \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(aq) + \mathrm{H}_2\mathrm{O}(l) \rightarrow 2\mathrm{C}_2\mathrm{H}_5\mathrm{OH}(aq) + 4\mathrm{CO}_2(g) + \mathrm{H}_2\mathrm{O}(l) \] ewline Now, since there are 12 oxygen atoms on both sides, the equation is balanced.

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is respected in a chemical reaction. The aim is to have the same number of each type of atom on both sides of the equation. When first learning to balance equations, it can seem like a trial and error process, but there are systematic steps you can follow, as demonstrated in the solution provided.

For example, in the fermentation of sucrose, we start with the unbalanced equation and work our way through each element. Balancing carbon atoms first, followed by hydrogens, and finally balancing oxygen last tends to simplify the process. It's important to adjust the coefficients of the compounds—these are the numbers placed in front of each formula—to balance the atoms. Hints such as starting with the most complex molecule, typically the one with the most different elements, can often streamline the process.

In more complex reactions, you might find that balancing one element affects another previously balanced element. In such cases, it's necessary to iterate through the balancing steps until you reach a fully balanced equation. Remember, the coefficients represent the relative number of molecules or moles of each compound involved in the reaction, not the absolute quantities, making the process a bit more intuitive.

Fermentation Process

The fermentation process is an anaerobic (occurring in the absence of oxygen) biochemical reaction carried out by microorganisms like yeasts or bacteria. In the context of the textbook problem, we're looking at yeast fermentation, which is used in the production of alcoholic beverages and bread.

In simple terms, yeast breaks down sugars like sucrose in the absence of oxygen to produce ethyl alcohol and carbon dioxide, as shown by the balanced chemical equation. This biochemical process is essential in various industries and also plays a role in cellular biology as a form of energy production in cells.

Key Notes in Fermentation:

• Fermentation transforms glucose and other six-carbon sugars into cellular energy and produces ethanol and CO₂ as byproducts.
• It has been used historically for food preservation in products like yogurt and sauerkraut.
• It allows organisms to regenerate NAD⁺ from NADH, enabling sustained energy production in the absence of oxygen.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It involves calculations based on the balanced equation and allows chemists to predict the amounts of substances consumed and produced in a reaction.

Using stoichiometry in the example of sucrose fermentation, you can determine how much sucrose is needed to produce a certain amount of ethyl alcohol or carbon dioxide. It forms the basis for quantitative analysis in chemistry and is crucial in fields such as pharmaceuticals, engineering, and environmental science.

Practical Stoichiometry Tips:

• Always start with a balanced chemical equation.
• Convert mass to moles using molecular weights if necessary.
• Use molar ratios from the balanced equation to relate quantities of reactants and products.
• Calculate yields and identify limiting reactants where applicable.

Understanding stoichiometry allows you to scale reactions for practical applications, whether it's brewing beer or synthesizing a new medicine. It also underpins the principle that 'molecules count'—enabling you to accurately manipulate and measure reactions based on the number of molecules involved.