Question

Ethanol, used in alcoholic beverages, can be produced by the fermentation of sucrose, which is found in sugar cane and other plants. The balanced equation for the fermentation process is $$ \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{\mathrm{n}}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}(l)+4 \mathrm{CO}_{2}(\mathrm{~g}) $$ (a) What mass of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}\), would be produced when \(2.50 \mathrm{~g}\) sucrose reacts by this process? (b) What mass of \(\mathrm{CO}_{2}\) would also be produced?

Short answer

When 2.50 g of sucrose reacts by this process, the mass of ethanol (\(C_{2}H_{5}OH\)) produced is 1.34 g and the mass of \(CO_{2}\) produced is 1.28 g.

Step-by-step solution

Converting the given mass of sucrose to moles

First, convert the mass of sucrose (\(C_{12}H_{22}O_{11}\)) to moles by dividing it by its molar mass. The molar mass of sucrose is 342.3 g/mol (based on atomic masses of C, H, and O), and the given mass is 2.50 g. So, the number of moles = \(2.50 \, g / 342.3 \, g/mol = 0.0073 \, mol\)

Determining the quantity of ethanol produced

Using balanced chemical equation, analyze the stoichiometric ratio. According to the reaction, one mole of sucrose produces 4 moles of ethanol (\(C_{2}H_{5}OH\)). The number of moles of ethanol produced can be calculated as: Number of moles of \(C_{2}H_{5}OH = 4 * 0.0073 \, mol = 0.0292 \, mol\)To convert this into grams, multiply by the molar mass of ethanol: Mass of \(C_{2}H_{5}OH = 0.0292 \, mol * 46.07 \, g/mol = 1.34 \, g\)

Determining the quantity of CO2 produced

According to the reaction, one mole of sucrose produces 4 moles of \(CO_{2}\). The number of moles of \(CO_{2}\) produced can be calculated as: Number of moles of \(CO_{2} = 4 * 0.0073 \, mol = 0.0292 \, mol\)To convert this into grams, multiply by the molar mass of \(CO_{2}\): Mass of \(CO_{2} = 0.0292 \, mol * 44.01 \, g/mol = 1.28 \, g\)

Key concepts

Stoichiometry

Stoichiometry is like a recipe in chemistry. It helps us understand how much of each ingredient is needed in a chemical reaction. In this exercise, we are looking at how much sucrose is needed to produce ethanol through fermentation. The balanced chemical reaction shows that one molecule of sucrose produces four molecules of ethanol. This 1:4 ratio is the stoichiometry of the reaction.
It's important because it tells us exactly how the substances react with each other to form products. By using this ratio, we can predict how much product (like ethanol) we will get from a certain amount of reactant (like sucrose).
Without stoichiometry, we would not be able to calculate these quantities accurately. It's vital for determining the masses and volumes in any chemical experiment to ensure we have the correct amounts.

Chemical Reactions

Chemical reactions involve changing the arrangement of atoms to form new substances. In this exercise, we look at the fermentation of sucrose to form ethanol and carbon dioxide. The balanced chemical equation represents the reaction clearly: \(\mathrm{C_{12}H_{22}O_{11} + H_{2}O \rightarrow 4\, \mathrm{C_{2}H_{5}OH} + 4\, \mathrm{CO_2}}\).
This means that solid sucrose reacts with water to produce liquid ethanol and gaseous carbon dioxide. The balanced equation is essential because it reflects the conservation of mass. It tells us that the number of each type of atom is the same in the reactants and the products.

• The equation helps us see how the atoms rearrange to form new products.
• This reaction is a multi-step process where starting materials are transformed into products.

Understanding chemical reactions is crucial for predicting products and their quantities.

Molar Mass

Molar mass is the mass of a given substance (chemical element or chemical compound) divided by the amount of substance in moles. It is expressed in units of grams per mole (g/mol). For example, the molar mass of sucrose, \(\mathrm{C_{12}H_{22}O_{11}}\), is 342.3 g/mol.
To find this, we add up the atomic masses of all the atoms in the formula: Carbon (C), Hydrogen (H), and Oxygen (O).

• Molar mass helps us convert between grams and moles.
• Knowing this helps us understand how much of a substance is involved in the reaction.

In the exercise, you use molar mass to convert the mass of sucrose from grams to moles, which is a key step in using stoichiometry. By understanding molar mass, we gain insight into the weight of substances we deal with in chemical reactions.

Ethanol Production

Ethanol, also known as alcohol, is produced by the fermentation process described in this exercise. In fermentation, microbes such as yeast break down sugars like sucrose into ethanol and carbon dioxide.
Here, we emphasize that one mole of sucrose results in the formation of four moles of ethanol. This understanding is crucial in industries where ethanol production is essential, such as beverage production and biofuels.
Ethanol production process involves:

• Utilizing yeast bacteria to catalyze the reaction.
• Converting sugars to ethanol under anaerobic (absence of oxygen) conditions.
• Collecting ethanol and CO₂ as by-products.

This process is economically significant because ethanol is used in multiple industries. Understanding the chemistry behind it can help improve production methods.