Question

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) also known as grain alcohol, can be made from the fermentation of sugar \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) The unbalanced chemical equation for the reaction is shown below. ___ \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \rightarrow\) ___ \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\)___ \(\mathrm{CO}_{2}\) Balance the chemical equation and determine the mass of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) produced from 750 \(\mathrm{g}\) of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

Short answer

The balanced chemical equation for the fermentation of sugar is: \(C_6H_{12}O_6 \rightarrow 2C_2H_5OH + 2CO_2\). From 750 g of sugar (C6H12O6), approximately 383.15 g of ethanol (C2H5OH) is produced.

Step-by-step solution

Balance the chemical equation

In order to balance the chemical equation, we need to make sure that the number of atoms for each element is equal on both sides of the equation. The unbalanced equation is: C6H12O6 → C2H5OH + CO2 To balance the equation, let's try the following coefficients: C6H12O6 → 2C2H5OH + 2CO2 Now, let's check if the equation is balanced: - Carbon atoms: 6 = (2x2) + (2x1) - Hydrogen atoms: 12 = (2x5) + 0 - Oxygen atoms: 6 = (2x1) + (2x2) The equation is now balanced: C6H12O6 → 2C2H5OH + 2CO2

Calculate the molar mass of sugar and ethanol

To convert the given mass of sugar to moles and then to mass of ethanol, we need the molar mass of both sugar and ethanol. The molar mass of sugar (C6H12O6): (6 x C) + (12 x H) + (6 x O) = (6 x 12.01) + (12 x 1.01) + (6 x 16.00) = 72.06 + 12.12 + 96.00 = 180.18 g/mol The molar mass of ethanol (C2H5OH): (2 x C) + (6 x H) + (1 x O) = (2 x 12.01) + (6 x 1.01) + (1 x 16.00) = 24.02 + 6.06 + 16.00 = 46.08 g/mol

Convert the mass of sugar to moles

Now, we will convert the given mass of sugar (750g) to moles using its molar mass. moles of C6H12O6 = mass of C6H12O6 / molar mass of C6H12O6 moles of C6H12O6 = 750 g / 180.18 g/mol ≈ 4.16 mol

Use stoichiometry to find the moles of ethanol produced

From the balanced chemical equation, we can see that 1 mole of sugar (C6H12O6) produces 2 moles of ethanol (C2H5OH). Now we will use this stoichiometric ratio to find the moles of ethanol produced. moles of C2H5OH = moles of C6H12O6 × (2 moles of C2H5OH / 1 mole of C6H12O6) moles of C2H5OH = 4.16 mol × (2/1) = 8.32 mol

Calculate the mass of ethanol produced

Now, we will convert the moles of ethanol calculated in step 4 to mass using its molar mass. mass of C2H5OH = moles of C2H5OH × molar mass of C2H5OH mass of C2H5OH = 8.32 mol × 46.08 g/mol ≈ 383.15 g Thus, the mass of ethanol (C2H5OH) produced from 750g of sugar (C6H12O6) is approximately 383.15g.

Key concepts

Chemical Reaction Stoichiometry

Understanding chemical reaction stoichiometry is vital when exploring any chemical process, including the synthesis of ethanol through fermentation. Stoichiometry is the calculation of the quantities of reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Hence, the atoms on the reactant side must equal the atoms on the product side.

The first step is always to balance the chemical equation. For the fermentation reaction, balancing starts with C₆H₁₂O₆ and ends with 2C₂H₅OH + 2CO₂. This shows the proportions in which reactants and products interact and are formed. One mole of glucose yields two moles of ethanol and two moles of carbon dioxide.

A common improvement advice for students is to practice balancing equations. Start with simple reactions, then gradually move to more complex ones. Remember, the coefficients represent mole ratios, which are pivotal in stoichiometric calculations, as seen in the exercise.

Molar Mass Calculation

The term molar mass refers to the mass of one mole of a substance, expressed in grams per mole (g/mol). It can be determined by summing the atomic masses of all atoms in a molecule. For instance, the molar mass of glucose (C₆H₁₂O₆) is calculated by adding the masses of 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. As outlined in the exercise solution, the result is 180.18 g/mol.

Similarly, the calculation for ethanol (C₂H₅OH) involves adding the masses of 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom, yielding a molar mass of 46.08 g/mol. Understanding how to calculate molar mass is a fundamental skill that allows students to convert between mass and moles, a crucial step in solving stoichiometry problems.

When studying, focus on familiarizing yourself with the atomic masses of common elements and practice calculating the molar mass for various compounds. This skill is not only essential for stoichiometry but also for broader applications within chemistry.

Fermentation of Sugar

The fermentation of sugar is a fascinating biological and chemical process where microorganisms such as yeast break down sugar in the absence of oxygen to produce ethanol and carbon dioxide. The balanced chemical reaction for the fermentation of glucose to ethanol provided in the exercise is a classic example.

Fermentation is not only significant in the production of alcoholic beverages but also in biofuel industries. The process takes place in anaerobic conditions and has been utilized by humans for thousands of years. During fermentation, enzymes from yeast cells convert glucose into ethanol and CO₂, a transformation that has both chemical and economic significance.

To truly appreciate this process, one must not only focus on the balanced reaction but also understand the role of enzymes and yeasts, the conditions required for fermentation, and the significance of glucose as an energy source. As such, whether you're a student or a hobbyist, delving into the science of fermentation can be as satisfying as the products it creates.