Chapter 11, Problem 60A

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

Interpretation Introduction

Interpretation:

The balanced chemical equation for the fermentation reaction of sugar to form ethanol and carbon dioxide gas needs to be determined. Also, the mass of ethanol produced from 750 g of sugar needs to be determined.

Concept introduction:

The mole concept provides the relation between moles, mass and molar mass. The mathematical expression of mole concept can write as:

$\text{Mole =}\frac{\text{Mass}}{\text{Molar mass}}$

1 mole of any substance contains $\text{6}\text{.022 }\times {\text{ 10}}^{\text{23}}$ number of particles or atoms or molecules.

Answer to Problem 60A

${\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}\stackrel{}{\to }{\text{ 2 C}}_{\text{2}}{\text{H}}_{\text{5}}{\text{OH + 2 CO}}_{\text{2}}$

Mass of ethanol = 383 g

Explanation of Solution

The reaction of fermentation reaction of sugar produces ethanol and carbon dioxide gas. The chemical formula of reactant and products are:

Sugar = ${\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}$

Ethanol = ${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}$

Carbon dioxide = ${\text{CO}}_{\text{2}}$

Thus the balance chemical equation must be:

${\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}\stackrel{}{\to }{\text{ 2 C}}_{\text{2}}{\text{H}}_{\text{5}}{\text{OH + 2 CO}}_{\text{2}}$

The mole ratio relates the moles of reactant with other reactant and product molecules in the balance chemical equation.

Mass of sugar = 750 g

Molar mass of sugar = 180 g/mol

Molar mass of ethanol = 46.0 g/mol

Calculate mass of ethanol produces with the help of mole ratio:

1 mole of sugar = 2 moles of ethanol

${\text{750 g C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}\text{ ×}\frac{{\text{1 mole C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}}{{\text{180g C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}}\text{×}\frac{{\text{2 mole C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH }}{{\text{1 mole C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}}\text{×}\frac{{\text{46 g C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH }}{{\text{1 mole C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH }}{\text{= 383 g C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH }$

Conclusion

Thus, the mass of ethanol = 383 g