Chapter 7, Problem 42A

Interpretation Introduction

Interpretation:

The balanced chemical equation corresponding to the reaction of a solution of sucrose in the presence of yeast forming ethanol and carbon dioxide needs to be balanced.

Concept Introduction:

• A chemical reaction is expressed as a chemical equation having reactants and products on left and right side of the reaction arrow respectively.

  $\text{Reactants }\to \text{ Products}$

• A balanced chemical equation is one in which the number of atoms of various elements on the reactants side is equal to that on the product side. It depicts the stoichiometry of a given reaction.
• The equations are balanced in two steps:

1) Balance the atoms by matching the number of atoms of each type on the reactants and product side.

2) Adjust the coefficients to the smallest whole number. A coefficient of '1' is implied and therefore not explicitly written.

Answer to Problem 42A

  ${\text{C}}_{\text{12}}{\text{H}}_{22}{\text{O}}_{11}\text{(aq)}+{\text{ H}}_{\text{2}}\text{O (l)}\stackrel{\text{yeast}}{\to }{\text{ 4C}}_2{\text{H}}_5{\text{OH (aq) + 4CO}}_2\text{(g) }$

Explanation of Solution

The given equation involves the reaction of an aqueous solution of sucrose in the presence of an enzyme to form aqueous ethanol and carbon dioxide gas. The reactants and products are:

Reactants:

  $\begin{array}{l}{\text{Sucrose, aqueous - C}}_{\text{12}}{\text{H}}_{22}{\text{O}}_{11}\text{(aq)}\\ {\text{Water, liquid - H}}_{\text{2}}\text{O (l)}\end{array}$

Products:

  $\begin{array}{l}{\text{Carbon dioxide, gas - CO}}_2\text{ (g)}\\ {\text{Ethanol, aqueous - C}}_2{\text{H}}_5\text{OH (aq)}\end{array}$

Unbalanced equation:

  ${\text{C}}_{\text{12}}{\text{H}}_{22}{\text{O}}_{11}\text{(aq)}+{\text{ H}}_{\text{2}}\text{O (l)}\stackrel{\text{yeast}}{\to }{\text{C}}_2{\text{H}}_5{\text{OH (aq) + CO}}_2\text{(g) }$

The above equation is not balanced since the number of atoms of C, H and O on the reactant side is 12, 24 and 12 respectively while that on the products side is 3, 6 and 3 respectively. In order to balance the above equation, multiply both C₂H₅OH and CO₂ by 4 to get:

  ${\text{C}}_{\text{12}}{\text{H}}_{22}{\text{O}}_{11}\text{(aq)}+{\text{ H}}_{\text{2}}\text{O (l)}\stackrel{\text{yeast}}{\to }{\text{ 4C}}_2{\text{H}}_5{\text{OH (aq) + 4CO}}_2\text{(g) }$

Conclusion

Therefore, 1 mole of sucrose reacts with 1 mole of water to form 4 moles each of ethanol and carbon dioxide.