Problem 8 - Campbell Biology

Question

What coefficients must be placed in the following blanks so that all atoms are accounted for in the products? $$\mathrm { C } _ { 6 } \mathrm { H } _ { 12 } \mathrm { O } _ { 6 } \rightarrow _ { \mathrm { C } _ { 2 } \mathrm { H } _ { 6 } \mathrm { O } + } \mathrm { CO } _ { 2 }$$ $$\begin{array} { l l } { \text { (A) } 2 ; 1 } & { \text { (C) } 1 ; 3 } \\\ { \text { (B) } 3 ; 1 } & { \text { (D) } 2 ; 2 } \end{array}$$

Step-by-Step Solution

Answer

The coefficients are 2 and 2.

Step 1: Write the unbalanced equation

Start by writing down the chemical equation you need to balance: \[ \mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6} \rightarrow \mathrm{C}_{2}\mathrm{H}_{6}\mathrm{O} + \mathrm{CO}_{2} \]

Step 2: List the number of each type of atom on both sides

Count the number of each atom in the reactants and products: Reactants: 6 Carbon (C), 12 Hydrogen (H), 6 Oxygen (O)Products: (2 Carbon in \(\mathrm{C}_2\mathrm{H}_6\mathrm{O}\) + 1 Carbon in \(\mathrm{CO}_2\)) = 3 Carbon (C), 6 Hydrogen (H), (1 Oxygen in \(\mathrm{C}_2\mathrm{H}_6\mathrm{O}\) + 2 Oxygen in \(\mathrm{CO}_2\)) = 3 Oxygen (O)

Step 3: Identify the imbalance and set coefficients

To balance the carbons, place a 2 in front of \(\mathrm{C}_2\mathrm{H}_6\mathrm{O}\) and a 2 in front of \(\mathrm{CO}_2\):\[\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 \rightarrow 2\mathrm{C}_2\mathrm{H}_6\mathrm{O} + 2\mathrm{CO}_2\]Now count the atoms again to ensure they are balanced. Reactants: 6 C, 12 H, 6 O. Products: 6 C, 12 H, 6 O.

Step 4: Verify the balance of each atom

After placing the coefficients, recheck all atoms to confirm they match on both sides of the equation: Reactants: 6 Carbon, 12 Hydrogen, and 6 Oxygen Products: 6 Carbon, 12 Hydrogen, and 6 Oxygen The equation is now balanced.

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances (reactants) are transformed into different substances (products).
These transformations involve breaking and forming chemical bonds.
During the reaction, atoms are rearranged but not created or destroyed.
For example, in the reaction \( \mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6} \rightarrow 2 \mathrm{C}_{2}\mathrm{H}_{6}\mathrm{O} + 2\mathrm{CO}_{2} \) glucose ( \(\text{C}_6\text{H}_{12}\text{O}_6\) ) is broken down into ethanol ( \(2\text{C}_2\text{H}_6\text{O}\) ) and carbon dioxide ( \(2\text{CO}_2\) ).
Understanding chemical reactions helps explain how substances interact, change, and produce new materials.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions.
It involves using balanced chemical equations to determine the proportions of substances involved.
To balance an equation, you need it to have the same number of each type of atom on both sides.
In our example: \( \mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6} = 6\text{C} ( 6 \text { Carbon atoms} ), 12\text{H} ( 12 \text { Hydrogen atoms}), \text{and }6 \text { O} ( 6 \text{Oxygen atoms}) \) \rightarrowscience \( 2 \mathrm{C}_{2}\mathrm{H}_{6}\mathrm{O} = 4 \text{C} (carbon atoms) + 6 \text{H} ( Hydrogen atoms) + 2 \text{O} (Oxygen atoms)\) + \( 2 \mathrm{CO}_{2} \rightarrow 2 \text{C} (carbon atoms) + 4 \text O (Oxygen atoms)\)
The coefficients are adjusted until the number of each type of atom is the same on both sides.
This ensures the equation respects the law of conservation of mass.


Conservation of Mass

The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction.
This means the total mass of the reactants must equal the total mass of the products.
For our balanced equation: \( \mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6} \rightarrow 2 \mathrm{C}_{2}\mathrm{H}_{6}\mathrm{O} + 2 \mathrm{CO}_{2} : 6 \text{C} + 12 \text{H} + 6 \text{O} = 6\text { C } + 6 \text{ H} + 6\text{ O}\) This shows that the number of atoms (and thus mass) is the same on both sides.
Observing this principle helps ensure the accuracy of chemical equations and promotes a deeper understanding of reactions.