Fill in the gaps to balance the equation.
Use the smallest set of whole numbers to balance the equation and include coefficients of "1" when appropriate.
[tex]$\square$ $C _6 H _{12} O _6+$ $\square$ $O _2 \rightarrow$ $\square$ $CO _2+$ $\square$ $H _2 O$[/tex]
Complete the table to determine how many atoms of each element are present in the reactants and products.
| Element | Reactant | Products |
| :------ | :------- | :------- |
| C | | |
| H | | |
| O | | |
Answer (1)
Balance the carbon atoms by placing a coefficient of 6 in front of C O 2 : C 6 H 12 O 6 + O 2 → 6 C O 2 + H 2 O .
Balance the hydrogen atoms by placing a coefficient of 6 in front of H 2 O : C 6 H 12 O 6 + O 2 → 6 C O 2 + 6 H 2 O .
Balance the oxygen atoms by placing a coefficient of 6 in front of O 2 : C 6 H 12 O 6 + 6 O 2 → 6 C O 2 + 6 H 2 O .
The balanced equation is C 6 H 12 O 6 + 6 O 2 → 6 C O 2 + 6 H 2 O , and the atom counts are C: 6, H: 12, O: 18 on both sides.
Explanation
Analyzing the Problem We are given the unbalanced chemical equation: C 6 H 12 O 6 + O 2 → C O 2 + H 2 O Our goal is to find the smallest whole number coefficients that balance the equation and to complete the table showing the number of atoms of each element on both sides of the balanced equation.
Balancing Carbon Atoms
Balance the carbon atoms: There are 6 carbon atoms on the left side ( C 6 H 12 O 6 ). To balance the carbon atoms, we need 6 carbon atoms on the right side. So, we put a coefficient of 6 in front of C O 2 :
C 6 H 12 O 6 + O 2 → 6 C O 2 + H 2 O
Balancing Hydrogen Atoms
Balance the hydrogen atoms: There are 12 hydrogen atoms on the left side ( C 6 H 12 O 6 ). To balance the hydrogen atoms, we need 12 hydrogen atoms on the right side. So, we put a coefficient of 6 in front of H 2 O :
C 6 H 12 O 6 + O 2 → 6 C O 2 + 6 H 2 O
Balancing Oxygen Atoms
Balance the oxygen atoms: On the right side, we have 6 C O 2 which contains 6 × 2 = 12 oxygen atoms, and 6 H 2 O which contains 6 × 1 = 6 oxygen atoms. So, there are a total of 12 + 6 = 18 oxygen atoms on the right side. On the left side, C 6 H 12 O 6 contains 6 oxygen atoms. Therefore, we need 18 − 6 = 12 more oxygen atoms on the left side. Since oxygen appears as O 2 , we need 12/2 = 6 molecules of O 2 . So, we put a coefficient of 6 in front of O 2 :
C 6 H 12 O 6 + 6 O 2 → 6 C O 2 + 6 H 2 O
Checking for Simplification
Check if the coefficients are the smallest whole numbers: The coefficients are 1, 6, 6, and 6. The greatest common divisor of these numbers is 1, so the coefficients are already in the smallest whole numbers.
Balanced Equation
Write the balanced equation: The balanced equation is: C 6 H 12 O 6 + 6 O 2 → 6 C O 2 + 6 H 2 O
Atom Counts Table
Complete the table:
Element
Reactant
Products
C
6
6
H
12
12
O
18
18
Final Answer The balanced equation is: C 6 H 12 O 6 + 6 O 2 → 6 C O 2 + 6 H 2 O The table showing the number of atoms of each element on both sides of the balanced equation is:
Element
Reactant
Products
C
6
6
H
12
12
O
18
18
Examples
Balancing chemical equations is crucial in many real-world applications. For example, in designing combustion engines, engineers need to ensure the correct ratio of fuel (like glucose, C 6 H 12 O 6 ) to oxygen to achieve complete combustion, maximizing energy output and minimizing harmful emissions like carbon monoxide. Similarly, in pharmaceutical manufacturing, balancing equations helps chemists determine the precise amounts of reactants needed to synthesize drugs, ensuring product purity and yield. In environmental science, understanding balanced equations is essential for modeling and mitigating pollution, such as predicting the impact of greenhouse gases on climate change. By mastering this concept, students gain a fundamental tool for solving practical problems across various scientific and engineering fields.
