Balance the entire chemical reaction using an atom inventory. Remember to balance each element in the reaction.
[tex]H_2 O_2 \rightarrow O_2+H_2 O[/tex]
What is the coefficient for the water, [tex]H _2 O[/tex], in the balanced equation?
Answer (2)
Balance the chemical equation: a H 2 O 2 i g h t ha r p oo n u p b O 2 + c H 2 O .
Set up equations based on conservation of atoms: 2 a = 2 c and 2 a = 2 b + c .
Solve the equations to find a = 2 , b = 1 , and c = 2 .
The coefficient for water, H 2 O , in the balanced equation is 2 .
Explanation
Analyzing the Problem We are given the unbalanced chemical reaction: H 2 O 2 i g h t ha r p oo n u p O 2 + H 2 O Our goal is to balance this equation and find the coefficient for water ( H 2 O ).
Setting up the Balanced Equation To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's represent the balanced equation as: a H 2 O 2 i g h t ha r p oo n u p b O 2 + c H 2 O where a , b , and c are the coefficients we need to determine.
Conservation of Atoms Now, let's set up equations based on the conservation of atoms: For Hydrogen (H): 2 a = 2 c (2 hydrogen atoms in H 2 O 2 and H 2 O )
For Oxygen (O): 2 a = 2 b + c (2 oxygen atoms in H 2 O 2 , 2 in O 2 , and 1 in H 2 O )
Solving the Equations From the hydrogen equation, we have 2 a = 2 c , which simplifies to a = c .
Substitute a for c in the oxygen equation: 2 a = 2 b + a . This simplifies to a = 2 b .
Finding the Coefficients Now, we can express a , b , and c in terms of a single variable. Let's choose b = 1 . Then, from the equation a = 2 b , we get a = 2 ( 1 ) = 2 . Since a = c , we also have c = 2 .
The Balanced Equation and the Coefficient for Water So, the balanced equation is: 2 H 2 O 2 i g h t ha r p oo n u p 1 O 2 + 2 H 2 O This means that the coefficient for water, H 2 O , is 2.
Final Answer Therefore, the coefficient for the water, H 2 O , in the balanced equation is 2.
Examples
Balancing chemical equations is essential in many real-world applications, such as calculating the amount of reactants needed for a chemical reaction or determining the amount of products formed. For example, in the production of hydrogen peroxide ( H 2 O 2 ) for use as a disinfectant, it's crucial to know the exact amount of reactants needed to produce a specific amount of H 2 O 2 . Proper balancing ensures that resources are used efficiently and safely, preventing waste and potential hazards. In this specific reaction, understanding the balanced equation helps in controlling the decomposition of hydrogen peroxide into oxygen and water, which is important for its storage and handling.
The coefficient for water, H 2 O , in the balanced equation is 2. The balanced chemical equation is 2 H 2 O 2 → O 2 + 2 H 2 O . This ensures that the number of atoms for each element is conserved on both sides of the reaction.
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