Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To find the overall reaction from the given chemical equations, we will sum the equations step-by-step while ensuring the substances on both the reactant and product sides balance out. Here are the given chemical equations:
1. [tex]\( 2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g) \)[/tex]
2. [tex]\( 2 \, NO(g) \rightarrow N_2(g) + O_2(g) \)[/tex]
3. [tex]\( N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \)[/tex]
### Step-by-Step Solution:
1. First Equation:
[tex]\[ 2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g) \][/tex]
This means that 2 molecules of nitrogen dioxide decompose to produce 2 molecules of nitric oxide and 1 molecule of oxygen gas.
2. Second Equation:
[tex]\[ 2 \, NO(g) \rightarrow N_2(g) + O_2(g) \][/tex]
Here, 2 molecules of nitric oxide decompose to produce 1 molecule of nitrogen gas and 1 molecule of oxygen gas.
3. Combining the First Two Equations:
First, add the first and second equations:
[tex]\[ (2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g)) + (2 \, NO(g) \rightarrow N_2(g) + O_2(g)) \][/tex]
Combine the products and reactants and then cancel out the common species on both sides:
[tex]\[ 2 \, NO_2(g) + 2 \, NO(g) \rightarrow 2 \, NO(g) + O_2(g) + N_2(g) + O_2(g) \][/tex]
Cancel out [tex]\( 2 \, NO(g) \)[/tex] from both sides:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g) \][/tex]
4. Third Equation:
[tex]\[ N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \][/tex]
This equation shows 1 molecule of nitrogen gas reacting with 2 molecules of oxygen gas to form dinitrogen tetroxide.
5. Combining All Equations:
Now, combine the result from step 3 with the third equation:
[tex]\[ (2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g)) + (N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g)) \][/tex]
Combine them:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g) + N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \][/tex]
Cancel out [tex]\( N_2(g) \)[/tex] and [tex]\( 2 \, O_2(g) \)[/tex] from both sides:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2O_4(g) \][/tex]
### Final Overall Reaction:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2O_4(g) \][/tex]
Thus, the overall reaction obtained by adding the given equations is:
[tex]\[ 2 NO_2(g) \rightarrow N_2O_4(g) \][/tex]
1. [tex]\( 2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g) \)[/tex]
2. [tex]\( 2 \, NO(g) \rightarrow N_2(g) + O_2(g) \)[/tex]
3. [tex]\( N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \)[/tex]
### Step-by-Step Solution:
1. First Equation:
[tex]\[ 2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g) \][/tex]
This means that 2 molecules of nitrogen dioxide decompose to produce 2 molecules of nitric oxide and 1 molecule of oxygen gas.
2. Second Equation:
[tex]\[ 2 \, NO(g) \rightarrow N_2(g) + O_2(g) \][/tex]
Here, 2 molecules of nitric oxide decompose to produce 1 molecule of nitrogen gas and 1 molecule of oxygen gas.
3. Combining the First Two Equations:
First, add the first and second equations:
[tex]\[ (2 \, NO_2(g) \rightarrow 2 \, NO(g) + O_2(g)) + (2 \, NO(g) \rightarrow N_2(g) + O_2(g)) \][/tex]
Combine the products and reactants and then cancel out the common species on both sides:
[tex]\[ 2 \, NO_2(g) + 2 \, NO(g) \rightarrow 2 \, NO(g) + O_2(g) + N_2(g) + O_2(g) \][/tex]
Cancel out [tex]\( 2 \, NO(g) \)[/tex] from both sides:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g) \][/tex]
4. Third Equation:
[tex]\[ N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \][/tex]
This equation shows 1 molecule of nitrogen gas reacting with 2 molecules of oxygen gas to form dinitrogen tetroxide.
5. Combining All Equations:
Now, combine the result from step 3 with the third equation:
[tex]\[ (2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g)) + (N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g)) \][/tex]
Combine them:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2(g) + 2 \, O_2(g) + N_2(g) + 2 \, O_2(g) \rightarrow N_2O_4(g) \][/tex]
Cancel out [tex]\( N_2(g) \)[/tex] and [tex]\( 2 \, O_2(g) \)[/tex] from both sides:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2O_4(g) \][/tex]
### Final Overall Reaction:
[tex]\[ 2 \, NO_2(g) \rightarrow N_2O_4(g) \][/tex]
Thus, the overall reaction obtained by adding the given equations is:
[tex]\[ 2 NO_2(g) \rightarrow N_2O_4(g) \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.