Find accurate and reliable answers to your questions on IDNLearn.com. Discover in-depth and trustworthy answers to all your questions from our experienced community members.
Sagot :
To balance the combustion equation for ethane ([tex]\(\text{C}_2\text{H}_6\)[/tex]), we need to ensure that the number of each type of atom on the reactant side is equal to the number on the product side. The equation is:
[tex]\[a \, \text{C}_2\text{H}_6 + b \, \text{O}_2 \rightarrow c \, \text{CO}_2 + d \, \text{H}_2\text{O}\][/tex]
Let's break this down step-by-step:
1. Balance the Carbon atoms:
[tex]\[ \text{C}_2\text{H}_6 \rightarrow 2 \text{C atoms} \][/tex]
[tex]\[ \text{CO}_2 \rightarrow \text{C atoms on product side} \][/tex]
To balance the carbon atoms, we need 2 CO[tex]\(_2\)[/tex] molecules on the product side:
[tex]\[ c = 2 \][/tex]
The equation now looks like:
[tex]\[ \text{C}_2\text{H}_6 + b \, \text{O}_2 \rightarrow 2 \, \text{CO}_2 + d \, \text{H}_2\text{O} \][/tex]
2. Balance the Hydrogen atoms:
[tex]\[ \text{C}_2\text{H}_6 \rightarrow 6 \text{H atoms} \][/tex]
[tex]\[ \text{H}_2\text{O} \rightarrow 2 \text{H atoms per molecule} \][/tex]
To balance the hydrogen atoms, we need [tex]\( \frac{6}{2} = 3 \)[/tex] H[tex]\(_2\)[/tex]O molecules:
[tex]\[ d = 3 \][/tex]
The equation now looks like:
[tex]\[ \text{C}_2\text{H}_6 + b \, \text{O}_2 \rightarrow 2 \, \text{CO}_2 + 3 \, \text{H}_2\text{O} \][/tex]
3. Balance the Oxygen atoms:
[tex]\[ \text{O}_2 \rightarrow 2 \text{O atoms per molecule} \][/tex]
[tex]\[ \text{CO}_2 \rightarrow 2 \times 2 = 4 \text{O atoms} \][/tex]
[tex]\[ \text{H}_2\text{O} \rightarrow 3 \times 1 = 3 \text{O atoms} \][/tex]
In total, we need [tex]\(4 + 3 = 7\)[/tex] Oxygen atoms on the reactant side:
[tex]\[ b = \frac{7}{2} = 3.5 \][/tex]
So the equation becomes:
[tex]\[ \text{C}_2\text{H}_6 + 3.5 \, \text{O}_2 \rightarrow 2 \, \text{CO}_2 + 3 \, \text{H}_2\text{O} \][/tex]
To avoid fractions, multiply the entire equation by 2:
[tex]\[ 2 \text{C}_2\text{H}_6 + 7 \text{O}_2 \rightarrow 4 \text{CO}_2 + 6 \text{H}_2\text{O} \][/tex]
Hence, the balanced equation is:
[tex]\[2 \, \text{C}_2\text{H}_6 + 7 \, \text{O}_2 \rightarrow 4 \, \text{CO}_2 + 6 \, \text{H}_2\text{O}\][/tex]
Therefore, the coefficients are:
[tex]\[ \boxed{2} \, \text{C}_2\text{H}_6 + \boxed{7} \, \text{O}_2 \rightarrow \boxed{4} \, \text{CO}_2 + \boxed{6} \, \text{H}_2\text{O} \][/tex]
[tex]\[a \, \text{C}_2\text{H}_6 + b \, \text{O}_2 \rightarrow c \, \text{CO}_2 + d \, \text{H}_2\text{O}\][/tex]
Let's break this down step-by-step:
1. Balance the Carbon atoms:
[tex]\[ \text{C}_2\text{H}_6 \rightarrow 2 \text{C atoms} \][/tex]
[tex]\[ \text{CO}_2 \rightarrow \text{C atoms on product side} \][/tex]
To balance the carbon atoms, we need 2 CO[tex]\(_2\)[/tex] molecules on the product side:
[tex]\[ c = 2 \][/tex]
The equation now looks like:
[tex]\[ \text{C}_2\text{H}_6 + b \, \text{O}_2 \rightarrow 2 \, \text{CO}_2 + d \, \text{H}_2\text{O} \][/tex]
2. Balance the Hydrogen atoms:
[tex]\[ \text{C}_2\text{H}_6 \rightarrow 6 \text{H atoms} \][/tex]
[tex]\[ \text{H}_2\text{O} \rightarrow 2 \text{H atoms per molecule} \][/tex]
To balance the hydrogen atoms, we need [tex]\( \frac{6}{2} = 3 \)[/tex] H[tex]\(_2\)[/tex]O molecules:
[tex]\[ d = 3 \][/tex]
The equation now looks like:
[tex]\[ \text{C}_2\text{H}_6 + b \, \text{O}_2 \rightarrow 2 \, \text{CO}_2 + 3 \, \text{H}_2\text{O} \][/tex]
3. Balance the Oxygen atoms:
[tex]\[ \text{O}_2 \rightarrow 2 \text{O atoms per molecule} \][/tex]
[tex]\[ \text{CO}_2 \rightarrow 2 \times 2 = 4 \text{O atoms} \][/tex]
[tex]\[ \text{H}_2\text{O} \rightarrow 3 \times 1 = 3 \text{O atoms} \][/tex]
In total, we need [tex]\(4 + 3 = 7\)[/tex] Oxygen atoms on the reactant side:
[tex]\[ b = \frac{7}{2} = 3.5 \][/tex]
So the equation becomes:
[tex]\[ \text{C}_2\text{H}_6 + 3.5 \, \text{O}_2 \rightarrow 2 \, \text{CO}_2 + 3 \, \text{H}_2\text{O} \][/tex]
To avoid fractions, multiply the entire equation by 2:
[tex]\[ 2 \text{C}_2\text{H}_6 + 7 \text{O}_2 \rightarrow 4 \text{CO}_2 + 6 \text{H}_2\text{O} \][/tex]
Hence, the balanced equation is:
[tex]\[2 \, \text{C}_2\text{H}_6 + 7 \, \text{O}_2 \rightarrow 4 \, \text{CO}_2 + 6 \, \text{H}_2\text{O}\][/tex]
Therefore, the coefficients are:
[tex]\[ \boxed{2} \, \text{C}_2\text{H}_6 + \boxed{7} \, \text{O}_2 \rightarrow \boxed{4} \, \text{CO}_2 + \boxed{6} \, \text{H}_2\text{O} \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.
