Let's analyze and work through the given chemical reactions, and discuss the provided formula [tex]\( M = \frac{m}{n} \)[/tex].
### 1st Equation:
[tex]\[ C_8H_{18} + O_2 \rightarrow CO_2 + H_2O \][/tex]
First, let's balance this equation.
1. Count the number of atoms of each element on both sides of the reaction.
- Reactants: [tex]\( C_8H_{18} + O_2 \)[/tex].
- Carbon (C): 8
- Hydrogen (H): 18
- Oxygen (O): 2 (from [tex]\( O_2 \)[/tex])
- Products: [tex]\( CO_2 + H_2O \)[/tex].
- Carbon (C): 1 per [tex]\( CO_2 \)[/tex]
- Hydrogen (H): 2 per [tex]\( H_2O \)[/tex]
- Oxygen (O): 2 per [tex]\( CO_2 \)[/tex] and 1 per [tex]\( H_2O \)[/tex]
2. Balance the carbon atoms:
[tex]\[ C_8H_{18} + O_2 \rightarrow 8CO_2 + H_2O \][/tex]
3. Balance the hydrogen atoms:
[tex]\[ C_8H_{18} + O_2 \rightarrow 8CO_2 + 9H_2O \][/tex]
4. Balance the oxygen atoms:
- Reactants: [tex]\( O_2 \)[/tex], need to have the same number of oxygen atoms as the products.
- Products: [tex]\( 8 \times 2 + 9 \times 1 = 16 + 9 = 25 \, \text{oxygen atoms} \)[/tex].
Therefore, the reactants should have [tex]\( 25 \)[/tex] oxygen atoms from [tex]\( O_2 \)[/tex]:
[tex]\[ C_8H_{18} + 12.5O_2 \rightarrow 8CO_2 + 9H_2O \][/tex]
5. To avoid fractional coefficients, multiply through by 2:
[tex]\[ 2C_8H_{18} + 25O_2 \rightarrow 16CO_2 + 18H_2O \][/tex]
The balanced equation is:
[tex]\[ 2C_8H_{18} + 25O_2 \rightarrow 16CO_2 + 18H_2O \][/tex]
### 2nd Equation:
[tex]\[ 2H_2S + 3O_2 \rightarrow 2SO_2 + 2H_2O \][/tex]
This equation is already balanced:
- Sulfur (S): 2 on each side.
- Oxygen (O): 6 on each side (3 [tex]\( O_2 \)[/tex] on the left, 2 [tex]\( SO_2 \)[/tex] and 2 [tex]\( H_2O \)[/tex] on the right).
- Hydrogen (H): 4 on each side (2 [tex]\( H_2S \)[/tex], 2 [tex]\( H_2O \)[/tex]).
### M = [tex]\(\frac{m}{n}\)[/tex]
The formula [tex]\( M = \frac{m}{n} \)[/tex] needs additional context such as:
- [tex]\( m \)[/tex]: It could represent the mass of a substance.
- [tex]\( n \)[/tex]: It could represent the number of moles of the substance.
Without specific values or additional details, we cannot perform a precise quantitative analysis using this formula. If there are more details regarding the quantities involved (mass, mole amounts, etc.), specific calculations can be completed.
In summary, the balanced chemical equations are:
1. [tex]\( 2C_8H_{18} + 25O_2 \rightarrow 16CO_2 + 18H_2O \)[/tex]
2. [tex]\( 2H_2S + 3O_2 \rightarrow 2SO_2 + 2H_2O \)[/tex]
Further detailed numerical calculations require additional information.
