Sure, let's solve this step-by-step.
First, let's consider the balanced chemical equation for the combustion of butane (C₄H₁₀):
[tex]\[ 2C_4H_{10} + 13O_2 \rightarrow 8CO_2 + 10H_2O \][/tex]
According to the balanced equation:
1. Moles of Butane (C₄H₁₀):
- The coefficient for butane is 2.
2. Moles of Carbon Dioxide (CO₂):
- The coefficient for carbon dioxide is 8.
Now, we need to find the mole ratio of butane to carbon dioxide.
To find this, we'll use the coefficients from the balanced equation:
[tex]\[ \text{Mole ratio of Butane to Carbon Dioxide} = \frac{\text{Moles of carbon dioxide}}{\text{Moles of butane}} \][/tex]
So, substituting the values we have:
[tex]\[ \frac{8 \, \text{moles of CO₂}}{2 \, \text{moles of C₄H₁₀}} \][/tex]
This simplifies to:
[tex]\[ \frac{8}{2} = 4 \][/tex]
Thus, the mole ratio of butane to carbon dioxide is [tex]\( 4:1 \)[/tex].
However, looking at the given choices, they seem to present the ratios differently. Since our solution yields a numerical ratio, we should closely examine the ratio forms presented:
The correct interpretation aligns with any direct numerical equivalence. So, when simplified the ratio [tex]\( 4:1 \)[/tex] fits right into an absolute, so:
[tex]\[ 1:\ 4 \][/tex]
Since [tex]\( C_4H_{20}\)[/tex] has 2 initiators to 8 products, a 1:4 ratio, thus numerically consist with required answers of equivalent product splits.
So interpreting this handsomely, it mentions the close interpretation to [tex]\( \ 4.0\ has suffix fitting\)[/tex].
Therefore, the accurate mole ratio here re-interatively :
The ratio given fits the context.
