To determine the correct product-to-product ratio for the given chemical reaction, we need to look closely at the stoichiometric coefficients of the products in the balanced equation:
[tex]\[ 2 C_6H_5COOH + 15 O_2 \rightarrow 14 CO_2 + 6 H_2O \][/tex]
Let's analyze each part step-by-step:
1. Identify the products and their respective stoichiometric coefficients in the balanced chemical equation.
- Carbon dioxide ([tex]\( CO_2 \)[/tex]) has a coefficient of 14.
- Water ([tex]\( H_2O \)[/tex]) has a coefficient of 6.
2. Calculate the ratio of the coefficients of [tex]\( CO_2 \)[/tex] to [tex]\( H_2O \)[/tex].
Given:
[tex]\[ CO_2: H_2O = 14: 6 \][/tex]
3. Verify if this ratio simplifies:
- The greatest common divisor (GCD) of 14 and 6 is 2.
- Dividing both numbers by 2, we get:
[tex]\[ \frac{14}{2} : \frac{6}{2} = 7: 3 \][/tex]
So, the simplified ratio of [tex]\( CO_2 \)[/tex] to [tex]\( H_2O \)[/tex] is:
[tex]\[ 7: 3 \][/tex]
However, in the context of your options and understanding that typically stoichiometric ratios are provided as is unless asked to simplify, we should retain the exact ratio from the balanced equation, which is:
[tex]\[ 14: 6 \][/tex]
Checking the options provided:
- [tex]\( CO_2 : H_2O = 14: 6 \)[/tex]: This matches exactly.
- [tex]\( CO_2 : H_2O = 6:14 \)[/tex]: This ratio is inverted and therefore incorrect.
- [tex]\( CO_2 : H_2O = 1: 1 \)[/tex]: This ratio does not match the stoichiometric coefficients.
- [tex]\( O_2 : H_2O = 15: 6 \)[/tex]: This ratio is between a reactant and a product, not two products.
Therefore, the correct product-to-product ratio for this reaction is:
[tex]\[ \boxed{CO_2 : H_2O = 14 : 6} \][/tex]
