Let's solve this problem step-by-step.
## Part 1: Grams of \( CO_2 \) produced from \( 2.6 \) moles of \( C_8H_{18} \)
Using the balanced chemical equation:
[tex]\[ 2 C_8H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O \][/tex]
We note that 2 moles of \( C_8H_{18} \) produce 16 moles of \( CO_2 \).
Thus,
[tex]\[ \text{Moles of } CO_2 = 2.6 \text{ moles of } C_8H_{18} \times \frac{16 \text{ moles of } CO_2}{2 \text{ moles of } C_8H_{18}} = 2.6 \times 8 = 20.8 \text{ moles of } CO_2 \][/tex]
Next, we calculate the grams of \( CO_2 \) produced. The molar mass of \( CO_2 \) is:
[tex]\[ 12.01 \text{ (C)} + 2 \times 16 \text{ (O)} = 44.01 \text{ g/mol} \][/tex]
Therefore,
[tex]\[ \text{Grams of } CO_2 = 20.8 \text{ moles of } CO_2 \times 44.01 \text{ g/mol} = 915.408 \text{ g} \][/tex]
So,
[tex]\[ \boxed{9.15408} \times 10^2 \text{ g CO}_2 \][/tex]
## Part 2: Grams of \( H_2O \) produced from \( 0.57 \) moles of \( C_8H_{18} \)
Using the balanced chemical equation:
[tex]\[ 2 C_8H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O \][/tex]
We note that 2 moles of \( C_8H_{18} \) produce 18 moles of \( H_2O \).
Thus,
[tex]\[ \text{Moles of } H_2O = 0.57 \text{ moles of } C_8H_{18} \times \frac{18 \text{ moles of } H_2O}{2 \text{ moles of } C_8H_{18}} = 0.57 \times 9 = 5.13 \text{ moles of } H_2O \][/tex]
Next, we calculate the grams of \( H_2O \) produced. The molar mass of \( H_2O \) is:
[tex]\[ 2 \times 1.008 \text{ (H)} + 16 \text{ (O)} = 18.016 \text{ g/mol} \][/tex]
Therefore,
[tex]\[ \text{Grams of } H_2O = 5.13 \text{ moles of } H_2O \times 18.016 \text{ g/mol} = 92.42208 \text{ g} \][/tex]
So,
[tex]\[ \boxed{9.24221} \times 10 \text{ g H}_2O \][/tex]
