Final answer:
The sum of the integer coefficients for the correctly balanced equation C₈H₁₈ + O₂ → CO₂ + H₂O is 61, which is not an option presented in the multiple choices (10, 12, 14, 18). There may be a typo in the provided choices or in the student's question.
Step-by-step explanation:
To balance the equation C₈H₁₈ + O₂ → CO₂ + H₂O with the smallest set of integers, we balance the carbon (C) atoms first, followed by hydrogen (H) atoms, and then oxygen (O) atoms. The correct balanced equation is C₈H₁₈ + 12.5 O₂ → 8 CO₂ + 9 H₂O. When we add up the coefficients of the balanced equation, (1 for C₈H₁₈, 12.5 for O₂, 8 for CO₂, and 9 for H₂O), we obtain a sum of 30.5. However, since we need integer-only coefficients, we multiply all the terms by 2 to eliminate the fraction and get a new set of coefficients: 2 C₈H₁₈ + 25 O₂ → 16 CO₂ + 18 H₂O. The sum of these new coefficients is 2+25+16+18, which equals 61. Since this answer is not present in the options provided by the student, it is likely there was a typo or error present in the question or the options themselves. The sum of the coefficients of the correctly balanced equation is therefore not represented by the choices given (a. 10, b. 12, c. 14, d. 18).