Which sequence of coefficients should be placed in the blanks to balance the following chemical equation? __C_2H_6 + __O_2 → __CO_2 + __H_2O

• A. 1, 2, 2, 2
• B. 1, 3, 2, 3
• C. 2, 7, 4, 6
• D. 2, 6, 4, 6

Answer: (C)

Verified step by step guidance

1. Write down the unbalanced chemical equation: \(\_\_ C_2H_6 + \_\_ O_2 \rightarrow \_\_ CO_2 + \_\_ H_2O\).
2. Assign variables to the coefficients: let \(a\) be the coefficient for \(C_2H_6\), \(b\) for \(O_2\), \(c\) for \(CO_2\), and \(d\) for \(H_2O\).
3. Balance carbon atoms first by equating the number of carbon atoms on both sides: since \(C_2H_6\) has 2 carbons, set \$2a = c$.
4. Balance hydrogen atoms next: \(C_2H_6\) has 6 hydrogens, and \(H_2O\) has 2 hydrogens per molecule, so set \$6a = 2d$.
5. Balance oxygen atoms last: oxygen atoms appear in \(O_2\), \(CO_2\), and \(H_2O\). The total oxygen atoms on the right side are \$2c + d\(, so set \)2b = 2c + d\(. Use the previous relations to express all coefficients in terms of \)a$ and solve for the smallest whole numbers.