Which set of coefficients correctly balances the chemical equation: __C_2H_6 + __O_2 → __CO_2 + __H_2O?

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

Answer: (D)

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 the coefficient of \(C_2H_6\) be \(a\), \(O_2\) be \(b\), \(CO_2\) be \(c\), and \(H_2O\) be \(d\).
3. Balance carbon atoms first: since there are 2 carbons in \(C_2H_6\), set \(c = 2a\) to balance carbon atoms on both sides.
4. Balance hydrogen atoms next: there are 6 hydrogens in \(C_2H_6\), so set \(d = \frac{6a}{2} = 3a\) to balance hydrogen atoms (each \(H_2O\) has 2 hydrogens).
5. Balance oxygen atoms last: total oxygen atoms on the right are \$2c + d = 2(2a) + 3a = 4a + 3a = 7a\(. Since each \)O_2\( molecule has 2 oxygen atoms, set \)b = \frac{7a}{2}$. To avoid fractional coefficients, multiply all coefficients by 2 to get whole numbers.