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
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1
Write down the unbalanced chemical equation: \(\_\_ C_2H_6 + \_\_ O_2 \rightarrow \_\_ CO_2 + \_\_ H_2O\).
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 \(H_2O\).
Balance carbon atoms first by equating the number of carbon atoms on both sides: since \(C_2H_6\) has 2 carbons, set \(2a = c\).
Balance hydrogen atoms next: \(C_2H_6\) has 6 hydrogens, and \(H_2O\) has 2 hydrogens per molecule, so set \(6a = 2d\).
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.