Which set of coefficients correctly balances the chemical equation: C_3H_8 + O_2 → CO_2 + H_2O?

• A. 1, 5, 3, 4
• B. 1, 4, 3, 4
• C. 1, 3, 2, 4
• D. 2, 7, 6, 8

Answer: (A)

Verified step by step guidance

1. Identify the chemical equation to balance: \(\mathrm{C_3H_8 + O_2 \rightarrow CO_2 + H_2O}\).
2. Assign variables to the coefficients of each compound: let \(a\) for \(\mathrm{C_3H_8}\), \(b\) for \(\mathrm{O_2}\), \(c\) for \(\mathrm{CO_2}\), and \(d\) for \(\mathrm{H_2O}\).
3. Write balance equations for each element based on the law of conservation of mass: - Carbon (C): \$3a = c$ - Hydrogen (H): \$8a = 2d$ - Oxygen (O): \$2b = 2c + d$
4. Choose \(a = 1\) as a starting point (usually the hydrocarbon is set to 1), then solve for \(c\) and \(d\) using the carbon and hydrogen equations: - \(c = 3 \times 1 = 3\) - \(d = \frac{8 \times 1}{2} = 4\)
5. Substitute \(c\) and \(d\) into the oxygen balance equation to find \(b\): - \$2b = 2 \times 3 + 4$ - Solve for \(b\) to get the coefficient for \(\mathrm{O_2}\).