$a C_3H_8(g) + b O_2(g) ightarrow d CO_2(g) + e H_2O(l)
ext{For the above balanced equation, } a, b, d ext{ and } e ext{ are respectively :}$

Q: $a C_3H_8(g) + b O_2(g) \rightarrow d CO_2(g) + e H_2O(l) \text{For the above balanced equation, } a, b, d \text{ and } e \text{ are respectively :}$

$a C_3H_8(g) + b O_2(g) \rightarrow d CO_2(g) + e H_2O(l) \text{For the above balanced equation, } a, b, d \text{ and } e \text{ are respectively :}$

Question

$a C_3H_8(g) + b O_2(g) ightarrow d CO_2(g) + e H_2O(l)
	ext{For the above balanced equation, } a, b, d 	ext{ and } e 	ext{ are respectively :}$

Accepted Answer

To determine the correct coefficients for the balanced chemical equation of the combustion of propane ($C_3H_8$), we need to ensure that the number of atoms of each element is the same on both sides of the equation. The equation is:

$$ a \, C_3H_8(g) + b \, O_2(g) \rightarrow d \, CO_2(g) + e \, H_2O(l) $$

Let's balance the equation step by step:

1. **Balance Carbon Atoms:**
   - Propane ($C_3H_8$) has 3 carbon atoms. Therefore, we need 3 $CO_2$ molecules to balance the carbon atoms.
   - This gives us: $ d = 3 $.

2. **Balance Hydrogen Atoms:**
   - Propane has 8 hydrogen atoms. Water ($H_2O$) has 2 hydrogen atoms per molecule. Therefore, we need 4 $H_2O$ molecules to balance the hydrogen atoms.
   - This gives us: $ e = 4 $.

3. **Balance Oxygen Atoms:**
   - We have 3 $CO_2$ molecules, each containing 2 oxygen atoms, contributing a total of $3 \times 2 = 6$ oxygen atoms.
   - We have 4 $H_2O$ molecules, each containing 1 oxygen atom, contributing a total of $4 \times 1 = 4$ oxygen atoms.
   - In total, we need $6 + 4 = 10$ oxygen atoms.
   - Since each $O_2$ molecule contains 2 oxygen atoms, we need $ \frac{10}{2} = 5 $ $O_2$ molecules.
   - This gives us: $ b = 5 $.

4. **Balance the Entire Equation:**
   - We have 1 $C_3H_8$ molecule, so $ a = 1 $.

Thus, the balanced equation is:

$$ 1 \, C_3H_8(g) + 5 \, O_2(g) \rightarrow 3 \, CO_2(g) + 4 \, H_2O(l) $$

This corresponds to the coefficients $ a = 1 $, $ b = 5 $, $ d = 3 $, and $ e = 4 $, which matches Option 4: 1, 5, 3, 4.

**Explanation of Incorrect Options:**

- **Option 1 (1, 2, 3, 4):** This option suggests using only 2 $O_2$ molecules, which would provide only 4 oxygen atoms, insufficient to balance the 10 oxygen atoms needed for 3 $CO_2$ and 4 $H_2O$.

- **Option 2 (1, 4, 3, 2):** This option suggests using 4 $O_2$ molecules, which would provide only 8 oxygen atoms, still insufficient to balance the 10 oxygen atoms needed.

- **Option 3 (4, 3, 5, 1):** This option suggests using 4 $C_3H_8$ molecules, which would require a different set of coefficients to balance the equation, not matching the given balanced equation.

Therefore, Option 4 is the correct choice, as it accurately balances the chemical equation for the combustion of propane.