The combustion reaction occuring in an automobile is `2C_(8)H_(18)+25O_(2)(g) to16CO_(2)(g)+18H_(2)O(g)` This reaction is accompanied with signs of change in enthalpy, entropy and gibbs free energy

Options

A. `+,-,+`
B. `-,+,-`
C. `-,+,+`
D. `+,+,-`

Explanation

To determine the signs of the changes in enthalpy (ΔH), entropy (ΔS), and Gibbs free energy (ΔG) for the combustion reaction of octane (C₈H₁₈), we can follow these steps:

### Step 1: Identify the Reaction
The combustion reaction is given as:
\[ 2C_{8}H_{18} + 25O_{2} \rightarrow 16CO_{2} + 18H_{2}O \]

### Step 2: Determine ΔH (Change in Enthalpy)
Since this is a combustion reaction, it is exothermic, meaning it releases heat. In thermodynamics, for exothermic reactions, the change in enthalpy (ΔH) is negative.
- **ΔH = -** (negative)

### Step 3: Determine ΔS (Change in Entropy)
To find the change in entropy (ΔS), we need to calculate the change in the number of moles of gaseous products and reactants.

- **Moles of gaseous products:**
- From the products: 16 moles of CO₂ + 18 moles of H₂O = 34 moles
- **Moles of gaseous reactants:**
- From the reactants: 2 moles of C₈H₁₈ + 25 moles of O₂ = 27 moles

Now, we can calculate Δn (the change in the number of moles of gas):
\[ \Delta n = \text{Moles of gaseous products} - \text{Moles of gaseous reactants} \]
\[ \Delta n = 34 - 27 = 7 \]

Since Δn is positive, the change in entropy (ΔS) is also positive.
- **ΔS = +** (positive)

### Step 4: Determine ΔG (Change in Gibbs Free Energy)
We can use the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]

Given:
- ΔH is negative
- ΔS is positive

Since ΔH is negative and ΔS is positive, the term \( -T \Delta S \) will be negative (because temperature T is always positive). Therefore, the overall expression for ΔG will be:
\[ \Delta G = \text{(negative)} - \text{(positive)} \]

This means ΔG will also be negative.
- **ΔG = -** (negative)

### Final Summary of Signs
- ΔH = negative (exothermic reaction)
- ΔS = positive (increase in disorder)
- ΔG = negative (spontaneous reaction)