Heat of combustion of `CH_(4),C_(2)H_(4),C_(2)H_(6)` are `-890,-1411` and `-1560 kJ //mol` respectively. Which has the lowest calorific fuel value ?

Options

A. `CH_(4)`
B. `C_(2)H_(4)`
C. `C_(2)H_(6)`
D. All of these

Answer

To determine which of the given hydrocarbons (methane, ethane, and ethylene) has the lowest calorific fuel value, we will follow these steps:

### Step 1: Understand the Concept of Calorific Value
The calorific value of a fuel is defined as the amount of heat energy released when one mole of the substance is completely burned. It can also be expressed in terms of energy released per gram of the substance.

### Step 2: Gather the Given Data
The heat of combustion for the given hydrocarbons is as follows:
- Methane (CH₄): -890 kJ/mol
- Ethylene (C₂H₄): -1411 kJ/mol
- Ethane (C₂H₆): -1560 kJ/mol

### Step 3: Calculate the Molar Mass of Each Hydrocarbon
- Molar mass of Methane (CH₄) = 12 (C) + 4 (H) = 16 g/mol
- Molar mass of Ethylene (C₂H₄) = 2(12) + 4 = 28 g/mol
- Molar mass of Ethane (C₂H₆) = 2(12) + 6 = 30 g/mol

### Step 4: Calculate the Calorific Value for Each Hydrocarbon
The calorific value can be calculated using the formula:
\[ \text{Calorific Value} = \frac{\text{Heat of Combustion}}{\text{Molar Mass}} \]

1. **For Methane (CH₄)**:
\[ \text{Calorific Value} = \frac{-890 \text{ kJ/mol}}{16 \text{ g/mol}} = -55.63 \text{ kJ/g} \]

2. **For Ethylene (C₂H₄)**:
\[ \text{Calorific Value} = \frac{-1411 \text{ kJ/mol}}{28 \text{ g/mol}} = -50.39 \text{ kJ/g} \]

3. **For Ethane (C₂H₆)**:
\[ \text{Calorific Value} = \frac{-1560 \text{ kJ/mol}}{30 \text{ g/mol}} = -52.00 \text{ kJ/g} \]

### Step 5: Compare the Calorific Values
Now we can compare the calorific values calculated:
- Methane: -55.63 kJ/g
- Ethylene: -50.39 kJ/g
- Ethane: -52.00 kJ/g

### Step 6: Identify the Hydrocarbon with the Lowest Calorific Value
From the values calculated, we can see that:
- Methane has the highest calorific value (least negative).
- Ethane has a calorific value of -52.00 kJ/g.
- Ethylene has the lowest calorific value of -50.39 kJ/g.

Thus, **Ethylene (C₂H₄)** has the lowest calorific fuel value.

### Final Answer:
The hydrocarbon with the lowest calorific fuel value is **Ethylene (C₂H₄)**.

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