The ratio of heat liberated at 298 K from the combustion of one kg of coke and by burning, water gas obtained from 1 kg of coke is (assume coke to be 100% carbon, enthalpies of combustion of C, CO and `H_(2)` as 393.5 kJ, 285 kJ, 285 kJ respectively all at 298 K).

Options

A. `0.79 : 1`
B. `0.69 : 1`
C. `0.86 : 1`
D. `0.96 : 1`

Explanation

To solve the problem, we need to calculate the heat liberated from the combustion of 1 kg of coke (assumed to be 100% carbon) and the heat liberated from burning the water gas obtained from the same amount of coke.

### Step 1: Calculate the number of moles of carbon in 1 kg of coke.
- The molar mass of carbon (C) is approximately 12 g/mol.
- Therefore, the number of moles of carbon in 1 kg (1000 g) of coke is calculated as follows:

\[ \text{Number of moles of C} = \frac{1000 \, \text{g}}{12 \, \text{g/mol}} \approx 83.33 \, \text{moles} \]

### Step 2: Calculate the heat liberated from the combustion of carbon.
- The enthalpy of combustion of carbon (C) is given as 393.5 kJ/mol.
- The total heat liberated (ΔH1) from the combustion of 83.33 moles of carbon is:

\[ \Delta H_1 = \text{Number of moles} \times \text{Enthalpy of combustion of C} \]
\[ \Delta H_1 = 83.33 \, \text{moles} \times 393.5 \, \text{kJ/mol} \approx 32700.5 \, \text{kJ} \]

### Step 3: Calculate the heat liberated from burning water gas.
- Water gas is a mixture of carbon monoxide (CO) and hydrogen (H2). The combustion reactions are:
- For CO: \( \text{C} + \text{O}_2 \rightarrow \text{CO}_2 \) with ΔH = 285 kJ/mol
- For H2: \( \text{2H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2\text{O} \) with ΔH = 285 kJ/mol

- The total heat liberated (ΔH2) from burning water gas (CO + H2) is:

\[ \Delta H_2 = \text{Number of moles} \times (\text{Enthalpy of combustion of CO} + \text{Enthalpy of combustion of H2}) \]
\[ \Delta H_2 = 83.33 \, \text{moles} \times (285 \, \text{kJ/mol} + 285 \, \text{kJ/mol}) = 83.33 \, \text{moles} \times 570 \, \text{kJ/mol} \approx 47500.1 \, \text{kJ} \]

### Step 4: Calculate the ratio of heat liberated.
- The ratio of heat liberated from the combustion of coke to the heat liberated from burning water gas is:

\[ \text{Ratio} = \frac{\Delta H_1}{\Delta H_2} = \frac{32700.5 \, \text{kJ}}{47500.1 \, \text{kJ}} \approx 0.688 \]

### Final Answer:
The ratio of heat liberated at 298 K from the combustion of 1 kg of coke to that from burning water gas obtained from 1 kg of coke is approximately **0.688**.