One gram of an organic liquid `X (` molecular mass 78) liberates `160J` of heat on solidification. `DeltaH_(fusion)(X)` is `:`

Options

A. `19.2 kJ//mol`
B. `12.48 kJ//mol`
C. `124.8 kJ//mol`
D. None of these

Explanation

To find the heat of fusion (ΔH_fusion) for the organic liquid X, we can follow these steps:

### Step 1: Understand the process
When the organic liquid X solidifies, it releases 160 J of heat. This means that the process of solidification is exothermic, and we can denote this heat as negative (-160 J) since it is released.

### Step 2: Relate solidification to fusion
The heat of fusion (ΔH_fusion) is the heat required to convert a solid into a liquid. Therefore, the heat of fusion will be the opposite of the heat released during solidification. Thus, we can express it as:
\[ \Delta H_{fusion} = +160 \text{ J} \]

### Step 3: Calculate the number of moles of the substance
To find the heat of fusion per mole, we need to calculate the number of moles of the organic liquid X. The formula to calculate the number of moles is:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Given that the mass of X is 1 g and its molar mass is 78 g/mol:
\[ \text{Number of moles} = \frac{1 \text{ g}}{78 \text{ g/mol}} = 0.01282 \text{ moles} \]

### Step 4: Calculate the heat of fusion per mole
Now, we need to find the heat of fusion per mole by dividing the total heat absorbed (160 J) by the number of moles calculated:
\[ \Delta H_{fusion} \text{ (per mole)} = \frac{160 \text{ J}}{0.01282 \text{ moles}} \approx 12448.49 \text{ J/mol} \]

### Step 5: Convert Joules to Kilojoules
Since the answer is typically expressed in kilojoules per mole, we convert the result from joules to kilojoules:
\[ \Delta H_{fusion} \text{ (per mole)} = \frac{12448.49 \text{ J/mol}}{1000} \approx 12.44849 \text{ kJ/mol} \]

### Step 6: Round the answer
Rounding this value gives us:
\[ \Delta H_{fusion} \approx 12.48 \text{ kJ/mol} \]

### Final Answer
Thus, the heat of fusion (ΔH_fusion) for the organic liquid X is approximately **12.48 kJ/mol**.

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