The heat of combustion of C, S and `CS_(2)` are `-393.3kJ, -293.7kJ and -1108.76kJ.` What will be the heat of formation of `CS_(2)` ?

Options

A. `-128.02kJ`
B. `+970kJ`
C. `+1108.7kJ`
D. `+128.06kJ`

Explanation

To find the heat of formation of carbon disulfide (CS₂), we can use the given heats of combustion for carbon (C), sulfur (S), and carbon disulfide (CS₂) along with Hess's law. Here’s a step-by-step solution:

### Step 1: Write the combustion reactions
1. **Combustion of Carbon:**
\[ C + O_2 \rightarrow CO_2 \quad \Delta H_1 = -393.3 \, \text{kJ} \]

2. **Combustion of Sulfur:**
\[ S + O_2 \rightarrow SO_2 \quad \Delta H_2 = -293.7 \, \text{kJ} \]

3. **Combustion of Carbon Disulfide:**
\[ CS_2 + 3O_2 \rightarrow CO_2 + 2SO_2 \quad \Delta H_3 = -1108.76 \, \text{kJ} \]

### Step 2: Write the formation reaction for CS₂
The heat of formation reaction for CS₂ is:
\[ C + 2S \rightarrow CS_2 \quad \Delta H_f = ? \]

### Step 3: Use Hess's Law
According to Hess's law, we can manipulate the combustion reactions to find the heat of formation of CS₂. We need to add the combustion reactions in such a way that they yield the formation reaction.

1. **Add the combustion of carbon and double the combustion of sulfur:**
\[ C + O_2 \rightarrow CO_2 \quad (\Delta H_1) \]
\[ 2S + 2O_2 \rightarrow 2SO_2 \quad (2 \times \Delta H_2 = 2 \times -293.7 \, \text{kJ}) \]

Adding these gives:
\[ C + 2S + 3O_2 \rightarrow CO_2 + 2SO_2 \]

2. **Subtract the combustion of CS₂:**
\[ CS_2 + 3O_2 \rightarrow CO_2 + 2SO_2 \quad (-\Delta H_3) \]

### Step 4: Combine the equations
Now we combine these equations:
\[ (C + 2S + 3O_2) + (-CS_2 - 3O_2) \rightarrow (CO_2 + 2SO_2) - (CO_2 + 2SO_2) \]

This simplifies to:
\[ C + 2S \rightarrow CS_2 \]

### Step 5: Calculate the heat of formation
Now we can calculate the heat of formation using the heats of combustion:
\[ \Delta H_f = \Delta H_1 + 2 \Delta H_2 - \Delta H_3 \]
Substituting the values:
\[ \Delta H_f = -393.3 + 2(-293.7) - (-1108.76 \]
\[ \Delta H_f = -393.3 - 587.4 + 1108.76 \]
\[ \Delta H_f = 128.06 \, \text{kJ/mol} \]

### Final Answer
The heat of formation of CS₂ is:
\[ \Delta H_f = +128.06 \, \text{kJ/mol} \]