Certainly! Let's solve the problem step-by-step.
### Step 1: Determine the Molar Mass of Sulfur (S)
The molar mass of sulfur (S) is given as 32 grams per mole (g/mol).
### Step 2: Calculate the Number of Moles of Sulfur
We are provided with 4 grams of sulfur. To find the number of moles, we use the formula:
[tex]\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \][/tex]
Substituting the given values,
[tex]\[ \text{Number of moles of S} = \frac{4 \text{ g}}{32 \text{ g/mol}} = 0.125 \text{ moles} \][/tex]
### Step 3: Determine the Heat of Formation of SO[tex]\(_2\)[/tex]
The heat of formation of SO[tex]\(_2\)[/tex] is given as -298 kJ. This means that when one mole of sulfur dioxide (SO[tex]\(_2\)[/tex]) is formed, -298 kJ of energy is released.
### Step 4: Calculate the Heat of Combustion
Since the heat of combustion represents the energy released when a substance undergoes complete combustion, and we know the heat of formation is -298 kJ per mole for SO[tex]\(_2\)[/tex], we calculate the total heat released for 0.125 moles of sulfur combusted.
The total heat of combustion is calculated as:
[tex]\[ \text{Heat of combustion} = (\text{Number of moles of S}) \times (\text{Heat of formation of SO}_2) \][/tex]
[tex]\[ \text{Heat of combustion} = 0.125 \text{ moles} \times (-298 \text{ kJ/mole}) \][/tex]
[tex]\[ \text{Heat of combustion} = -37.25 \text{ kJ} \][/tex]
### Step 5: Choose the Correct Option
From the calculated heat of combustion, -37.25 kJ, the option closest to this value appears to be:
[tex]\[ \boxed{B: -37.15 \text{ kJ}} \][/tex]
This is the correct answer based on the given options.
