Heat evolved during the combustion of 32 gm methanol is a bomb calorimeter was determined to be 470 kcal/mol at `25^(@)`C. The value of `Delta`u of the reaction at the same temperature is

Options

A. `-335.24` kcal
B. `-669.28`kcal
C. `-470` kcal/mol
D. `-196.5 xx 10^(4)` J

Answer

To find the value of ΔU (change in internal energy) for the combustion of methanol, we can follow these steps:

### Step 1: Understand the given data
We know that the heat evolved during the combustion of 32 grams of methanol is 470 kcal/mol. Methanol has the chemical formula CH₃OH.

### Step 2: Calculate the number of moles of methanol
To find the number of moles of methanol, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of methanol (CH₃OH) is:

- C: 12.01 g/mol
- H: 1.008 g/mol × 4 = 4.032 g/mol
- O: 16.00 g/mol

Calculating the molar mass:

\[ \text{Molar mass of CH₃OH} = 12.01 + 4.032 + 16.00 = 32.042 \text{ g/mol} \approx 32 \text{ g/mol} \]

Now, substituting the values:

\[ \text{Number of moles} = \frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mol} \]

### Step 3: Relate heat evolved to ΔU
The heat released during the combustion in a bomb calorimeter is equal to the change in internal energy (ΔU) at constant volume. Since the heat evolved is given as 470 kcal for 1 mole of methanol, we can directly state:

\[ \Delta U = -470 \text{ kcal/mol} \]

### Step 4: Final answer
Thus, the value of ΔU for the combustion of methanol at 25°C is:

\[ \Delta U = -470 \text{ kcal/mol} \]

### Summary of the solution:
- The heat evolved during the combustion of 32 grams of methanol is 470 kcal/mol.
- The number of moles of methanol is 1.
- Therefore, ΔU = -470 kcal/mol.