`DeltaC_(P)` for a reaction is given by 0.2k cal/deg. Its enthalpy of reaction at 10K is `-14.2` kcal. Its enthalpy of reaction at 100K in kcal will be

Options

A. `-13.21`
B. `-15.31`
C. `3.8`
D. `7.08`

Answer

To find the enthalpy of reaction at 100 K, we can use the relationship between the change in heat capacity (ΔCₚ) and the change in enthalpy (ΔH) over a temperature range. The formula we will use is:

\[ \Delta C_p = \frac{\Delta H_2 - \Delta H_1}{T_2 - T_1} \]

Where:
- ΔCₚ = change in heat capacity
- ΔH₁ = enthalpy at T₁
- ΔH₂ = enthalpy at T₂
- T₁ = initial temperature
- T₂ = final temperature

### Step 1: Identify the given values
- ΔCₚ = 0.2 kcal/°C
- ΔH₁ = -14.2 kcal (at T₁ = 10 K)
- T₁ = 10 K
- T₂ = 100 K

### Step 2: Substitute the known values into the formula
We rearrange the formula to solve for ΔH₂:

\[ \Delta H_2 = \Delta H_1 + \Delta C_p \cdot (T_2 - T_1) \]

Substituting the values:

\[ \Delta H_2 = -14.2 \, \text{kcal} + 0.2 \, \text{kcal/°C} \cdot (100 \, \text{K} - 10 \, \text{K}) \]

### Step 3: Calculate the temperature difference
Calculate \(T_2 - T_1\):

\[ T_2 - T_1 = 100 \, \text{K} - 10 \, \text{K} = 90 \, \text{K} \]

### Step 4: Calculate the change in enthalpy
Now substitute this back into the equation:

\[ \Delta H_2 = -14.2 \, \text{kcal} + 0.2 \, \text{kcal/°C} \cdot 90 \, \text{K} \]

Calculating the second term:

\[ 0.2 \, \text{kcal/°C} \cdot 90 \, \text{K} = 18 \, \text{kcal} \]

Now substitute this value into the equation:

\[ \Delta H_2 = -14.2 \, \text{kcal} + 18 \, \text{kcal} \]

### Step 5: Final calculation
\[ \Delta H_2 = 3.8 \, \text{kcal} \]

Thus, the enthalpy of reaction at 100 K is **3.8 kcal**.

### Summary
The enthalpy of reaction at 100 K is **3.8 kcal**.