`DeltaC_(p)` for the change, `N_(2)(g) + 3H_(2)(g) = 2NH_(3)(g)` is

Options

A. `C C_(pNH_(3)) - C_(pN_(2))`
B. `2C_(pNH_(3)) -(C_(pH_(2))+3C_(pH_(3)))`
C. `C_(pNH_(3))-C_(pH_(2))`
D. `2C_(pNH_(3))-(C_(pH_(2)) + 3C_(pH_(2)))`

Answer

To find the change in heat capacity (\(\Delta C_p\)) for the reaction:

\[ N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \]

we can follow these steps:

### Step 1: Identify the Reaction
The reaction given is the synthesis of ammonia from nitrogen and hydrogen gases.

### Step 2: Write the Expression for \(\Delta C_p\)
The change in heat capacity at constant pressure (\(\Delta C_p\)) for a reaction can be calculated using the formula:

\[ \Delta C_p = \sum (C_{p,\text{products}}) - \sum (C_{p,\text{reactants}}) \]

### Step 3: Identify the Products and Reactants
In our reaction:
- **Products**: 2 moles of \(NH_3\)
- **Reactants**: 1 mole of \(N_2\) and 3 moles of \(H_2\)

### Step 4: Write the \(\Delta C_p\) Expression
Using the formula from Step 2, we can express \(\Delta C_p\) as follows:

\[ \Delta C_p = [2 \cdot C_{p}(NH_3)] - [1 \cdot C_{p}(N_2) + 3 \cdot C_{p}(H_2)] \]

### Step 5: Simplify the Expression
Now, we can simplify the expression:

\[ \Delta C_p = 2C_{p}(NH_3) - C_{p}(N_2) - 3C_{p}(H_2) \]

### Final Expression
Thus, the final expression for \(\Delta C_p\) for the given reaction is:

\[ \Delta C_p = 2C_{p}(NH_3) - C_{p}(N_2) - 3C_{p}(H_2) \]