Ammonia under a pressure of `15 atm`, at `27^(@)C` is heated to `327^(@)C` in a vessel in the presence of catalyst. Under these conditions, `NH_(3)` partially decomposes to `H_(2)` and `N_(2)`. The vessel is such that the volume remains effectively constant, whereas the pressure increases to `50 atm`. Calculate the precentage of `NH_(3)` actually decomposed.

Explanation

To solve the problem of calculating the percentage of ammonia (NH₃) that has decomposed under the given conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Decomposition Reaction:**
The decomposition of ammonia can be represented as:
\[
2 \text{NH}_3 \rightarrow \text{N}_2 + 3 \text{H}_2
...