Question

The half-life periods of decomposition of $\mathrm{NH_3}$ for different initial pressures are given below :

The order of the reaction is :

• A. zero order
• B. first order
• C. 0·5
• D. second order

Hint:

Half-life stays the same as pressure changes → that only happens for first order.

Answer 1

The Correct Option is B

Concept: The clue here is to watch how the half-life behaves when we change the starting pressure. Each order of reaction has its own pattern, so the pattern tells us the order.

Step 1: Read the table
In the table the starting pressure of $\mathrm{NH_3}$ changes a lot, going from a high value down to a much smaller one. But the half-life listed against each pressure stays the same value every time. So the half-life does not depend on how much gas we start with.

Step 2: Match the pattern to an order
A half-life that does not depend on the starting amount is the special mark of a first-order reaction. For first order: \[ t_{1/2} = \frac{0.693}{k} \] which depends only on the rate constant $k$ and not at all on the starting pressure.

Step 3: Conclude
Since the half-life stays constant as the pressure changes, the reaction must be first order.

Answer: Option (B), first order.