Question

For given zero order reaction AB $\longrightarrow$ A$_2$ + B$_2$, the graph is given for decomposition of [AB]. Find half-life (t$_{1/2}$) in minutes?

Hint:

For zero-order reactions, the half-life depends on the initial concentration of the reactant and the rate constant.

Answer 1

Correct Answer: 10

Step 1: Understand the zero order reaction.
For zero order reactions, the rate law is: \[ [AB] = k t \]

Step 2: Calculate the rate constant (k).
From the graph, \[ [AB] \] decreases from 0.60 M to 0.55 M in 100 seconds. So, the rate constant is:
\[ k = \frac{0.60 - 0.55}{100} = 5 \times 10^{-4} \, \text{M/s} \]

Step 3: Find the half-life using the zero order equation.
For a zero-order reaction, the half-life is given by: \[ t_{1/2} = \frac{[AB]_0}{2k} \]

Step 4: Substitute the values.
\[ t_{1/2} = \frac{0.60}{2 \times 5 \times 10^{-4}} = 600 \, \text{seconds} = 10 \, \text{minutes} \]

Step 5: Conclusion.
The half-life of the reaction is 10 minutes.