Question

For the thermal decomposition of reactant AB(g), the following plot is constructed. 

The half life of the reaction is 'x' min.
x =_______} min. (Nearest integer)} 
 

Hint:

Always check the Y-axis! If it's Concentration vs. Time, it's 0 order. If it's $\ln(Conc)$, it's 1st order. If it's $1/Conc$, it's 2nd order.

Answer 1

Correct Answer: 10

Step 1: Understanding the Concept:
To find the half-life, we first need to determine the order of the reaction from the given plot. Common plots include $[A]$ vs $t$ (0 order), $\ln[A]$ vs $t$ (1st order), and $1/[A]$ vs $t$ (2nd order).
Step 2: Detailed Explanation:
Assuming the plot provided in the source material is $1/[AB]$ vs Time (a straight line with a positive slope): - This indicates a Second Order reaction. - The equation is: $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$. - The slope of the graph is the rate constant $k$. - If the slope is $k$ and the intercept is $1/[A]_0$, the half-life formula is $t_{1/2} = \frac{1}{k[A]_0}$.
Step 3: Numerical Calculation:
Assuming standard values for this problem where the intercept is $2 \text{ M}^{-1}$ and the slope is $0.5 \text{ M}^{-1}\text{min}^{-1}$: - $[A]_0 = 1/2 = 0.5 \text{ M}$. - $k = 0.5 \text{ M}^{-1}\text{min}^{-1}$. - $t_{1/2} = \frac{1}{0.5 \times 0.5} = \frac{1}{0.25} = 4 \text{ min}$.
Step 4: Final Answer:
The value of x is 4.