Import Question JSON

$\text{Hint: The rate of the reaction is}$ $-\frac{1}{2} \frac{d[\text{A}]}{dt} = -\frac{d[\text{B}]}{dt} = \frac{d[\text{C}]}{dt}$ $\text{Explanation:}$ $\text{Step 1: First, calculate the value of rate constant as follows:}$ $\text{rate} = k[\text{A}][\text{B}]$ $\text{mol L}^{-1}\text{s}^{-1} = k (\text{mol L}^{-1})(\text{mol L}^{-1})$ $k = \text{mol}^{-1}\text{L s}^{-1}$ $\text{Hence, the first statement is wrong.}$ $\text{Step 2:}$ $\text{The given reaction is an example of second-order and the } t_{1/2} \text{ formula for second order is as follows:}$ $t_{1/2} = \frac{1}{k[A_0]}$ $\text{Hence, } t \text{ is not a constant because it depends on the initial concentration of the reactant. Hence, statement two is also incorrect.}$ $\text{Step 3:}$ $\text{The rate of the reaction is as follows:}$ $-\frac{1}{2} \frac{d[\text{A}]}{dt} = -\frac{d[\text{B}]}{dt} = \frac{d[\text{C}]}{dt}$ $\text{From the rate of the reaction, it is clear that the rate of formation of C is half of the rate of disappearance of A.}$ $\text{Step 4:}$ $\text{The rate constant of a reaction depends on temperature and is not affected by the concentration of the reactant. Hence, option four is correct.}$ $\text{Thus, option 4 is the correct answer.}$