Question

For the first order reaction given below select the set having correct statements
$2N_2{O}_5\to 4N{O}_2\left(g\right)+O_2\left(g\right)$

• A. The concentration of the reactant decreases exponentially with time
• B. The reaction proceeds to $99.6$% completion in eight half-life duration
• C. The half-life of the reaction depends on the initial concentration of the reactant
• D. The half-life of the reaction decreases with increasing temperature

Answer 1

Answer: (A), (B), (D)

The half-life of the reaction decreases with increasing temperature

The concentration of reactant which is following first order kinetics always decreases exponentially and becomes zero at infinity.
As the temperature increases, the rate constant increases and the half-life decreases since half-life is inversely dependent on rate constant.
$C_t=C\cdot e^{-kt}{t}_{\frac{1}{2}}\propto \frac{1}{K},$
K increase on increasing T.
After eight half-live.
$C=\frac{C_0}{2^8}\text{\% completion}=\frac{C_0-\frac{C_0}{2^8}}{C_0}\times 100=99.6$