Question

Consider the reaction ALaTeX: \longrightarrow ⟶ Products. The rate law for this reaction is rate = k[A]2 where k=2.90 LaTeX: \times × 10-2 M-1s-1 at a particular temperature. If the initial [A] = 0.0500 M, what is the value of the half-life?
478 s
34.5 s
690. s
23.9 s

Answer 1

Answer: 690 s

Explanation: Rate law says that rate of a reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.

For a reaction: $A\rightarrow Products$

$Rate=k[A]^2$

k= rate constant=$2.90\times 10^{-2}$

x = 2= order with respect to A

For a second order reaction, $t_\frac{1}{2}=\frac{1}{k\times [A_0]}$

$t_{\frac{1}{2}$= half life = time taken for a reaction to complete to half.  

$[A_0]$=initial concentration= 0.0500 M

Thus $t_{\frac{1}{2}=\frac{1}{2.90\times 10^{-2}\times [0.0500]}=690s$