Question

The second-order rate constant for the following gas-phase reaction is 0.041 1/MLaTeX: \cdotâs. We start with 0.438 mol C2F4 in a 2.42 liter container, with no C4F8 initially present. C2F4 LaTeX: \longrightarrowⶠ1/2 C4F8 What is the half-life (in seconds) of the reaction for the initial C2F4 concentration? Enter to 1 decimal place.

Answer 1

Answer:

134.8 seconds is the half-life (in seconds) of the reaction for the initial $C_2F_4$ concentration

Explanation:

Half life for second order kinetics is given by:

$t_{\frac{1}{2}=\frac{1}{k\times a_0}$

Integrated rate law for second order kinetics is given by:

$\frac{1}{a}=kt+\frac{1}{a_0}$

$t_{\frac{1}{2}$ = half life

k = rate constant

$a_0$ = initial concentration

a = Final concentration of reactant after time t

We have :

$C_2F_4 \longrightarrow \frac{1}{2} C_4F_8$

Initial concentration of $C_2F_4=[a_o]=\frac{0.438 mol}{2.42 L}=0.1810 mol/L$

Rate constant = k = $0.041 M^{-1} s^{-1}$

$t_{\frac{1}{2}=\frac{1}{k\times a_0}$

$=\frac{1}{0.041 M^{-1} s^{-1}\times 0.1810 mol/L}$

$t_{1/2}=134.8 s$

134.8 seconds is the half-life (in seconds) of the reaction for the initial $C_2F_4$ concentration