Answer:
134.8 seconds is the half-life (in seconds) of the reaction for the initial [tex]C_2F_4[/tex] concentration
Explanation:
Half life for second order kinetics is given by:
[tex]t_{\frac{1}{2}=\frac{1}{k\times a_0}[/tex]
Integrated rate law for second order kinetics is given by:
[tex]\frac{1}{a}=kt+\frac{1}{a_0}[/tex]
[tex]t_{\frac{1}{2}[/tex] = half life
k = rate constant
[tex]a_0[/tex] = initial concentration
a = Final concentration of reactant after time t
We have :
[tex]C_2F_4 \longrightarrow \frac{1}{2} C_4F_8[/tex]
Initial concentration of [tex]C_2F_4=[a_o]=\frac{0.438 mol}{2.42 L}=0.1810 mol/L[/tex]
Rate constant = k = [tex]0.041 M^{-1} s^{-1}[/tex]
[tex]t_{\frac{1}{2}=\frac{1}{k\times a_0}[/tex]
[tex]=\frac{1}{0.041 M^{-1} s^{-1}\times 0.1810 mol/L}[/tex]
[tex]t_{1/2}=134.8 s[/tex]
134.8 seconds is the half-life (in seconds) of the reaction for the initial [tex]C_2F_4[/tex] concentration
The second-order rate constant for the following gas-phase reaction
C₂F₄ ⇒ 1/2 C₄F₈
is 0.0411 M⁻¹.s⁻¹. We start with 0.438 mol C₂F₄ in a 2.42-liter container, with no C₄F₈ initially present. What is the half-life (in seconds) of the reaction for the initial C₂F₄ concentration? Enter to 1 decimal place.
The reaction C₂F₄ ⇒ 1/2 C₄F₈, with a second-order rate constant of 0.0411 M⁻¹.s⁻¹, that starts with 0.438 mol C₂F₄ in a 2.42-liter container, has a half-life of 134.4 s.
Let's consider the following reaction following second-order kinetics.
C₂F₄ ⇒ 1/2 C₄F₈
Initially, we have 0.438 mol C₂F₄ in a 2.42-liter container. The initial concentration of C₂F₄ is:
[tex][C_2F_4]_0 = \frac{0.438 mol}{2.42 L} = 0.181 M[/tex]
Given the rate constant (k) is 0.041 M⁻¹.s⁻¹, we can calculate the half-life of a second-order reaction using the following expression.
[tex]t_{1/2}= \frac{1}{k \times [C_2F_4]_0} = \frac{1}{0.0411 M^{-1}s^{-1} \times 0.181 M} = 134.4 s[/tex]
The reaction C₂F₄ ⇒ 1/2 C₄F₈, with a second-order rate constant of 0.0411 M⁻¹.s⁻¹, that starts with 0.438 mol C₂F₄ in a 2.42-liter container, has a half-life of 134.4 s.
You can learn more about kinetics here: https://brainly.com/question/3334857
