Respuesta :
Answer is: the temperature of the reaction is 546°C.
k₁ = 1,1·10⁻⁴ 1/s.
T₁ = 470 °C = 743,15 K.
Ea = 264 kJ/mol = 264000 J/mol.
k₂ = 4,36·10⁻³ 1/s.
R = 8,314 J/K·mol.
T₂ = ?
Natural logarithm of Arrhenius' equation:
lnk₁ = lnA - Ea/RT₁.
lnk₂ = lnA - Ea/RT₂.
ln(k₂/k₁) = (Ea/R) · (1/T₁ - 1/T₂).
ln( 4,36·10⁻³ 1/s / 1,1·10⁻⁴ 1/s) = (264000J/mol ÷ 8,314 J/K·mol) · ·(1/743,15K - 1/T₂).
3,68 = 31753,66 K · (0,00134 1/K - 1/T₂).
3,68 = 42,728 - 31753,66 · (1/T₂).
1/T₂ = 0,00122.
T₂ = 819 K = 546 °C.
k₁ = 1,1·10⁻⁴ 1/s.
T₁ = 470 °C = 743,15 K.
Ea = 264 kJ/mol = 264000 J/mol.
k₂ = 4,36·10⁻³ 1/s.
R = 8,314 J/K·mol.
T₂ = ?
Natural logarithm of Arrhenius' equation:
lnk₁ = lnA - Ea/RT₁.
lnk₂ = lnA - Ea/RT₂.
ln(k₂/k₁) = (Ea/R) · (1/T₁ - 1/T₂).
ln( 4,36·10⁻³ 1/s / 1,1·10⁻⁴ 1/s) = (264000J/mol ÷ 8,314 J/K·mol) · ·(1/743,15K - 1/T₂).
3,68 = 31753,66 K · (0,00134 1/K - 1/T₂).
3,68 = 42,728 - 31753,66 · (1/T₂).
1/T₂ = 0,00122.
T₂ = 819 K = 546 °C.
The temperature of the reaction when rate constant is [tex]4.36 \times {10^{ - 3}}{\text{ }}{{\text{s}}^{ - 1}}[/tex] comes out to be [tex]\boxed{540{\text{ }}^\circ {\text{C}}}[/tex].
Further Explanation:
Chemical kinetics:
The branch of chemistry that deals with rates of chemical reactions is called chemicalkinetics. This study includes speed of reactions, reaction mechanism, transition states, and characteristics of chemical reaction.
Arrhenius equation:
This equation describes quantitative relationship between rate constant, activation energy and temperatures. This is used for comparison of two rate constants at two different temperatures. Mathematical expression for Arrhenius equation is mentioned below.
[tex]\log \dfrac{{{k_2}}}{{{k_1}}} = \dfrac{{{{\text{E}}_{\text{a}}}}}{{2.303{\text{ R}}}}\left( {\dfrac{1}{{{T_1}}} - \dfrac{1}{{{T_2}}}} \right)[/tex] …… (1)
Here,
[tex]{k_2}[/tex] is rate constant at temperature [tex]{T_2}[/tex] .
[tex]{k_1}[/tex] is rate constant temperature [tex]{T_1}[/tex].
[tex]{{\text{E}}_{\text{a}}}[/tex] is activation energy.
[tex]{T_2}[/tex] isfinal temperature.
[tex]{T_1}[/tex] isinitial temperature.
R is universal gas constant.
The activation energy is to be converted from kilojoule to joule. The conversion factor for this is,
[tex]1{\text{ kJ}} = {10^3}{\text{ J}}[/tex]
Therefore activation energy can be calculated as follows:
[tex]\begin{aligned}{{\text{E}}_{\text{a}}} &= \left( {264{\text{ kJ/mol}}} \right)\left( {\frac{{{{10}^3}{\text{ J}}}}{{1{\text{ kJ}}}}} \right) \\&= 264000{\text{ J/mol}}\\\end{aligned}[/tex]
The temperature is to be converted into Kelvin. The conversion factor for this is,
[tex]0{\text{ }}^\circ {\text{C}} = 273.15{\text{ K}}[/tex]
Therefore temperature can be calculated as follows:
[tex]\begin{aligned}{T_1} &= \left( {470 + 273.14} \right){\text{ K}} \\&= {\text{743}}{\text{.15 K}} \\\end{aligned}[/tex]
The value of [tex]{k_2}[/tex] is [tex]4.36 \times {10^{ - 3}}{\text{ }}{{\text{s}}^{ - 1}}[/tex] .
The value of [tex]{k_1}[/tex] is [tex]1.1 \times {10^{ - 4}}{\text{ }}{{\text{s}}^{ - 1}}[/tex].
The value of [tex]{{\text{E}}_{\text{a}}}[/tex] is 264000 J/mol.
The value of R is 8314 J/K.mol.
The value of [tex]{T_1}[/tex] is 743.15 K.
Substitute these values in equation (1).
[tex]\text{log}\left(\dfrac{4.36\times10^{-3}\text{s}^{-1}}{1.1\times10^{-4}\text{s}^{-1}}\right)=\dfrac{264000\:\text{J/mol}}{2.303(8.314\:\text{J/K mol})}\left(\dfrac{1}{743.15\:\text{K}}-\dfrac{1}{T_2}\right)[/tex]
Solving for [tex]{T_2}[/tex],
[tex]{T_2} = {\text{813 K}}[/tex]
This temperature is to be converted into degrees Celsius. Therefore [tex]{T_2}[/tex] can be calculated as follows:
[tex]\begin{aligned}{T_2} &= \left( {813 - 273.15} \right){\text{ }}^\circ {\text{C}} \\&= {\text{540 }}^\circ {\text{C}} \\\end{aligned}[/tex]
Learn more:
- Rate of chemical reaction: https://brainly.com/question/1569924
- The main purpose of conducting experiments: https://brainly.com/question/5096428
Answer Details:
Grade: Senior School
Subject: Chemistry
Chapter: Chemical Kinetics
Keywords: k2, k1, T1, T2, Ea, R, joule, kilojoule, 540 degrees Celsius, Kelvin, 813 K, 273.15 K, 264000 J/mol, 8.314 J/K.mol.
