Answer
397.2k+ views
Hint: Rate is defined as the speed at which a chemical reaction occurs. Rate is generally expressed in the terms of concentration of reactant which is consumed during the reaction in a unit of time or the concentration of product which is produced during the reaction in a unit of time.
Complete answer:
Given in the question:
The reaction involved in the first order decomposition of ethyl iodide:
\[{{C}_{2}}{{H}_{5}}I(g)\to {{C}_{2}}{{H}_{4}}(g)+HI(g)\]
The first order rate constant for the reaction is = $(1.60)({{10}^{-5}}){{S}^{-1}}$
Temperature given ${{T}_{1}}$= 600 K
${{T}_{2}}$= 700 K
The activation energy given: 209 KJ/mol
\[\log \dfrac{{{k}_{2}}}{{{k}_{1}}}=\dfrac{{{E}_{a}}}{2.303R}(\dfrac{1}{{{T}_{1}}}-\dfrac{1}{{{T}_{2}}})\]
\[\log \dfrac{{{k}_{2}}}{(1.6)({{10}^{-5}})}=\dfrac{209000}{(2.303)(8.314)}(\dfrac{1}{600}-\dfrac{1}{700})\]
The value of ${{k}_{2}}=(6.39)({{10}^{-3}}){{S}^{-1}}$
The rate constant of the reaction at 700K is ${{k}_{2}}=(6.39)({{10}^{-3}}){{S}^{-1}}$
Hence the correct answer is option (D).
Additional information:
Activation energy can be calculated using various methods. It can be calculated using the Arrhenius equation and also when then two temperatures and the rate constant at both temperatures are known. The temperature should be converted to kelvin while calculating activation energy using the Arrhenius equation.
Note:
If the reaction is a third order reaction, the unit for third order reaction is ${{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$. The negative and positive sign in the expression of the rate or reaction only means the change in concentration. A negative charge indicates that the concentration of the reactant is decreasing, similarly a positive charge means that the concentration of product is increasing.
Complete answer:
Given in the question:
The reaction involved in the first order decomposition of ethyl iodide:
\[{{C}_{2}}{{H}_{5}}I(g)\to {{C}_{2}}{{H}_{4}}(g)+HI(g)\]
The first order rate constant for the reaction is = $(1.60)({{10}^{-5}}){{S}^{-1}}$
Temperature given ${{T}_{1}}$= 600 K
${{T}_{2}}$= 700 K
The activation energy given: 209 KJ/mol
\[\log \dfrac{{{k}_{2}}}{{{k}_{1}}}=\dfrac{{{E}_{a}}}{2.303R}(\dfrac{1}{{{T}_{1}}}-\dfrac{1}{{{T}_{2}}})\]
\[\log \dfrac{{{k}_{2}}}{(1.6)({{10}^{-5}})}=\dfrac{209000}{(2.303)(8.314)}(\dfrac{1}{600}-\dfrac{1}{700})\]
The value of ${{k}_{2}}=(6.39)({{10}^{-3}}){{S}^{-1}}$
The rate constant of the reaction at 700K is ${{k}_{2}}=(6.39)({{10}^{-3}}){{S}^{-1}}$
Hence the correct answer is option (D).
Additional information:
Activation energy can be calculated using various methods. It can be calculated using the Arrhenius equation and also when then two temperatures and the rate constant at both temperatures are known. The temperature should be converted to kelvin while calculating activation energy using the Arrhenius equation.
Note:
If the reaction is a third order reaction, the unit for third order reaction is ${{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$. The negative and positive sign in the expression of the rate or reaction only means the change in concentration. A negative charge indicates that the concentration of the reactant is decreasing, similarly a positive charge means that the concentration of product is increasing.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)