Answer
427.5k+ views
Hint:A first-order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration.The square brackets in the formula are used to express molar concentrations.
Complete step by step answer:
Order of reaction: ${1^{st}}$;
${t_{1/2}} = 24\,\min $; ${t_{1/2}}$ is known as half-life of the reaction. It is the time in which the concentration of a reactant is reduced to one half of its initial concentration.
For \[{1^{st}}\]order reaction - ${t_{1/2}} = \dfrac{{0.693}}{k}$. Initial pressure of $A = 400\,mm\,Hg.$
Final pressure after $48\,\min $ is to be calculated.
Formula used= $[A] = [{A_0}]{e^{ - kt}}$;
Where , $[A]$= Final pressure
$[{A_0}]$= Initial pressure
$k = $Rate constant;
$t = $time
In \[{1^{st}}\]order reaction - ${t_{1/2}} = \dfrac{{o.693}}{k}$
$k = \dfrac{{0.693}}{{{t_{1/2}}}}\,$
$A(g)\xrightarrow{{}}2B(g) + C(s)$
$[{A_0}]$ $0$ $0$
$[{A_0}]$$ - a$ $2$$a$ $a$
Initial pressure= $[{A_0}]$=$400\,mm\,Hg.$;
Final pressure=$[{A_0}] - a + 2a = [{A_0}]\, + a$;
Put the values in equation:
$
([{A_0}] + a) = [{A_0}]{e^{ - kt}}\, \\
(400 + a) = 400{e^{ - \dfrac{{0.693}}{{24}}*48}}\, \\
$
calculated $k = \dfrac{{0.693}}{{{t_{1/2}}}}\,$$ \Rightarrow k = \dfrac{{0.693}}{{24}}\,$
$a = 300$;
The final pressure of the reaction mixture after the expiry of $48\,\min $ will be:
$[{A_0}] + a$
Put the value of $[{A_0}]$ and $a$ in the above equation; we get
$700\,mm\,of\,Hg$ because $[{A_0}] = 400$ and $a = 300$;
Note:Rate constant is the proportionality factor in the rate law. It can be determined from rate law or its integrated rate equation. It is unique for each reaction.
Complete step by step answer:
Order of reaction: ${1^{st}}$;
${t_{1/2}} = 24\,\min $; ${t_{1/2}}$ is known as half-life of the reaction. It is the time in which the concentration of a reactant is reduced to one half of its initial concentration.
For \[{1^{st}}\]order reaction - ${t_{1/2}} = \dfrac{{0.693}}{k}$. Initial pressure of $A = 400\,mm\,Hg.$
Final pressure after $48\,\min $ is to be calculated.
Formula used= $[A] = [{A_0}]{e^{ - kt}}$;
Where , $[A]$= Final pressure
$[{A_0}]$= Initial pressure
$k = $Rate constant;
$t = $time
In \[{1^{st}}\]order reaction - ${t_{1/2}} = \dfrac{{o.693}}{k}$
$k = \dfrac{{0.693}}{{{t_{1/2}}}}\,$
$A(g)\xrightarrow{{}}2B(g) + C(s)$
$[{A_0}]$ $0$ $0$
$[{A_0}]$$ - a$ $2$$a$ $a$
Initial pressure= $[{A_0}]$=$400\,mm\,Hg.$;
Final pressure=$[{A_0}] - a + 2a = [{A_0}]\, + a$;
Put the values in equation:
$
([{A_0}] + a) = [{A_0}]{e^{ - kt}}\, \\
(400 + a) = 400{e^{ - \dfrac{{0.693}}{{24}}*48}}\, \\
$
calculated $k = \dfrac{{0.693}}{{{t_{1/2}}}}\,$$ \Rightarrow k = \dfrac{{0.693}}{{24}}\,$
$a = 300$;
The final pressure of the reaction mixture after the expiry of $48\,\min $ will be:
$[{A_0}] + a$
Put the value of $[{A_0}]$ and $a$ in the above equation; we get
$700\,mm\,of\,Hg$ because $[{A_0}] = 400$ and $a = 300$;
Note:Rate constant is the proportionality factor in the rate law. It can be determined from rate law or its integrated rate equation. It is unique for each reaction.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![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)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english 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)
How do you graph the function fx 4x class 9 maths 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)