cx-chem-day-24-chemical-kienetics

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Topics to be covered </B></Primary>

<hr>

<main>

1. Algorithm to find integrated rate law
2. Zero Order Reaction
3. Integrated rate law derivation
4. Alternative to find integrated rate law
5. Zero order graph
6. Example of Zero order reaction
7. First order reaction
8. Derivation of integrated first rate law
9. Alternative to find integrated rate law
10. First order graph
11. Gas phase first order reaction
12. Examples of first order reaction

</div>

1. एकीकृत दर कानून खोजने के लिए एल्गोरिदम
2. शून्य आदेश प्रतिक्रिया
3. एकीकृत दर कानून व्युत्पत्ति
4. एकीकृत दर कानून खोजने का विकल्प
5. शून्य क्रम ग्राफ
6. शून्य कोटि अभिक्रिया का उदाहरण
7. प्रथम कोटि की प्रतिक्रिया
8. एकीकृत प्रथम श्रेणी कानून की व्युत्पत्ति
9. एकीकृत दर कानून खोजने का विकल्प
10. प्रथम क्रम ग्राफ
11. गैस चरण प्रथम क्रम प्रतिक्रिया
12. प्रथम कोटि अभिक्रिया के उदाहरण

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Algorithm to find integrated rate law </B></Primary>

<hr>

<main>

- Write the differential form of rate law.
- Rearrange the equation such that the one with the same coeffecient are on the same side.
- Integrate both sides.
- Put the proper limits to get the final equation.

</div>

- दर कानून का विभाजनी रूप लिखें।
- समीकरण को पुन: व्यवस्थित करें ताकि वही सहसंख्यक वाले एक ही ओर हों।
- दोनों ओरों का समाकलन करें।
- अंतिम समीकरण प्राप्त करने के लिए उचित सीमाएं लगाएं।

</div>

</main>

<hr>

<footer style="font-size:16px"> <span style="color:blue">Algorithm to find integrated rate law</span> $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Zero Order Reaction </B></Primary>

<hr>

<main>

- Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants.
- Consider the reaction,

<p>
$$\small{
\begin{aligned}
& R \to P \\\
& \text{ Rate }=-\frac{d[R]}{d t}=k[R]^0
\end{aligned}
}$$
</p>

</div>

- शून्य क्रम की प्रतिक्रिया का अर्थ है कि प्रतिक्रिया की दर प्रतिक्रियाशीलों के संघटक की शून्य शक्ति के अनुपात में होती है।
- प्रतिक्रिया पर विचार करें,

<p>
$$\small{
\begin{aligned}
& R \to P \\\
& \text{ दर }=-\frac{d[R]}{d t}=k[R]^0
\end{aligned}
}$$
</p>

</div>

![Zero_order_rate_vs_time](/subject-images/chemistry/Zero_order_rate_vs_time.png)

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ <span style="color:blue">Zero Order Reaction</span> $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Integrated rate law derivation(I/II) </B></Primary>

<hr>

<main>

For a Zero order reaction:

$$\small{
\text{ Rate }=-\frac{d[R]}{d t}=k[R]^0
}$$

As any quantity raised to power zero is unity

<p>
$$\small{
\begin{aligned}
& \text{ Rate }=-\frac{d[R]}{d t}=k \times 1 \\\
& d[R]=-k d t
\end{aligned}
}$$
</p>

</div>

शून्य क्रम की प्रतिक्रिया के लिए:

$$\small{
\text{ दर }=-\frac{d[R]}{d t}=k[R]^0
}$$

जैसा कि किसी भी मात्रा को शून्य की शक्ति देने से एकता होती है

<p>
$$\small{
\begin{aligned}
& \text{ दर }=-\frac{d[R]}{d t}=k \times 1 \\\
& d[R]=-k d t
\end{aligned}
}$$
</p>

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ <span style="color:blue">Integrated rate law derivation</span> $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Integrated rate law derivation(I/II) </B></Primary>

<hr>

<main>

As any quantity raised to power zero is unity

<p>
$$\small{
\begin{aligned}
& \text{ Rate }=-\frac{d[R]}{d t}=k \times 1 \\\
& d[R]=-k d t
\end{aligned}
}$$
</p>

</div>

जैसा कि किसी भी मात्रा को शून्य की शक्ति देने से एकता होती है

<p>
$$\small{
\begin{aligned}
& \text{ दर }=-\frac{d[R]}{d t}=k \times 1 \\\
& d[R]=-k d t
\end{aligned}
}$$
</p>

</div>

</main>

<hr>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Integrated rate law derivation(II/II) </B></Primary>

<hr>

<main>

Integrating both sides

$\small{[R]=-k t+I}$

where, I is the constant of integration.

At $\small{t=0}$, the concentration of the reactant $\small{R=[R]_0}$, where $\small{[R]_0}$ is initial concentration of the reactant.

Substituting in equation

<p>
$$\small{
\begin{aligned}
& {[R]_0=-k \times 0+I} \\\
& {[R]_0=I}
\end{aligned}
}$$
</p>

</div>

दोनों ओरों का समाकलन करते हैं

$\small{[R]=-k t+I}$

जहाँ, I समाकलन का स्थिरांक है।

$\small{t=0}$ पर, प्रतिक्रियाशील का संचय $\small{R=[R]_0}$ होता है, जहाँ $\small{[R]_0}$ प्रतिक्रियाशील का प्रारंभिक संचय है।

समीकरण में प्रतिस्थापन करते हैं

<p>
$$\small{
\begin{aligned}
& {[R]_0=-k \times 0+I} \\\
& {[R]_0=I}
\end{aligned}
}$$
</p>

</div>

</main>

<hr>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Integrated rate law derivation(II/II) </B></Primary>

<hr>

<main>

Substituting the value of I in the equation

<p>
$$\small{
[R]=-k t+[R]_0
}$$
</p>

</div>

समीकरण में I का मान प्रतिस्थापित करते हैं

<p>
$$\small{
[R]=-k t+[R]_0
}$$
</p>

</div>

</main>

<hr>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Alternative to find integrated rate law </B></Primary>

<hr>

<main>

$$\small{\begin{aligned} & \int _{[A]_0}^{[A]_t} d[A]=\int _{t=0}^{t=1} k d t \\\ & ⇒ \int _{|A|_0}^{[A]_t} d[A]=k \int_0^t d t \\\ & ⇒ [A] _{[A]_0.}^{[A]_t}=k[t]_0^t \\\ & ⇒ ([A]_t-[A]_0)=k t \\\ & \therefore[A]_0- [A]_t=k t \\\ & \therefore k=\frac{[A]_0- [A]_t}{t} \\\ & \end{aligned}}$$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ <span style="color:blue">Alternative to find integrated rate law</span> $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Zero order graph </B></Primary>

<hr>

<main>

Zero order Integerated rate equation

<p>
$$\small{
[R]=-k t+[R]_0
}$$
</p>

Comparing it with the equation of straight line:

$\small{y = mx + c}$

we get,

$$\small{slope = -k}$$

$$\small{\text{x-axis} = t}$$

$$\small{\text{y-axis} = \text{concentration at time t}}$$

</div>

शून्य क्रम एकीकृत दर समीकरण

<p>
$$\small{
[R]=-k t+[R]_0
}$$
</p>

इसे सीधी रेखा की समीकरण के साथ तुलना करते हैं:

$\small{y = mx + c}$

हमें मिलता है,

$$\small{ढलान = -k}$$

$$\small{\text{x-अक्ष} = t}$$

$$\small{\text{y-अक्ष} = \text{समय t पर संचय}}$$

</div>

![शून्य क्रम प्रतिक्रिया ग्राफ](https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/1abe7eaa-abad-4268-ead2-112f36d49f00/public)

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ <span style="color:blue">Zero order graph</span> $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Example of Zero order reaction </B></Primary>

<hr>

<main>

- Zero order reactions are relatively uncommon but they occur under special conditions. 
- Some enzyme catalysed reactions and reactions which occur on metal surfaces are a few examples of zero order reactions. 
- The decomposition of gaseous ammonia on a hot platinum surface is a zero order reaction at high pressure

$$\small{
2 NH_3(g) \xrightarrow[\text{ Pt catalyst }]{1130 K} N_2(g)+3 H_2(g)
}$$

$$\small{
\text{ Rate }=k[NH_3]^0=k
}$$

</div>

- शून्य क्रम की प्रतिक्रियाएं अपेक्षाकृत असामान्य होती हैं लेकिन वे विशेष स्थितियों में होती हैं। 
- कुछ एनजाइम ड्राइवन प्रतिक्रियाएं और धातु की सतह पर होने वाली प्रतिक्रियाएं शून्य क्रम की प्रतिक्रियाओं के कुछ उदाहरण हैं। 
- गैसीय अमोनिया का विघटन एक गर्म प्लैटिनम सतह पर उच्च दबाव में शून्य क्रम की प्रतिक्रिया है

$$\small{
2 NH_3(g) \xrightarrow[\text{ Pt catalyst }]{1130 K} N_2(g)+3 H_2(g)
}$$

$$\small{
\text{ Rate }=k[NH_3]^0=k
}$$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ <span style="color:blue">Example of Zero order reaction</span> $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Example of Zero order reaction </B></Primary>

<hr>

<main>

- In this reaction, platinum metal acts as a catalyst. 
- At high pressure, the metal surface gets saturated with gas molecules. 
- So, a further change in reaction conditions is unable to alter the amount of ammonia on the surface of the catalyst making rate of the reaction independent of its concentration. 
- The thermal decomposition of HI on gold surface is another example of zero order reaction.

</div>

- इस प्रतिक्रिया में, प्लैटिनम धातु एक कैटलिस्ट के रूप में कार्य करती है। 
- उच्च दबाव पर, धातु की सतह गैस के अणुओं से संतृप्त हो जाती है। 
- इसलिए, प्रतिक्रिया की स्थितियों में आगे की कोई भी परिवर्तन कैटलिस्ट की सतह पर अमोनिया की मात्रा को बदलने में सक्षम नहीं होता है जिससे प्रतिक्रिया की दर उसकी संघनन से स्वतंत्र हो जाती है। 
- HI का तापीय विघटन सोने की सतह पर शून्य क्रम की प्रतिक्रिया का एक और उदाहरण है।

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ <span style="color:blue">Example of Zero order reaction</span> $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> First order reaction </B></Primary>

<hr>

<main>

- The rate of the reaction is proportional to the first power of the concentration of the reactant R.
- Consider the reaction,

<p>
$$
\begin{aligned}
& R \to P \\\
& \text{ Rate }=-\frac{d[R]}{d t}=k[R] \\\
& \text{ or } \frac{d[R]}{[R]}=-k d t
\end{aligned}
$$
</p>

</div>

- प्रतिक्रिया की दर प्रतिक्रियाशील R की संघटन की पहली शक्ति के अनुपातिक होती है।
- प्रतिक्रिया पर विचार करें,

<p>
$$
\begin{aligned}
& R \to P \\\
& \text{ दर }=-\frac{d[R]}{d t}=k[R] \\\
& \text{ या } \frac{d[R]}{[R]}=-k d t
\end{aligned}
$$
</p>

</div>

![Rate_law_graph_first_order](/subject-images/chemistry/Rate_law_graph_first_order.png)

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ <span style="color:blue">First order reaction</span> $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Derivation of integrated first rate law(I/II) </B></Primary>

<hr>

<main>

Consider the reaction,

<p>
$$\small{
\begin{aligned}
& R \to P \\\
& \text{ Rate }=-\frac{d[R]}{d t}=k[R] \\\
& \text{ or } \frac{d[R]}{[R]}=-k d t
\end{aligned}
}$$
</p>

Integrating this equation, we get
$$\small{
\ln [R]=-k t+I
}$$

Again, I is the constant of integration and its value can be determined easily.

</div>

विचार करें, अभिक्रिया,

<p>
$$\small{
\begin{aligned}
& R \to P \\\
& \text{ दर }=-\frac{d[R]}{d t}=k[R] \\\
& \text{ या } \frac{d[R]}{[R]}=-k d t
\end{aligned}
}$$
</p>

इस समीकरण का समाकलन करते हैं, हमें मिलता है
$$\small{
\ln [R]=-k t+I
}$$

फिर से, I समाकलन का स्थिरांक है और इसका मान आसानी से निर्धारित किया जा सकता है।

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ <span style="color:blue">Derivation of integrated first rate law</span> $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Derivation of integrated first rate law(I/III) </B></Primary>

<hr>

<main>

When $\small{t=0, R=[R]_0}$, where $\small{[R]_0}$ is the initial concentration of the reactant.

<p>
$$\small{
\begin{aligned}
& \ln [R]_0=-k \times 0+I \\\
& \ln [R]_0=I
\end{aligned}
}$$
</p>

Substituting the value of I in equation 
$$\small{
\ln [R]=-k t+\ln [R]_0
}$$

</div>

जब $\small{t=0, R=[R]_0}$, जहाँ $\small{[R]_0}$ प्रतिक्रियाशील पदार्थ की प्रारंभिक संचयन है।

<p>
$$\small{
\begin{aligned}
& \ln [R]_0=-k \times 0+I \\\
& \ln [R]_0=I
\end{aligned}
}$$
</p>

समीकरण  में I का मान प्रतिस्थापित करना
$$\small{
\ln [R]=-k t+\ln [R]_0
}$$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ <span style="color:blue">Derivation of integrated first rate law</span> $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Derivation of integrated first rate law(I/III) </B></Primary>

<hr>

<main>

Rearranging this equation

<p>
$$
\begin{aligned}
& \ln \frac{[R]}{[R]_0}=-k t \\
& \text { or } k=\frac{1}{t} \ln \frac{[R]_0}{[R]}
\end{aligned}
$$
</p>

</div>

इस समीकरण को पुन: व्यवस्थित करना

<p>
$$\small{
\begin{aligned}
& \ln \frac{[R]}{[R]_0}=-k t \\\
& \text{ या } k=\frac{1}{t} \ln \frac{[R]_0}{[R]}
\end{aligned}
}$$
</p>

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ <span style="color:blue">Derivation of integrated first rate law</span> $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Derivation of integrated first rate law(II/III) </B></Primary>

<hr>

<main>

At time $t_1$ from equation

$$\small{
{ }^* \ln [R]_1=-k t_1+{ }^* \ln [R]_0
}$$

At time $\small{t_2}$

$$\small{
\ln [R]_2=-k t_2+\ln [R]_0
}$$

</div>

समय $t_1$ पर समीकरण से

$$\small{
{ }^* \ln [R]_1=-k t_1+{ }^* \ln [R]_0
}$$

समय $\small{t_2}$ पर

$$\small{
\ln [R]_2=-k t_2+\ln [R]_0
}$$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ <span style="color:blue">Derivation of integrated first rate law</span> $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Derivation of integrated first rate law(II/III) </B></Primary>

<hr>

<main>

where, $\small{[R]_1}$ and $\small{[R]_2}$ are the concentrations of the reactants at time $\small{t_1}$ and $t_2$ respectively.

<p>
$$\small{
\begin{aligned}
& \ln [R]_1-\ln [R]_2=-k t_1-(-k t_2) \\\
& \ln \frac{[R]_1}{[R]_2}=k(t_2-t_1) \\\
& k=\frac{1}{(t_2-t_1)} \ln \frac{[R]_1}{[R]_2}
\end{aligned}
}$$
</p>

$$\small{
\ln \frac{[R]}{[R]_0}=-k t
}$$

</div>

जहाँ, $\small{[R]_1}$ और $\small{[R]_2}$ समय $\small{t_1}$ और $t_2$ पर प्रतिक्रियात्मकों की संघटनाएं हैं।

<p>
$$\small{
\begin{aligned}
& \ln [R]_1-\ln [R]_2=-k t_1-(-k t_2) \\\
& \ln \frac{[R]_1}{[R]_2}=k(t_2-t_1) \\\
& k=\frac{1}{(t_2-t_1)} \ln \frac{[R]_1}{[R]_2}
\end{aligned}
}$$
</p>

$$\small{
\ln \frac{[R]}{[R]_0}=-k t
}$$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ <span style="color:blue">Derivation of integrated first rate law</span> $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Derivation of integrated first rate law(III/III) </B></Primary>

<hr>

<main>

Taking antilog of both sides
$$\small{
[R]=[R]_0 e^{-k t}
}$$

The first order rate equation can also be written in the form

<p>
$$\small{
\begin{aligned}
& k=\frac{2.303}{t} \log \frac{[R]_0}{[R]} \\\
& { }^* \log \frac{[R]_0}{[R]}=\frac{k t}{2.303}
\end{aligned}
}$$
</p>

</div>

दोनों पक्षों का एंटीलॉग लेते हैं
$$\small{
[R]=[R]_0 e^{-k t}
}$$

प्रथम क्रम दर समीकरण को भी इस रूप में लिखा जा सकता है

<p>
$$\small{
\begin{aligned}
& k=\frac{2.303}{t} \log \frac{[R]_0}{[R]} \\\
& { }^* \log \frac{[R]_0}{[R]}=\frac{k t}{2.303}
\end{aligned}
}$$
</p>

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ <span style="color:blue">Derivation of integrated first rate law</span> $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Alternative to find integrated rate law </B></Primary>

<hr>

<main>

<p>

$ \int _{A _0} ^{A} \frac {-d[A]} {[A]}  $

$=k \int _0 ^t d t \Rightarrow  - \ln [A] _ {A _0} ^{A} =k(t) _0^t $

$ \Rightarrow - \ln [A]+(In[A _0])$

$=k(t-0)  \Rightarrow In[A _0] - \ln [A]=kt  \ln (\frac{[A _0]}{[A]})=k t$
</p>

</div>

$ \int _{A _0} ^{A} \frac {-d[A]} {[A]}  $

$=k \int _0 ^t d t \Rightarrow  - \ln [A] _ {A _0} ^{A} =k(t) _0^t $

$ \Rightarrow - \ln [A]+(In[A _0])$

$=k(t-0)  \Rightarrow In[A _0] - \ln [A]=kt  \ln (\frac{[A _0]}{[A]})=k t$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ <span style="color:blue">Alternative to find integrated rate law</span> $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> First order graph(I/II) </B></Primary>
 
<hr>

<main>

For first order reaction:

$$\small{
[A]=[A]_0 e^{-k t}
}$$

Comparing it with the equation:

$$\small{y = e^{-x}}$$

we get,

$$\small{\text{x-axis} = t}$$

$$\small{\text{y-axis} = \text{concentration at time t}}$$

A first order reaction never goes to 100% completion

</div>

$$\small{
[A]=[A]_0 e^{-k t}
}$$

इसे समीकरण के साथ तुलना करते हैं:

$$\small{y = e^{-x}}$$

हमें मिलता है,

$$\small{\text{x-अक्ष} = t}$$

$$\small{\text{y-अक्ष} = \text{समय t पर संचय}}$$

पहले क्रम की प्रतिक्रिया कभी 100% पूर्णता तक नहीं जाती

</div>

![First order graph](https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/d1077c67-4f3f-4880-20c5-d991fb8ab400/public)

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ <span style="color:blue">First order graph</span> $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> First order graph(II/II) </B></Primary>

<hr>

<main>

For first order reaction:

$$\small{
ln[A]_t = -kt + ln[A]_o
}$$

Comparing it with the equation:
$$\small{y = mx +c}$$

we get,
$$\small{\text{x-axis} = t}$$

$$\small{\text{y-axis} = \text{Natural log concentration at time t}}$$

$$\small{slope = k}$$

$$\small{Intercept = \text{Natural log of initial concentration}}$$

</div>

पहले क्रम की प्रतिक्रिया के लिए:

$$\small{
ln[A]_t = -kt + ln[A]_o
}$$

इसे समीकरण के साथ तुलना करते हैं:
$$\small{y = mx +c}$$

हमें मिलता है,
$$\small{\text{x-अक्ष} = t}$$

$$\small{\text{y-अक्ष} = \text{समय t पर प्राकृतिक लॉग संचयन}}$$

$$\small{ढाल = k}$$

$$\small{अंतःकटि = \text{प्रारंभिक संचयन का प्राकृतिक लॉग}}$$

</div>

![First order graph](https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/239e977a-5568-4bc5-904c-8a60fb83b300/public)

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ <span style="color:blue">First order graph</span> $\rarr$ Gas phase first order reaction $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Gas phase first order reaction </B></Primary>

<hr>

<main>

|  | $A(g)$ | $\longrightarrow$ | $\mathrm{B}(\mathrm{g})+$ | $C(g)$ |
| :---: | :---: | :---: | :---: | :---: |
|  | 1 mole of $A$ |  | 1 mole of $B$ | 1 mole of $C$ |
| At $t-0$ | $P_0$ |  | 0 | 0 |
| At time | $0-P)_{\mathrm{atm}}$ |  | $\mathrm{P} _{\mathrm{atm}}$ | $P _{\mathrm{atm}}$ |

$$
k=\frac{2.303}{t} \log \frac{P_0}{P_A}
$$

</div>

| | $ए(जी)$ | $\longrightarrow$ | $\mathrm{B}(\mathrm{g})+$ | $सी(जी)$ |
| :---: | :---: | :---: | :---: | :---: |
| | $A$ का 1 मोल | | $B$ का 1 मोल | $C$ का 1 मोल |
| $t-0$ पर | $P_0$ | | 0 | 0 |
| समय पर | $0-P)_{\mathrm{atm}}$ | | $\mathrm{P} _{\mathrm{atm}}$ | $P _{\mathrm{atm}}$ |

$$
k=\frac{2.303}{t} \log \frac{P_0}{P_A}
$$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ <span style="color:blue">Gas phase first order reaction</span> $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Gas phase first order reaction </B></Primary>

<hr>

<main>

$P_A$ can be calculated using total pressure of the reaction mixture.

Total pressure $\left(P _t\right)=P$ artial pressure gaseous + reactants $\left(P _A\right)$

Partial pressure of gaseous products $\left(P_B+P_C\right)$

<p>
$$
\begin{aligned}
P _t & =\left(P _0-P\right)+P+P \\
& P t=P_0+P \\
P & =P_t-P_0 \\
& P_A=P_0-P \\
\therefore \quad & P _A = P _0-\left(P  _t-P _0\right) \\
& P _A=2 P _0-P _t
\end{aligned}
$$
</p>

</div>

$P_A$ की गणना प्रतिक्रिया मिश्रण के कुल दबाव का उपयोग करके की जा सकती है।

कुल दबाव $\left(P _t\right)=P$ कृत्रिम दबाव गैसीय + अभिकारक $\left(P _A\right)$

गैसीय उत्पादों का आंशिक दबाव $\left(P_B+P_C\right)$

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ <span style="color:blue">Gas phase first order reaction</span> $\rarr$ Examples of first order reaction $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kienetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Examples of first order reaction </B></Primary>

<hr>

<main>

- Hydrogenation of ethene is an example of first order reaction.

<p>
$$\small{
\begin{aligned}
& C_2 H_4(g)+H_2(g) \to C_2 H_6(g) \\\
& \text{ Rate }=k[C_2 H_4]
\end{aligned}
}$$
</p>

- All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.

<p>
$$\small{
\begin{aligned}
&     _{88}Ra^{226}  \to _2^4 He+  _{86}Rn^{222}  \\\
& \text{ Rate }=k[Ra]
\end{aligned}
}$$
</p>

Decomposition of $\small{N_2 O_5}$ and $\small{N_2 O}$ are some more examples of first order reactions.

</div>

- इथीन का हाइड्रोजनीकरण प्रथम क्रम की प्रतिक्रिया का उदाहरण है।

<p>
$$\small{
\begin{aligned}
& C_2 H_4(g)+H_2(g) \to C_2 H_6(g) \\\
& \text{ दर }=k[C_2 H_4]
\end{aligned}
}$$
</p>

- सभी प्राकृतिक और कृत्रिम रेडियोधर्मी अस्थिर नाभिकों का क्षय प्रथम क्रम के गतिकी द्वारा होता है।

<p>
$$\small{
\begin{aligned}
&   _{88}Ra^{226}  \to _2^4 He+  _{86}Ra^{222}  \\\
& \text{ दर }=k[Ra]
\end{aligned}
}$$
</p>

$\small{N_2 O_5}$ और $\small{N_2 O}$ का अपघटन प्रथम क्रम की प्रतिक्रियाओं के कुछ और उदाहरण हैं।

</div>

</main>

<hr>

<footer style="font-size:16px"> Algorithm to find integrated rate law $\rarr$ Zero Order Reaction $\rarr$ Integrated rate law derivation $\rarr$ Alternative to find integrated rate law $\rarr$ Zero order graph $\rarr$ Example of Zero order reaction $\rarr$ First order reaction $\rarr$ Derivation of integrated first rate law $\rarr$ Alternative to find integrated rate law $\rarr$ First order graph $\rarr$ Gas phase first order reaction $\rarr$ <span style="color:blue">Examples of first order reaction</span> $\rarr$ Example </footer>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kinetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Example </B></Primary>

<hr>

<main>

**Question :** The initial concentration of $\mathrm{N} _2 \mathrm{O} _5$ in the following first order reaction $\mathrm{N} _2 \mathrm{O} _5(\mathrm{g}) \rightarrow 2 \mathrm{NO} _2(\mathrm{g})+1 / 2 \mathrm{O} _2$ (g) was $1.24 \times 10^{-2} \mathrm{mol} \mathrm{L}^{-1}$ at $318 \mathrm{K}$. The concentration of $\mathrm{N} _2 \mathrm{O} _5$ after 60 minutes was $0.20 \times 10^{-2} \mathrm{mol} \mathrm{L}^{-1}$. Calculate the rate constant of the reaction at $318 \mathrm{K}$.

</div>

**सवाल :** निम्नलिखित प्रथम क्रम प्रतिक्रिया में $\mathrm{N} _2 \mathrm{O} _5$ की प्रारंभिक सांद्रता $\mathrm{N} _2 \mathrm{O} _5(\mathrm{g}) \rightarrow 2 \mathrm{NO} _2(\mathrm{g})+1/2 \mathrm{O} _2$(g) $1.24\times 10^{-2}\mathrm{mol}\mathrm{L} था ^{-1}$ $318 \mathrm{K}$ पर। 60 मिनट के बाद $\mathrm{N} _2\mathrm{O} _5$ की सांद्रता $0.20\times 10^{-2}\mathrm{mol}\mathrm{L}^{-1}$ थी। $318 \mathrm{K}$ पर प्रतिक्रिया की दर स्थिरांक की गणना करें।

</div>

</main>

<hr>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kinetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Example </B></Primary>

<hr>

<main>

**Solution :**  For a first order reaction

<p>
$
\begin{aligned}
\log \frac{[\mathrm{R}]_1}{[\mathrm{R}]_2} & =\frac{kt_2-t_1}{2.303} \\
k & =\frac{2.303}{t_2-t_1} \log \frac{[R]_1}{[R]_2} \\
& =\frac{2.303}{(60 \mathrm{min}-0 \mathrm{min})} \\
& \log \frac{1.24 \times 10^{-2} \mathrm{mol} \mathrm{L}^{-1}}{0.20 \times 10^{-2} \mathrm{mol} \mathrm{L}^{-1}} \\
& =\frac{2.303}{60} \log 6.2 \mathrm{min}^{-1} \\
k & =0.0304 \mathrm{min}^{-1}
\end{aligned}
$
</p>

</div>

समाधान: प्रथम कोटि की प्रतिक्रिया के लिए

<p>
$
\begin{aligned}
\log \frac{[\mathrm{R}]_1}{[\mathrm{R}]_2} & =\frac{kt_2-t_1}{2.303} \\
k & =\frac{2.303}{t_2-t_1} \log \frac{[R]_1}{[R]_2} \\
& =\frac{2.303}{(60 \mathrm{min}-0 \mathrm{min})} \\
& \log \frac{1.24 \times 10^{-2} \mathrm{mol} \mathrm{ L}^{-1}}{0.20 \times 10^{-2} \mathrm{mol} \mathrm{L}^{-1}} \\
& =\frac{2.303}{60} \log 6.2 \mathrm{min}^{-1} \\
k और =0.0304 \mathrm{min}^{-1}
\end{aligned}
$
</p>

</div>

</main>

<hr>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kinetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Example </B></Primary>

<hr>

<main>

**Question :** The following data were obtained during the first order thermal decomposition of $\mathrm{N} _2 \mathrm{O} _5(\mathrm{g})$ at constant volume:

| S.No. | Time/s | Total Pressure/(atm) |
| :---: | :---: | :---: |
| 1. | 0 | 0.5 |
| 2. | 100 | 0.512 |

Calculate the rate constant.

</div>

प्रश्न: स्थिर आयतन पर $\mathrm{N} _2 \mathrm{O} _5(\mathrm{g})$ के पहले क्रम के थर्मल अपघटन के दौरान निम्नलिखित डेटा प्राप्त किए गए थे:

| S.No. | Time/s | Total Pressure/(atm) |
| :---: | :---: | :---: |
| 1. | 0 | 0.5 |
| 2. | 100 | 0.512 |

दर स्थिरांक की गणना करें.

</div>

</main>

<hr>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kinetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Example </B></Primary>

<hr>

<main>

**Solution :** Let the pressure of $\mathrm{N} _2 \mathrm{O} _5(\mathrm{g})$ decrease by $2 \mathrm{x}$ atm. As two moles of $\mathrm{N} _2 \mathrm{O} _5$ decompose to give two moles of $\mathrm{N} _2 \mathrm{O} _4(\mathrm{g})$ and one mole of $\mathrm{O} _2(\mathrm{g})$, the pressure of $\mathrm{N} _2 \mathrm{O} _4(\mathrm{g})$ increases by $2 \mathrm{x}$ atm and that of $\mathrm{O} _2(\mathrm{g})$ increases by $\mathrm{x}$ atm.

|  | $2 \mathrm{N} _2 \mathrm{O} _5 \mathrm{g}$ | $2 \mathrm{N} _2 \mathrm{O} _4 \mathrm{g}$ | $\mathrm{O} _2 \mathrm{g}$ |
| :--- | :---: | :---: | :--- |
| Start $t=0$ | $0.5 \mathrm{atm}$ | $0 \mathrm{atm}$ | $0 \mathrm{atm}$ |
| At time $t$ | $(0.5-2 \mathrm{x}) \mathrm{atm}$ | $2 \mathrm{x}$ atm | $\mathrm{x} \mathrm{atm}$ |

</div>

समाधान: मान लीजिए कि $\mathrm{N} _2 \mathrm{O} _5(\mathrm{g})$ का दबाव $2 \mathrm{x}$ atm से कम हो जाता है। जैसे कि $\mathrm{N} _2 \mathrm{O} _5$ के दो मोल विघटित होकर $\mathrm{N} _2 \mathrm{O} _4(\mathrm{g})$ के दो मोल और एक मोल देते हैं $\mathrm{O} _2(\mathrm{g})$, $\mathrm{N} _2 \mathrm{O} _4(\mathrm{g})$ का दबाव $2 \mathrm{x} से बढ़ जाता है $atm और $\mathrm{O} _2(\mathrm{g})$ में $\mathrm{x}$ atm की वृद्धि होती है।

</div>

</main>

<hr>

<Success style=" font-size:25px ; text-align:center"><B>Chemical Kinetics</B></Success>

<Primary style=" font-size:23px ; text-align:center"><B> Example </B></Primary>

<hr>

<main>

$ p_{t} = p_{N_{2} O_{5} } + p_ {N_{2} O_{4} } + p_{O_{2}} $

$ =(0.5-2 \mathrm{x})+2 \mathrm{x}+\mathrm{x}=0.5+\mathrm{x} $
 
$ \mathrm{x}  p_t \quad 0.5 $

$ p _{\mathrm{N}_2 \mathrm{O}_5}=0.5-2 \mathrm{x} $
 
$ =0.5-2\left(p _{\mathrm{t}}-0.5\right)=1.5-2 p_t $

$ \text { At } t=100 \mathrm{s} ; p_{\mathrm{t}}=0.512 \mathrm{atm} $

</div>

$ p_{t} = p_{N_{2} O_{5} } + p_ {N_{2} O_{4} } + p_{O_{2}} $

$ =(0.5-2 \mathrm{x})+2 \mathrm{x}+\mathrm{x}=0.5+\mathrm{x} $
 
$ \mathrm{x}  p_t \quad 0.5 $

$ p _{\mathrm{N}_2 \mathrm{O}_5}=0.5-2 \mathrm{x} $
 
$ =0.5-2\left(p _{\mathrm{t}}-0.5\right)=1.5-2 p_t $

$ \text { At } t=100 \mathrm{s} ; p_{\mathrm{t}}=0.512 \mathrm{atm} $

</div>

</main>

<hr>